# migrations

dir: embeddings_queue
filename: 00001-embeddings.sqlite.sql
hash: d3755dfd232be8e8301f4d7fcfb3a486
sql:
CREATE TABLE embeddings_queue (
    seq_id INTEGER PRIMARY KEY,
    created_at TIMESTAMP NOT NULL DEFAULT CURRENT_TIMESTAMP,
    operation INTEGER NOT NULL,
    topic TEXT NOT NULL,
    id TEXT NOT NULL,
    vector BLOB,
    encoding TEXT,
    metadata TEXT
);


dir: sysdb
filename: 00001-collections.sqlite.sql
hash: 38352d725ad1c16074fac420b22b4633
sql:
CREATE TABLE collections (
    id TEXT PRIMARY KEY,
    name TEXT NOT NULL,
    topic TEXT NOT NULL,
    UNIQUE (name)
);

CREATE TABLE collection_metadata (
    collection_id TEXT REFERENCES collections(id) ON DELETE CASCADE,
    key TEXT NOT NULL,
    str_value TEXT,
    int_value INTEGER,
    float_value REAL,
    PRIMARY KEY (collection_id, key)
);


dir: sysdb
filename: 00002-segments.sqlite.sql
hash: 2913cb6a503055a95f625448037e8912
sql:
CREATE TABLE segments (
    id TEXT PRIMARY KEY,
    type TEXT NOT NULL,
    scope TEXT NOT NULL,
    topic TEXT,
    collection TEXT REFERENCES collection(id)
);

CREATE TABLE segment_metadata (
    segment_id TEXT  REFERENCES segments(id) ON DELETE CASCADE,
    key TEXT NOT NULL,
    str_value TEXT,
    int_value INTEGER,
    float_value REAL,
    PRIMARY KEY (segment_id, key)
);


dir: metadb
filename: 00001-embedding-metadata.sqlite.sql
hash: 2b4cf52c4bb2676e21d6860a4409f856
sql:
CREATE TABLE embeddings (
    id INTEGER PRIMARY KEY,
    segment_id TEXT NOT NULL,
    embedding_id TEXT NOT NULL,
    seq_id BLOB NOT NULL,
    created_at TIMESTAMP NOT NULL DEFAULT CURRENT_TIMESTAMP,
    UNIQUE (segment_id, embedding_id)
);

CREATE TABLE embedding_metadata (
    id INTEGER REFERENCES embeddings(id),
    key TEXT NOT NULL,
    string_value TEXT,
    int_value INTEGER,
    float_value REAL,
    PRIMARY KEY (id, key)
);

CREATE TABLE max_seq_id (
    segment_id TEXT PRIMARY KEY,
    seq_id BLOB NOT NULL
);

CREATE VIRTUAL TABLE embedding_fulltext USING fts5(id, string_value);


dir: metadb
filename: 00002-embedding-metadata.sqlite.sql
hash: 12a570f7121b3a8ce750a2a7c36da20f
sql:
-- SQLite does not support adding check with alter table, as a result, adding a check
-- involve creating a new table and copying the data over. It is over kill with adding
-- a boolean type column. The application write to the table needs to ensure the data
-- integrity.
ALTER TABLE embedding_metadata ADD COLUMN bool_value INTEGER


dir: metadb
filename: 00003-full-text-tokenize.sqlite.sql
hash: f97ad6334aeaa8f419f01110b648b97a
sql:
CREATE VIRTUAL TABLE embedding_fulltext_search USING fts5(string_value, tokenize='trigram');
INSERT INTO embedding_fulltext_search (rowid, string_value) SELECT rowid, string_value FROM embedding_metadata;
DROP TABLE embedding_fulltext;


# embeddings_queue

created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6102-934e-11ee-aa67-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 0, "chroma:document": "Increasing the Inference and Learning Speed of\nTsetlin Machines with Clause Indexing\nSaeed Rahimi Gorji1[0000\u22120002\u22122699\u22129903], Ole-Christo\ufb00er\nGranmo1[0000\u22120002\u22127287\u2212030X], Sondre Glimsdal1, Jonathan Edwards2, and\nMorten Goodwin1[0000\u22120002\u22127287\u2212030X]\n1Centre for Arti\ufb01cial Intelligence Research, University of Agder, Grimstad, Norway\n2Temporal Computing, Newcastle, United Kingdom\nsaeed.r.gorji@uia.no, ole.granmo@uia.no, sondre.glimsdal@uia.no,\njonny@temporalcomputing.com, morten.goodwin@uia.no"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6103-934e-11ee-8649-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 0, "chroma:document": "Abstract. The Tsetlin Machine (TM) is a machine learning algorithm\nfounded on the classical Tsetlin Automaton (TA) and game theory. It fur-\nther leverages frequent pattern mining and resource allocation principles\nto extract common patterns in the data, rather than relying on minimiz-\ning output error, which is prone to over\ufb01tting. Unlike the intertwined\nnature of pattern representation in neural networks, a TM decomposes"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6104-934e-11ee-b48a-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 0, "chroma:document": "problems into self-contained patterns, represented as conjunctive clauses.\nThe clause outputs, in turn, are combined into a classi\ufb01cation decision\nthrough summation and thresholding, akin to a logistic regression func-\ntion, however, with binary weights and a unit step output function. In\nthis paper, we exploit this hierarchical structure by introducing a novel\nalgorithm that avoids evaluating the clauses exhaustively. Instead we"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6105-934e-11ee-a32d-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 0, "chroma:document": "use a simple look-up table that indexes the clauses on the features that\nfalsify them. In this manner, we can quickly evaluate a large number of\nclauses through falsi\ufb01cation, simply by iterating through the features and\nusing the look-up table to eliminate those clauses that are falsi\ufb01ed. The\nlook-up table is further structured so that it facilitates constant time\nupdating, thus supporting use also during learning. We report up to 15"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6106-934e-11ee-b7c5-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 0, "chroma:document": "times faster classi\ufb01cation and three times faster learning on MNIST and\nFashion-MNIST image classi\ufb01cation, and IMDb sentiment analysis.\nKeywords: Tsetlin Machines \u00b7Pattern Recognition \u00b7Propositional Logic\n\u00b7Frequent Pattern Mining \u00b7Learning Automata \u00b7Pattern Indexing\n1 Introduction\nThe Tsetlin Machine (TM) is a recent machine learning approach that is based on\nthe Tsetlin Automaton (TA) by M. L. Tsetlin [ 1], one of the pioneering solutions"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6107-934e-11ee-8de2-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 0, "chroma:document": "to the well-known multi-armed bandit problem [ 2,3] and the \ufb01rst Learning\nAutomaton [ 4]. It further leverages frequent pattern mining [ 5] and resource\nallocation [ 6] to capture frequent patterns in the data, using a limited number\nof conjunctive clauses in propositional logic. The clause outputs, in turn, are\ncombined into a classi\ufb01cation decision through summation and thresholding,arXiv:2004.03188v1  [cs.LG]  7 Apr 2020"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6108-934e-11ee-8aed-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 1, "chroma:document": "2 S. R. Gorji et al.\nakin to a logistic regression function, however, with binary weights and a unit\nstep output function [ 7]. Being based on disjunctive normal form (DNF), like\nKarnaugh maps, the TM can map an exponential number of input feature value\ncombinations to an appropriate output [8].\nRecent Progress on TMs. Recent research reports several distinct TM prop-\nerties. The clauses that a TM produces have an interpretable form (e.g., ifX"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6109-934e-11ee-9b62-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 1, "chroma:document": "satis\ufb01es condition A and not condition B thenY = 1), similar to the branches\nin a decision tree [ 7]. For small-scale pattern recognition problems, up to three\norders of magnitude lower energy consumption and inference time has been\nreported, compared to neural networks alike [ 9]. The TM structure captures re-\ngression problems, comparing favourably with Regression Trees, Random Forests\nand Support Vector Regression [ 10]. Like neural networks, the TM can be used"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c610a-934e-11ee-9d7d-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 1, "chroma:document": "in convolution, providing competitive memory usage, computation speed, and\naccuracy on MNIST, F-MNIST and K-MNIST, in comparison with simple 4-\nlayer CNNs, K-Nereast Neighbors, SVMs, Random Forests, Gradient Boosting,\nBinaryConnect, Logistic Circuits, and ResNet [ 11]. By introducing clause weights\nthat allow one clause to represent multiple, it has been demonstrated that the\nnumber of clauses can be reduced up to 50\u00d7, without loss of accuracy, leading to"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c610b-934e-11ee-b783-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 1, "chroma:document": "more compact clause sets [ 8]. Finally, hyper-parameter search can be simpli\ufb01ed\nwith multi-granular clauses, eliminating the pattern speci\ufb01city parameter [12].\nPaper Contributions and Organization. The expression power of a TM is\ngoverned by the number of clauses employed. However, adding clauses to increase\naccuracy comes at the cost of linearly increasing computation time. In this paper,\nwe address this problem by exploiting the hierarchical structure of the TM. We"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c610c-934e-11ee-a7fc-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 1, "chroma:document": "\ufb01rst cover the basics of TMs in Sect. 2. Then, in Sect. 3, we introduce a novel\nindexing scheme that speeds up clause evaluation. The scheme is based on a\nsimple look-up tables that indexes the clauses on the features that falsify them.\nWe can then quickly evaluate a large number of clauses through falsi\ufb01cation,\nsimply by iterating through the features and using the look-up table to eliminate\nthose clauses that are falsi\ufb01ed. The look-up table is further structured so that"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c610d-934e-11ee-b5b8-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 1, "chroma:document": "it facilitates constant time updating, thus supporting indexing also during TM\nlearning. In Sect. 4, we report up to 15 times faster classi\ufb01cation and three times\nfaster learning on three di\ufb00erent datasets: IMDb sentiment analysis, and MNIST\nand Fashion-MNIST image classi\ufb01cation. We conclude the paper in Sect. 5.\n2 Tsetlin Machines\nThe Tsetlin Machine (TM)[ 13] is a novel machine learning approach that is\nparticularly suited to low power and explainable applications [ 9,7]. The structure"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c610e-934e-11ee-a6ba-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 1, "chroma:document": "of a TM is similar to the majority of learning classi\ufb01cation algorithms, with\nforward pass inference and backward pass parameter adjustment (Fig. 1). A\nkey property of the approach is that the whole system is Boolean, requiring an"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c610f-934e-11ee-8ef5-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 2, "chroma:document": "Tsetlin Machines with Clause Indexing 3\nencoder and decoder for any other form of data. Input data is de\ufb01ned as a set of\nfeature vectors: D={x1,x2, . . .}, and the output Yis formulated as a function\nparameterized by the actions Aof a team of TAs: Y=f(x;A).\nTA Team. The function fis parameterized by a team of TAs, each deciding the\nvalue of a binary parameter ak\u2208A(labelling the full collection of parameters A).\nEach TA has an integer state tk\u2208{1, . . . , 2N}, with 2Nbeing the size of the"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6110-934e-11ee-9e44-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 2, "chroma:document": "state space. The action akof a TA is decided by its state: ak= 1iftk> N else0.\nClassi\ufb01cation Function. The function fis formulated as an ensemble of\nnconjunctive clauses, each clause controlling the inclusion of a feature and\n(separately) its negation. A clause Cjis de\ufb01ned as:\nCj(x) =o\u22c0\nk=1(xk\u2228\u00acaj\nk)\u2227(\u00acxk\u2228\u00acaj\no+k). (1)\nHere, xkis the kth feature of input vector x\u2208Do,ois the total number of\nfeatures and aj\nkis the action of the TA that has been assigned to literal kfor"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6111-934e-11ee-94f8-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 2, "chroma:document": "clause j. A variety of ensembling methods can be used \u2013 most commonly a unit\nstep function, with half the clauses aimed at inhibition:\n\u02c6y= 1 if\uf8eb\n\uf8edn/2\u2211\nj=1C+\nj(x)\u2212n/2\u2211\nj=1C\u2212\nj(x)\uf8f6\n\uf8f8\u22650else 0. (2)\nWhen the problem is multi-classed (one-hot encoded [15]) thresholding is removed\nand the maximum vote is used to estimate the class:\n\u02c6y=argmaxi\uf8eb\n\uf8edn/2\u2211\nj=1Ci+\nj(x)\u2212n/2\u2211\nj=1Ci\u2212\nj(x)\uf8f6\n\uf8f8, (3)\nwith ireferring to the class that the clauses belong to."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6112-934e-11ee-8472-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 2, "chroma:document": "Learning. Learning controls the inclusion of features or their negation. A TA k\nis trained using rewards and penalties. If tk> N(action 1), a reward increases\nthe state, tk+= 1, up to 2N, whilst a penalty decreases the state, tk\u2212= 1. If\ntk<=N(action 0), a reward decreases the state, tk\u2212= 1, down to 1, whilst a\npenalty increases the state, tk+= 1. The learning rules are described in detail in\n[13], the basic premise being that individual TA can be controlled by examining"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6113-934e-11ee-9474-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 2, "chroma:document": "their e\ufb00ect on the clause output relative to the desired output, the clause output,\nthe polarity (an inhibitory or excitory clause), and the action. For example, if (i)\na feature is 1, (ii) the TA state governing the inclusion of the feature is resolved\nto action 1, and (iii) the overall clause outputs 1when a 1output is desired, then\nthe TA is rewarded, because it is trying to do the right action.\nThe learning approach has the following added randomness:"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6114-934e-11ee-af5d-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 3, "chroma:document": "4 S. R. Gorji et al.\nFig. 1.The backwards pass requires no gradient methods (just manipulation of all TA\nstates ( tk)). Due to the negation of features, clauses can singularly encode non-linearly\nseparable boundaries. There are no sigmoid style functions, all functions are compatible\nwith low level hardware implementations.\n\u2013An annealing style cooling parameter Tregulates how many clauses are\nactivated for updating. In general, increasing Ttogether with the number of"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6115-934e-11ee-a6a1-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 3, "chroma:document": "clauses leads to an increase in accuracy.\n\u2013A sensitivity swhich controls the ratio of reward to penalty, based on a split\nof the total probability, with values 1/sand1\u22121/s. This parameter governs\nthe \ufb01ne-grainedness of the clauses, with a higher sproducing clauses with\nmore features included.\nWhen comparing the TMs with a classical neural network [ 14] (Fig. 1), noteworthy\npoints include: Boolean/integer rather than \ufb02oating point internal representation;"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6116-934e-11ee-bc35-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 3, "chroma:document": "logic rather than linear algebra; and binary inputs/outputs.\n3 Fast Clause Falsi\ufb01cation Through Indexing\nIn this section we describe the details of our clause indexing scheme, including\nindex based inference and learning.\nOverall Clause Indexing Strategy. Recall that each TM clause is a conjunc-\ntion of literals. The way that the TM determines whether to include a literal in a\nclause is by considering the action of the corresponding TA. Thus, to successfully"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6117-934e-11ee-9ad5-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 4, "chroma:document": "Tsetlin Machines with Clause Indexing 5\nClass 1: x 1\nClass 1:\u00a0 x2\nClass 1: \u00acx 1\nClass 1: \u00acx 2\nClass 2: x 1\nClass 2:\u00a0 x2\nClass 2: \u00acx1\nClass 2: \u00acx2n: 3 C1C1C2+ + -\nn: 2 C1C2- -\nn: 2 C2C1- -\nn: 1 C2+\nn: 3 C2C1C2- + +\nn: 2 C1C2+ +\nn: 2 C2C1+ -\nn: 3 C2C1C1- + -C1C2C1C2+ + - -\n1 3 2\n2 11 2\n1\n2 3 1\n1 2\n1 2\n3 2 1Class 1: x 1\nClass 1:\u00a0 x2\nClass 1: \u00acx 1\nClass 1: \u00acx 2\nClass 2: x 1\nClass 2:\u00a0 x2\nClass 2: \u00acx1\nClass 2: \u00acx2\nFig. 2.Indexing structure."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6118-934e-11ee-9232-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 4, "chroma:document": "Class 2: \u00acx2\nFig. 2.Indexing structure.\nevaluate a clause, the TM must scan through all the actions of the team of\nTAs responsible for the clause, and perform the necessary logical operations to\ncalculate its truth value. However, being a conjunction of literals, it is actually\nsu\ufb03cient to merely identify a single literal that is false to determine that the\nclause itself is false. Conversely, if no false literals are present, we can conclude"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6119-934e-11ee-9a20-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 4, "chroma:document": "that the clause is true. Our approach is thus to maintain a list for each literal\nthat contains the clauses that include that literal, and to use these lists to speed\nup inference and learning.\nIndex Based Inference. We \ufb01rst consider the clause lists themselves (Fig. 2,\nleft), before we propose a position matrix that allows constant time updating of\nthe clause lists (Fig. 2, right). For each class-literal pair (i, k), we maintain an\ninclusion list Li"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c611a-934e-11ee-a842-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 4, "chroma:document": "inclusion list Li\nkthat contains all the clauses in class ithat include the literal\nlk. Let the cardinality of Li\nkbe|Li\nk|=ni\nk. Evaluating the complete set of class\niclauses then proceeds as follows. Given a feature vector x= (x1, x2, . . . , x o),\nwe de\ufb01ne the index set LFfor the false literals as LF={k|lk= 0}. Then\nCi\nF=\u22c3\nk\u2208LFLi\nkis the clauses of class ithat have been falsi\ufb01ed by x. We\npartitionCi\nFinto clauses with positive polarity and clauses with negative polarity:\nCi\nF=Ci+\nF\u222aCi\u2212"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c611b-934e-11ee-a6ef-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 4, "chroma:document": "Ci\nF=Ci+\nF\u222aCi\u2212\nF. The predicted class can then simply be determined based on\nthe cardinality of the sets of falsi\ufb01ed clauses:\n\u02c6y=argmaxi(\n|Ci\u2212\nF|\u2212|Ci+\nF|)\n, (4)\nAlongside the inclusion list, an m\u00d7n\u00d72omatrixM, with entries Mij\nk, keeps\ntrack of the position of each clause jin the inclusion list for literal k(Fig. 2,\nright). With the help of M, searching and removing a clause from a list can take\nplace in constant time."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c611c-934e-11ee-b113-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 5, "chroma:document": "6 S. R. Gorji et al.\nIndex Construction and Maintenance. Constructing the inclusion lists and\nthe accompanying position matrix is rather straightforward since one can initialize\nall of the TAs to select the exclude action. Then the inclusion lists are empty,\nand, accordingly, the position matrix is empty as well.\nInsertion can be done in constant time. When the TA responsible for e.g.\nliteral lkin clause Ci\njchanges its action from exclude to include, the corresponding\ninclusion list Li"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c611d-934e-11ee-b2bd-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 5, "chroma:document": "inclusion list Li\nkmust be updated accordingly. Adding a clause to the list is fast\nbecause it can be appended to the end of the list using the size of the list ni\nk:\nni\nk\u2190ni\nk+ 1\nLi\nk[ni\nk]\u2190Ci\nj\nMij\nk\u2190ni\nk.\nDeletion, however, requires that we know the position of the clause that we\nintend to delete. This happens when one of the TAs changes from including to\nexcluding its literal, say literal lkin clause Ci\nj. To avoid searching for Ci\njinLi\nk,\nwe use Mij\nkfor direct lookup:\nLi\nk[Mij\nk]\u2190Li\nk[ni"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c611e-934e-11ee-b870-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 5, "chroma:document": "kfor direct lookup:\nLi\nk[Mij\nk]\u2190Li\nk[ni\nk]\nni\nk\u2190ni\nk\u22121\nMi,Li\nk[Mij\nk]\nk\u2190Mij\nk\nMij\nk\u2190NA.\nAs seen, the clause is deleted by overwriting it with the last clause in the list,\nand then updating Maccordingly.\nMemory Footprint. To get a better sense of the impact of indexing on memory\nusage, assume that we have a classi\ufb01cation problem with mclasses and feature\nvectors of size o, to be solved with a TM. Thus, the machine has mclasses"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c611f-934e-11ee-b397-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 5, "chroma:document": "where each class contains nclauses. The memory usage for the whole machine is\nabout 2\u00d7m\u00d7n\u00d7obytes, considering a bitwise implementation and TAs with\n8-bit memory. The indexing data structure then requires two tables with m\u00d7o\nrows and ncolumns. Consequently, assuming 2-byte entries, each of these tables\nrequire 2\u00d7m\u00d7n\u00d7obytes of memory, which is roughly the same as the memory\nrequired by the TM itself. As a result, using the indexing data structure roughly\ntriples memory usage."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6120-934e-11ee-8b33-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 5, "chroma:document": "triples memory usage.\nStep-by-Step Example. Consider the indexing con\ufb01guration in Fig. 2 and the\nfeature vector x= (1,0). To evaluate the clauses of class 1, i.e., C+\n1,C\u2212\n1,C+\n2,\nandC\u2212\n2(omitting the class index for simplicity), we initially assume that they\nall are true. This provides two votes for and two votes against the class, which\ngives a class score of 0. We then look up the literals \u00acx1andx2, which both are\nfalse, in the corresponding inclusion lists. We \ufb01rst obtain C\u2212\n1andC\u2212"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6121-934e-11ee-bfc5-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 5, "chroma:document": "1andC\u2212\n2from\u00acx1,"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6122-934e-11ee-95be-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 6, "chroma:document": "Tsetlin Machines with Clause Indexing 7\nwhich falsi\ufb01es C\u2212\n1andC\u2212\n2. This changes the class score from 0to2because two\nnegative votes have been removed from the sum. We then obtain C\u2212\n1andC\u2212\n2\nfrom x2, however, these have already been falsi\ufb01ed, so are ignored. We have now\nderived a \ufb01nal class score of 2simply by obtaining a total of four clause index\nvalues, rather than fully evaluating four clauses over four possible literals.\nLet us now assume that the clause C+"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6123-934e-11ee-8902-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 6, "chroma:document": "Let us now assume that the clause C+\n1needs to be deleted from the inclusion\nlist of x1. The position matrix Mis then used to update the inclusion list in\nconstant time. By looking up x1andC+\n1for class 1 inM, we obtain the position\nofC+\n1in the inclusion list L1\n1ofx1, which is 1. Then the last element in the list,\nC+\n2, is moved to position 1, and the number of elements in the list is decremented.\nFinally, the entry 1at row Class 1 :x1and column C+\n1is erased, while the entry"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6124-934e-11ee-99c5-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 6, "chroma:document": "1is erased, while the entry\n3at row Class 1 :x1and column C+\n2is set to 1to re\ufb02ect the new position of\nC+\n2in the list. Conversely, if C+\n1needs to be added to e.g. the inclusion list of\nx2, it is simply added to the end of the Class 1 :x2list, in position 3. ThenM\nis updated by writing 3into row Class 1 : x2and column C+\n1.\nRemarks. As seen above, the maintenance of the inclusion lists and the position\nmatrix takes constant time. The performance increase, however, is signi\ufb01cant."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6125-934e-11ee-b54f-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 6, "chroma:document": "Instead of going through all the clauses, evaluating each and every one of them,\nconsidering all of the literals, the TM only goes through the relevant inclusion\nlists. Thus, the amount of work becomes proportional to the size of the clauses.\nFor instance, for the MNIST dataset, where the average length of clauses is\nabout 58, the algorithm goes through the inclusion list for half of the literals\n(the falsifying ones), each containing about 740clauses on average. Thus, instead"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6126-934e-11ee-a8aa-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 6, "chroma:document": "of evaluating 20 000clauses (the total number of clauses), by considering 1568\nliterals for each (in the worst case), the algorithm just considers 784falsifying\nliterals with an average of 740clauses in their inclusion lists. In other words,\nthe amount of work done to evaluate all the clauses with indexing is roughly\n0.02compared to the case without indexing. Similarly, for the IMDB dataset,\nthe average clause length is about 116, and each inclusion list contains roughly"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6127-934e-11ee-b5f4-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 6, "chroma:document": "232clauses on average. Without indexing, evaluating a clause requires assessing\n10 000literals, while indexing only requires assessing the inclusion lists for\n5 000falsifying literals. Using indexing reduces the amount of work to roughly\n0.006of the work performed without indexing. Thus, in both examples, using\nindexing reduces computation signi\ufb01cantly. We now proceed to investigate how\nthe indexing a\ufb00ect inference and learning speed overall.\n4 Empirical Results"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6128-934e-11ee-8d5f-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 6, "chroma:document": "4 Empirical Results\nTo measure the e\ufb00ect of indexing we use three well-known datasets, namely\nMNIST, Fashion-MNIST, and IMDb. We explore the e\ufb00ect of di\ufb00erent number of\nclauses and features, to determine the e\ufb00ect indexing has on performance under\nvarying conditions.\nOur \ufb01rst set of experiments covers the MNIST dataset. MNIST consists of\n28\u00d728-pixel grayscale images of handwritten digits. We \ufb01rst binarize the images,"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6129-934e-11ee-9681-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 7, "chroma:document": "8 S. R. Gorji et al.\nconverting each image into a 784-bit feature vector. We refer to this version of\nbinarized MNIST as M1. Furthermore, to investigate the e\ufb00ect of increasing\nthe number of features on indexing, we repeat the same experiment using 2, 3\nand 4 threshold-based grey tone levels. This leads to feature vectors of size 1568\n(= 2\u00d7784), 2352 ( = 3\u00d7784) and 3136 ( = 4\u00d7784), respectively. We refer to\nthese datasets as M2, M3 and M4."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c612a-934e-11ee-8bb2-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 7, "chroma:document": "these datasets as M2, M3 and M4.\nTable 1 summarizes the resulting speedups. Di\ufb00erent rows correspond to\ndi\ufb00erent number of clauses. The columns refer to di\ufb00erent numbers of features,\ncoveringtrainingandinference.Asseen,increasingthenumberofclausesincreases\nthe e\ufb00ect of indexing. In particular, using more than a few thousands clauses\nresults in about three times faster learning and seven times faster inference.\nTable 1. Indexing speedup for di\ufb00erent number of clauses and features on MNIST"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c612b-934e-11ee-a70c-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 7, "chroma:document": "Features 784 1568 2352 3136\nClauses TrainTestTrainTestTrainTestTrainTest\n10001.782.751.542.791.763.741.914.15\n20001.672.832.635.742.465.952.876.06\n50002.625.953.238.023.266.883.347.17\n10000 2.826.313.498.313.477.603.436.78\n20000 2.695.223.588.023.346.443.356.39\nFig. 3 and Fig. 4 plots the average time of each epoch across our experiments,\nas a function of the number of clauses. From the \ufb01gures, we see that after an\ninitial phase of irregular behavior, both indexed and unindexed versions of the"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c612c-934e-11ee-9903-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 7, "chroma:document": "TM suggest a linear growth with roughly the same slopes. Thus, the general e\ufb00ect\nof using indexing on MNIST is a several-fold speedup, while the computational\ncomplexity of the TM algorithm remains unchanged, being linearly related to\nthe number of clauses.\nIn our second set of experiments, we used the IMDb sentiment analysis dataset,\nconsisting of 50,000 highly polar movie reviews, divided in positive and negative"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c612d-934e-11ee-9723-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 7, "chroma:document": "reviews. We varied the problem size by using binary feature vectors of size 5000,\n10000, 15000 and 20000, which we respectively refer to as I1, I2, I3 and I4.\nTable 2 summarizes the resulting speedup for IMDb, employing di\ufb00erent\nnumber of clauses and features. Interestingly, in the training phase, indexing\nseems to slow down training by about 10%. On the \ufb02ip side, when it comes to\ninference, indexing provided a speedup of up to 15 times."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c612e-934e-11ee-97e2-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 7, "chroma:document": "Fig. 5 and Fig. 6 compare the average time of each epoch across our ex-\nperiments, as a function of the number of clauses. Again, we observe some\nirregularities for smaller clause numbers. However, as the number of clauses\nincreases, the computation time of both the indexed and unindexed versions of\nthe TM grows linearly with the number of clauses.\nIn our third and \ufb01nal set of experiments, we consider the Fashion-MNIST"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c612f-934e-11ee-a01b-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 7, "chroma:document": "dataset [15]. Here too, each example is a 28\u00d728-pixel grayscale image, associated"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6130-934e-11ee-af7e-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 8, "chroma:document": "Tsetlin Machines with Clause Indexing 9\n1,000 2,000 5,000 10,000 20,0001101001,000\nClausesTime [s]Unindexed M4\nUnindexed M3\nUnindexed M2\nUnindexed M1\nIndexed M4\nIndexed M3\nIndexed M2\nIndexed M1\nFig. 3.Average training time on MNIST\n1,000 2,000 5,000 10,000 20,0001101001,000\nClausesTime [s]Unindexed M4\nUnindexed M3\nUnindexed M2\nUnindexed M1\nIndexed M4\nIndexed M3\nIndexed M2\nIndexed M1\nFig. 4.Average inference time on MNIST"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6131-934e-11ee-976d-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 9, "chroma:document": "10 S. R. Gorji et al.\nTable 2. Indexing speedup for di\ufb00erent number of clauses and features on IMDb\nFeatures 5000 10000 15000 20000\nClauses TrainTestTrainTestTrainTestTrainTest\n10000.761.950.841.590.811.780.812.03\n20001.004.600.873.170.844.470.834.81\n50000.998.580.938.660.859.410.879.49\n10000 1.0615.400.9211.920.9013.170.8713.03\n20000 1.0515.190.9315.870.8613.840.8813.28\n1,000 2,000 5,000 10,000 20,000101001,00010,000\nClausesTime [s]Unindexed I4\nUnindexed I3\nUnindexed I2\nUnindexed I1\nIndexed I4"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6132-934e-11ee-bbf7-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 9, "chroma:document": "Unindexed I3\nUnindexed I2\nUnindexed I1\nIndexed I4\nIndexed I3\nIndexed I2\nIndexed I1\nFig. 5.Average training time on IMDb"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6133-934e-11ee-adde-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 10, "chroma:document": "Tsetlin Machines with Clause Indexing 11\n1,000 2,000 5,000 10,000 20,0001101001,000\nClausesTime [s]Unindexed I4\nUnindexed I3\nUnindexed I2\nUnindexed I1\nIndexed I4\nIndexed I3\nIndexed I2\nIndexed I1\nFig. 6.Average inference time on IMDb\nwith a label from 10 classes of di\ufb00erent kinds of clothing items. Similar to MNIST,\nwe binarized and \ufb02attened the data using di\ufb00erent numbers of bits for each pixel\n(ranging from one to four bits by means of thresholding). This process produced"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6134-934e-11ee-b543-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 10, "chroma:document": "four di\ufb00erent binary datasets with feature vectors of size 784, 1568, 2352 and\n3136. We refer to these datasets as F1, F2, F3 and F4, respectively. The results\nare summarized in Table 3 for di\ufb00erent number of clauses and features. Similar\nto MNIST, in the training phase, we see a slight speedup due to indexing, except\nwhen the number of clauses or the number of features are small. In that case,\nindexing slows down training to some extent (by about 10%). On the other hand,"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6135-934e-11ee-8ba1-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 10, "chroma:document": "for inference, we see a several-fold speedup (up to \ufb01ve-fold) due to indexing,\nespecially with more clauses.\nTable 3. Indexing speedup for di\ufb00erent number of clauses and features on Fashion-\nMNIST\nFeatures 784 1568 2352 3136\nClauses TrainTestTrainTestTrainTestTrainTest\n10000.860.820.971.331.041.681.041.77\n20000.921.171.232.551.242.931.253.13\n50001.232.211.322.851.332.841.332.95\n10000 1.553.811.584.361.674.921.563.95\n20000 1.553.541.654.541.704.741.675.05"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6136-934e-11ee-94ed-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 11, "chroma:document": "12 S. R. Gorji et al.\nFig. 7 and Fig. 8 compare the average time of each epoch as a function\nof the number of clauses. Again, we observe approximately linearly increasing\ncomputation time with respect to the number of clauses.\n1,000 2,000 5,000 10,000 20,000101001,000\nClausesTime [s]Unindexed F4\nUnindexed F3\nUnindexed F2\nUnindexed F1\nIndexed F4\nIndexed F3\nIndexed F2\nIndexed F1\nFig. 7.Average training time on Fashion-MNIST\n5 Conclusion and Further Work"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6137-934e-11ee-b8bd-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 11, "chroma:document": "5 Conclusion and Further Work\nIn this work, we introduced indexing-based evaluation of Tsetlin Machine clauses,\nwhich demonstrated a promising increase in computation speed. Using simple\nlook-up tables and lists, we were able to leverage the typical sparsity of clauses.\nWe evaluated the indexing scheme on MNIST, IMDb and Fashion-MNIST. For\ntraining, on average, the indexed TM produced a three-fold speedup on MNIST,\na roughly 50% speedup on Fashion-MNIST, while it slowed down IMDb training."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6138-934e-11ee-9119-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 11, "chroma:document": "Thus, the e\ufb00ect on training speed seems to be highly dependent on the data. The\noverhead from maintaining the indexing structure could counteract any speed\ngains.\nDuring inference, on the other hand, we saw a more consistent increase in\nperformance. We achieved a three- to eight-fold speedup on MNIST and Fashion-\nMNIST, and a 13-fold speedup on IMDb, which is reasonable considering there\nis no index maintenance overhead involved in classi\ufb01cation."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6139-934e-11ee-b951-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 11, "chroma:document": "In our further work, we intend to investigate how clause indexing can speed up\nMonte Carlo tree search for board games, by exploiting the incremental changes\nof the board position from parent to child node."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c613a-934e-11ee-adce-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 12, "chroma:document": "Tsetlin Machines with Clause Indexing 13\n1,000 2,000 5,000 10,000 20,0001101001,000\nClausesTime [s]Unindexed F4\nUnindexed F3\nUnindexed F2\nUnindexed F1\nIndexed F4\nIndexed F3\nIndexed F2\nIndexed F1\nFig. 8.Average inference time on Fashion-MNIST\nReferences\n1.Michael Lvovitch Tsetlin. On behaviour of \ufb01nite automata in random medium.\nAvtomat. i Telemekh , 22(10):1345\u20131354, 1961.\n2.Herbert Robbins. Some aspects of the sequential design of experiments. Bulletin of"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c613b-934e-11ee-82db-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 12, "chroma:document": "the American Mathematical Society , 1952.\n3.JC Gittins. Bandit processes and dynamic allocation indices. Journal of the Royal\nStatistical Society, Series B (Methodological) , 41(2):148\u2013177, 1979.\n4.K S Narendra and M A L Thathachar. Learning Automata: An Introduction .\nPrentice-Hall, Inc., 1989.\n5.Vegard Haugland et al. A two-armed bandit collective for hierarchical examplar\nbased mining of frequent itemsets with applications to intrusion detection. TCCI\nXIV, 8615:1\u201319, 2014."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c613c-934e-11ee-a19a-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 12, "chroma:document": "XIV, 8615:1\u201319, 2014.\n6.O.-C. Granmo et al. Learning Automata-based Solutions to the Nonlinear Fractional\nKnapsack Problem with Applications to Optimal Resource Allocation. IEEE Trans.\non Systems, Man, and Cybernetics, Part B , 37(1):166\u2013175, 2007.\n7.Geir Thore Berge, Ole-Christo\ufb00er Granmo, Tor Oddbj\u00f8rn Tveit, Morten Goodwin,\nLei Jiao, and Bernt Viggo Matheussen. Using the Tsetlin Machine to Learn\nHuman-Interpretable Rules for High-Accuracy Text Categorization with Medical"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c613d-934e-11ee-98d2-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 12, "chroma:document": "Applications. IEEE Access , 7:115134\u2013115146, 2019.\n8.Adrian Phoulady, Ole-Christo\ufb00er Granmo, Saeed Rahimi Gorji, and Hady Ahmady\nPhoulady. The Weighted Tsetlin Machine: Compressed Representations with Clause\nWeighting. In Ninth International Workshop on Statistical Relational AI (StarAI\n2020), 2020.\n9.Adrian Wheeldon, Rishad Sha\ufb01k, Alex Yakovlev, Jonathan Edwards, Ibrahim\nHaddadi, and Ole-Christo\ufb00er Granmo. Tsetlin Machine: A New Paradigm for"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c613e-934e-11ee-9008-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 13, "chroma:document": "14 S. R. Gorji et al.\nPervasive AI. In Proceedings of the SCONA Workshop at Design, Automation and\nTest in Europe (DATE) , 2020.\n10.K. Darshana Abeyrathna, Ole-Christo\ufb00er Granmo, Xuan Zhang, Lei Jiao, and\nMorten Goodwin. The Regression Tsetlin Machine - A Novel Approach to Inter-\npretable Non-Linear Regression. Philosophical Transactions of the Royal Society A ,\n378, 2019.\n11.Ole-Christo\ufb00er Granmo, Sondre Glimsdal, Lei Jiao, Morten Goodwin, Christian W."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c613f-934e-11ee-9d2d-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 13, "chroma:document": "Omlin, and Geir Thore Berge. The Convolutional Tsetlin Machine. arXiv preprint,\narXiv:1905.09688 , 2019.\n12.Saeed Rahimi Gorji, Ole-Christo\ufb00er Granmo, Adrian Phoulady, and Morten Good-\nwin. A Tsetlin Machine with Multigranular Clauses. In Lecture Notes in Computer\nScience: Proceedings of the Thirty-ninth International Conference on Innovative\nTechniques and Applications of Arti\ufb01cial Intelligence (SGAI-2019) , volume 11927.\nSpringer International Publishing, 2019."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6140-934e-11ee-bc72-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 13, "chroma:document": "Springer International Publishing, 2019.\n13.Ole-Christo\ufb00er Granmo. The Tsetlin Machine - A Game Theoretic Bandit Driven\nApproach to Optimal Pattern Recognition with Propositional Logic. arXiv preprint\narXiv:1804.01508 , 2018.\n14.D. E. Rumelhart, G. E. Hinton, and R. J. Williams. Learning representations by\nback-propagating errors. Nature, 323:533\u2013536, October 1986.\n15.Han Xiao, Kashif Rasul, and Roland Vollgraf. Fashion-MNIST: a Novel Image"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6141-934e-11ee-b955-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2004.03188.pdf", "page": 13, "chroma:document": "Dataset for Benchmarking Machine Learning Algorithms, 2017."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6142-934e-11ee-82a9-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 0, "chroma:document": "THECONVOLUTIONAL TSETLIN MACHINE\u02da\nA P REPRINT\nOle-Christoffer Granmo\nCAIR, University of AgderSondre Glimsdal\nCAIR, University of AgderLei Jiao\nCAIR, University of Agder\nMorten Goodwin\nCAIR, University of AgderChristian W. Omlin\nCAIR, University of AgderGeir Thore Berge\nSSHF and CAIR\nDecember 30, 2019\nABSTRACT\nConvolutional neural networks (CNNs) have obtained astounding successes for important pattern"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6143-934e-11ee-ab10-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 0, "chroma:document": "recognition tasks, but they suffer from high computational complexity and the lack of interpretability.\nThe recent Tsetlin Machine (TM) attempts to address this lack by using easy-to-interpret conjunctive\nclauses in propositional logic to solve complex pattern recognition problems. The TM provides\ncompetitive accuracy in several benchmarks, while keeping the important property of interpretability."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6144-934e-11ee-883a-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 0, "chroma:document": "It further facilitates hardware-near implementation since inputs, patterns, and outputs are expressed as\nbits, while recognition and learning rely on straightforward bit manipulation. In this paper, we exploit\nthe TM paradigm by introducing the Convolutional Tsetlin Machine (CTM), as an interpretable\nalternative to CNNs. Whereas the TM categorizes an image by employing each clause once to the\nwhole image, the CTM uses each clause as a convolution \ufb01lter. That is, a clause is evaluated multiple"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6145-934e-11ee-a8ba-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 0, "chroma:document": "times, once per image patch taking part in the convolution. To make the clauses location-aware,\neach patch is further augmented with its coordinates within the image. The output of a convolution\nclause is obtained simply by ORing the outcome of evaluating the clause on each patch. In the\nlearning phase of the TM, clauses that evaluate to 1are contrasted against the input. For the CTM,\nwe instead contrast against one of the patches, randomly selected among the patches that made the"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6146-934e-11ee-8770-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 0, "chroma:document": "clause evaluate to 1. Accordingly, the standard Type I and Type II feedback of the classic TM can be\nemployed directly, without further modi\ufb01cation. The CTM obtains a peak test accuracy of 99.4%\non MNIST, 96.31% on Kuzushiji-MNIST, 91.5% on Fashion-MNIST, and 100.0% on the 2D Noisy\nXOR Problem, which is competitive with results reported for simple 4-layer CNNs, BinaryConnect,\nLogistic Circuits, and a recent FPGA-accelerated Binary CNN.\n1 Introduction"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6147-934e-11ee-a078-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 0, "chroma:document": "1 Introduction\nThe Tsetlin Machine (TM) [ 12] is a novel machine learning paradigm introduced in 2018. It is based on the Tsetlin\nAutomaton (TA) [ 36], one of the pioneering solutions to the well-known multi-armed bandit problem [ 33,11] and the\n\ufb01rst Finite State Learning Automaton (FSLA) [ 25]. The TM has the following main properties that make it attractive\nas a building block for machine learning [ 12]: (a) it solves complex pattern recognition problems with interpretable"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6148-934e-11ee-97d3-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 0, "chroma:document": "propositional formulae. This is crucial for high stakes decisions [ 34]. (b) It learns on-line, persistently increasing both\ntraining- and test accuracy, before converging to a Nash equilibrium. The Nash equilibrium balances false positive\nagainst false negative classi\ufb01cations, while combating over\ufb01tting with frequent pattern mining principles. (c) Resource\nallocation dynamics are leveraged to optimize usage of limited pattern representation resources. By allocating resources"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6149-934e-11ee-b90d-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 0, "chroma:document": "uniformly across sub-patterns, local optima are avoided. (d) Inputs, patterns, and outputs are expressed as bits, while\nrecognition and learning rely on straightforward bit manipulation. This facilitates low-energy consuming hardware\ndesign [ 40]. (e) Finally, the TM has provided competitive accuracy in comparison with classical and neural network\nbased techniques, while keeping the important property of interpretability [3, 1]."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c614a-934e-11ee-b16a-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 0, "chroma:document": "\u02daSource code and demos for this paper can be found at https://github.com/cair/pyTsetlinMachineParallel.arXiv:1905.09688v5  [cs.LG]  27 Dec 2019"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c614b-934e-11ee-a2cb-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 1, "chroma:document": "APREPRINT - DECEMBER 30, 2019\nThe TM currently is state-of-the-art in FSLA-based pattern recognition. However, when compared with CNNs, it\nstruggles with attaining competitive accuracy, providing e.g. 98.5% mean accuracy on MNIST (without augmenting the\ndata) [ 12]. To address this de\ufb01ciency, we here introduce the Convolutional Tsetlin Machine (CTM), a new kind of TM\ndesigned for image classi\ufb01cation."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c614c-934e-11ee-8cab-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 1, "chroma:document": "designed for image classi\ufb01cation.\nFSLA. The simple Tsetlin Automaton approach has formed the core of more advanced FSLA designs that solve a\nwide range of problems. This includes resource allocation [ 15], decentralized control [ 37], knapsack problems [ 16],\nsearching on the line [ 27], meta-learning [ 28], the satis\ufb01ability problem [ 13], graph colouring [ 4], preference learning"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c614d-934e-11ee-ad8a-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 1, "chroma:document": "[42], frequent itemset mining [ 17], adaptive sampling [ 14], spatio-temporal event detection [ 43], equi-partitioning [ 29],\nstreaming sampling for social activity networks [ 10], routing bandwidth-guaranteed paths [ 26], faulty dichotomous\nsearch [ 44], and learning in deceptive environments [ 46], to list a few examples. The unique strength of all of these\nFSLA designs is that they provide state-of-the-art performance when problem properties are unknown and stochastic,"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c614e-934e-11ee-ad5d-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 1, "chroma:document": "and the problem must be solved as quickly as possible through trial and error.\nRule-based Machine Learning. While the present paper focuses on extending the \ufb01eld of FSLA, we acknowledge\nthe extensive work on rule-based interpretable pattern recognition from other \ufb01elds of machine learning. Learning\npropositional formulae to represent patterns in data has a long history. One prominent example is frequent itemset"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c614f-934e-11ee-933f-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 1, "chroma:document": "mining for association rule learning [ 2], for instance applied to predicting sequential events [ 35,24]. Other examples\ninclude the work of Feldman who investigated the hardness of learning formulae in disjunctive normal form (DNF)\n[9]. Furthermore, Probably Approximately Correct (PAC) learning has provided fundamental insight into machine\nlearning, as well as a framework for learning formulae in DNF [ 38]. Approximate Bayesian approaches have recently"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6150-934e-11ee-bd4c-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 1, "chroma:document": "been introduced to provide more robust learning of rules [ 39,18]. However, in general, rule-based machine learning\nscales poorly and is prone to noise. Indeed, for data-rich problems, in particular those involving natural language and\nsensory inputs, state-of-the-art rule-based machine learning is inferior to deep learning. The recent hybrid Logistic\nCircuits [ 22], however, have had success in image classi\ufb01cation. This approach uses local search to build Bayesian"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6151-934e-11ee-be1d-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 1, "chroma:document": "models that capture logical expressions, and learns to classify by employing stochastic gradient descent. The CTM, on\nthe other hand, attempts to bridge the gap between the interpretability of pure rule-based machine learning and the\naccuracy of deep learning, by allowing the TM to more effectively deal with images.\nCNNs. A myriad of image recognition techniques have been reported. However, after AlexNet won the ImageNet"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6152-934e-11ee-84a1-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 1, "chroma:document": "recognition challenge by a signi\ufb01cant margin in 2012, the entire \ufb01eld of computer vision has been dominated by\nCNNs. The AlexNet architecture was built upon earlier work by LeCun et al. [ 21] who introduced CNNs in 1998.\nCountless CNN architectures, all following the same basic principles, have since been published, including the now\nstate-of-the-art Squeeze-and-Excitation networks [ 19]. In this paper, we introduce convolution to the TM paradigm"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6153-934e-11ee-89f2-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 1, "chroma:document": "of machine learning. By doing so, we simultaneously propose a new kind of convolution \ufb01lter: an interpretable \ufb01lter\nexpressed as a propositional formula. Our intent is to address a well-known disadvantage of CNNs, namely, that the\nCNN models in general are complex and non-transparent, making them hard to interpret. Consequently, the knowledge\non why CNNs perform so well and what steps are need to improve the models is limited [45]."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6154-934e-11ee-93de-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 1, "chroma:document": "Binary CNNs. Relying on a large number of multiply-accumulate operations, training CNNs is computationally\nintensive. To mitigate this, there is an increasing interest in binarizing the CNNs. With only two possible values for the\nsynapse weights, e.g., \u00b41and1, many of the multiplication operations can be replaced with simple accumulations.\nThis could potentially open up for more specialized hardware and more compressed and ef\ufb01cient models. One recent"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6155-934e-11ee-8f4c-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 1, "chroma:document": "approach is BinaryConnect [ 6], which reached a near state-of-the-art accuracy of 98.99% on MNIST, and 99.13% in\ncombination with an SVM. Binary CNNs have been further improved with the introduction of XNOR-Nets, which\nreplace the standard CNN \ufb01lters with binary equivalents [ 32]. BNN+ [ 7] is the most recent binary CNN, extending the\nXNOR-Nets with two additional regularization functions and an adaptive scaling factor. The CTM can be seen as an"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6156-934e-11ee-ab83-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 1, "chroma:document": "extreme Binary CNN in the sense that it is entirely based on fast summation and logical operators. Additionally, learning\nin the CTM is bandit based (online learning from reinforcement), while Binary CNNs are based on backpropagation.\nContributions and Paper Outline. Our contributions can be summarized as follows. First, in Sect. 2, we provide a\nbrief introduction to the TM and a succinct de\ufb01nition of both recognition and learning. Then, in Sect. 3, we introduce"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6157-934e-11ee-9d05-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 1, "chroma:document": "the concept of convolution to TMs. Whereas the classic TM categorizes an image by employing each clause once\non the whole image, the CTM uses each clause as a convolution \ufb01lter. In all brevity, we propose a recognition and\nlearning approach for clause-based convolution that produces interpretable \ufb01lters. In Sect. 4, we evaluate the CTM\non MNIST, Kuzushiji-MNIST, Fashion-MNIST, and the 2D Noisy XOR Problem, and discuss the merits of the new"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6158-934e-11ee-81a1-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 1, "chroma:document": "scheme. Finally, we conclude and provide pointers to further work in Sect. 5.\n2"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6159-934e-11ee-bad3-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 2, "chroma:document": "APREPRINT - DECEMBER 30, 2019\nIncludeExcludex2x1\u00acx2\u00acx1\u2335\u2335\u2335x2x1\u00acx2\u00acx1\u2335\u2335\u2335Clause +Clause \u2014\nX = (x1, x2)Majority votingFeedback Type I or IIClause outputClause output\nInput feature vectorDecided classFeedback Type I or II+\u2014\n123456\n123456\n123456\n123456\n123456\n123456\n123456\n123456\nFigure 1: The basic TM structure.\n2 The Tsetlin Machine\nThe TM solves complex pattern recognition problems using conjunctive clauses in propositional logic, composed by a"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c615a-934e-11ee-9b5f-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 2, "chroma:document": "collective of TAs. Its roots in game theory, the bandit problem, resource allocation, and frequent pattern mining are\nexplored in depth in the original paper on the TM, which also includes pseudo code [ 12]. We here provide a more\nsuccinct overview, together with a running example to clarify core concepts.\n2.1 Structure\nThe structure of the TM is shown in Figure 1. As seen, the TM takes a vector Xofopropositional variables as input:"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c615b-934e-11ee-81f7-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 2, "chroma:document": "X\u201cpxkqPt0,1uo, with obeing the size of the vector and t0,1uoits domain. The input vector in the \ufb01gure, for\ninstance, is of size 2and consists of the variables x1andx2with domaintp0,0q,p0,1q,p1,0q,p1,1qu.\nThe TM formulates patterns using conjunctive clauses . A conjunctive clause is built from literals , that is, the input\nvariables and their negations. With oinput variables, we have 2oliterals, L\u201cplkqPt0,1u2o:\nlk\u201c\"xk if1\u010fk\u010fo,\n\u2423xk\u00b4ootherwisepi.e.,o`1\u010fk\u010f2oq.(1)"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c615c-934e-11ee-bac5-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 2, "chroma:document": "lk\u201c\"xk if1\u010fk\u010fo,\n\u2423xk\u00b4ootherwisepi.e.,o`1\u010fk\u010f2oq.(1)\nAbove, the \ufb01rst oliterals are the unnegated variables, while the ofollowing are the negated ones. Thus, in our example,\nthere are four literals: x1, x2,\u2423x1, and\u2423x2.\nThe number of clauses is a user set parameter that decides the expression power of the TM. Assume we have mclauses\nin our TM structure. Each clause, denoted by Cjand indexed by jPt1, . . . , mu, is simply a conjunction of a subset\nIj\u010et1, . . . , 2ouof the literals:\nCjpXq\u201c\u013e\nkPIjlk (2)"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c615d-934e-11ee-bcf5-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 2, "chroma:document": "CjpXq\u201c\u013e\nkPIjlk (2)\n3"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c615e-934e-11ee-8e79-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 3, "chroma:document": "APREPRINT - DECEMBER 30, 2019\nor equivalently:\nCjpXq\u201c\u017a\nkPIjlk. (3)\nThe subset Ijcontains the indexes of the literals that have been Included in the clause j. For the special case of Ij\u201cH ,\ni.e., an empty clause, we have:\nCjpXq\u201c\"\n1during learning\n0otherwise .(4)\nThat is, during learning, empty clauses output 1and during classi\ufb01cation they output 0. Accordingly, overall, the\noutput cj\u201cCjpXqPt0,1uof a clause is fully speci\ufb01ed by the input Xand the selection of literals Ij. Continuing"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c615f-934e-11ee-8fb7-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 3, "chroma:document": "our example, in the \ufb01gure we have two clauses ( m\u201c2). The \ufb01rst consists of the literals with indexes I1\u201ct1,4u:\nC1pXq\u201cx1^\u2423x2. The second consists of the literals with indexes I2\u201ct1,2u:C2pXq\u201cx1^x2.\nEach clause is further assigned a \ufb01xed polarity pPt\u00b41,`1u, which decides whether the clause output is negative or\npositive. In the \ufb01gure, the \ufb01rst clause has positive polarity, whereas the second has negative. Positive clauses are used to"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6160-934e-11ee-8c6b-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 3, "chroma:document": "recognize class y\u201c1, while negative clauses are used to recognize class y\u201c0. By default, half of the clauses are\npositive and half are negative.\nIn the last step, the outputs of the clauses decide the class \u02c6yPt0,1uassigned to the input X. That is, a summation\noperator aggregates the output of the clauses to form a majority vote.\n2.2 Recognition\nWe now look at recognition in more detail. First of all, the output cp\njof each clause is organized as vectors C`\u201cpc`\njqP\nt0,1um\n2andC\u00b4\u201cpc\u00b4\njqPt0,1um"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6161-934e-11ee-8265-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 3, "chroma:document": "jqP\nt0,1um\n2andC\u00b4\u201cpc\u00b4\njqPt0,1um\n2, grouped by polarity. Given an input X, these outputs can then be calculated as\nfollows (equivalent to Eqn. 2):\ncp\nj\u201c\"1ifIp\nj\u010eI1\nL,\n0otherwise .(5)\nHere, the subset I1\nL\u010et1, . . . , 2oucontains the indexes of the literals that take the value 1for the current input X:\nI1\nL\u201ctk|lk\u201c1,1\u010fk\u010f2ou. To express this, the lower index Lstands for the literals and the upper index 1constrains"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6162-934e-11ee-abea-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 3, "chroma:document": "these to those of value 1. Thus, Eqn. 5 compactly states that a clause outputs 1if and only if all of its literals are of\nvalue 1. In Figure 1, for instance, the input px1, x2q\u201cp1,0qproduces the literal values l1\u201c1,l2\u201c0,l3\u201c0, and\nl4\u201c1. Since the \ufb01rst clause only consists of l1andl4, it outputs 1. The second clause, on the other hand, consists of l1\nandl2, hence it outputs 0.\nThe \ufb01nal classi\ufb01cation decision is made as follows. A majority vote is \ufb01rst organized by summing the output C`of"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6163-934e-11ee-acfa-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 3, "chroma:document": "the positive clauses, and subtracting the output C\u00b4of the negative clauses: v\u201c\u0159\njc`\nj\u00b4\u0159\njc\u00b4\nj. This majority vote\ndecides the prediction of the TM: \u02c6y\u201cp0\u010fv), with a tie resolved in favor of y\u201c1.2So, in our example, the input\npx1, x2q\u201cp1,0qgathers a single positive vote, and no negative votes. Consequently, the classi\ufb01cation becomes \u02c6y\u201c1.\n2.3 Tsetlin Automata Collective\nWe now introduce the collective of TAs, which decides the composition of each clause. There are 2oTAs per clause j,"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6164-934e-11ee-af5d-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 3, "chroma:document": "one for each literal lkPtx1, . . . , x o,\u2423x1, . . . ,\u2423xou. Each individual TA has a state a\u00b4\nj,k, a`\nj,kPt1, . . . , 2Nu, and the\nstates of all of the TAs are organized in twom\n2\u02c6omatrices. The \ufb01rst matrix, A`\u201cpa`\nj,kqPt1, . . . , 2Num\n2\u02c62o, contains\nthe states of the TAs belonging to the positive polarity clauses, whereas the matrix A\u00b4\u201cpa\u00b4\nj,kqPt1, . . . , 2Num\n2\u02c62o\ncovers the negative polarity clauses. In Figure 1, there are eight TAs, one per literal for clause 1(positive polarity) and"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6165-934e-11ee-905f-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 3, "chroma:document": "one per literal for clause 2(negative polarity). Each of these TAs has 6states: ap\nj,kPt1, . . . , 6u.\nThe states decide the actions taken by the TAs. A TA decides to exclude its literal if in states ap\nj,k\u010fN, otherwise,\nit includes the literal. That is, for each clause j, some literals are Included :Ip\nj\u201c!\nk|ap\nj,k\u0105N,1\u010fk\u010f2o)\n, while\nthe remaining are Excluded :Ip\njc\u201ct1, . . . , 2ouzIp\nj(the complement of the included ones). So, in the \ufb01gure, the TA"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6166-934e-11ee-9e07-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 3, "chroma:document": "associated with literal x1in the \ufb01rst clause is in state 4and thus x1is included in that clause. The second TA, on the\nother hand, is in state 3and, accordingly, literal x2is excluded. By checking the state of each TA in this manner, the\ncomposition of all of the clauses is decided.\n2Multi-class pattern recognition problems are modelled by employing multiple instances of this structure, replacing the threshold\noperator with an argmax operator [12].\n4"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6167-934e-11ee-95c5-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 4, "chroma:document": "APREPRINT - DECEMBER 30, 2019\n2.4 Learning\nLearning in the TM is based on coordinating the collective of TAs using a novel FSLA game. The game leverages\nresource-allocation [ 16] and frequent pattern mining [ 17] principles, indicated by the feedback loop in Figure 1. The\nfeedback is handed out based on training examples pX, yq, consisting of an input Xand an output y.\nAs explored below, the TM employs two kinds of feedback: Type I and Type II. Type I feedback jointly combats"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6168-934e-11ee-bf88-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 4, "chroma:document": "false negatives and over\ufb01tting by stimulating recognition of frequent patterns. Type II feedback, on the other hand,\nsuppresses false positives by increasing the discrimination power of the patterns learnt.\nFeedback is further regulated by the sum of clause outputs v(the majority vote) and a target value TPZ\u0105set for vby\nthe user. A larger T(with a corresponding increase in the number of clauses) makes the learning more robust. This is"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6169-934e-11ee-9471-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 4, "chroma:document": "because more clauses are involved in learning each speci\ufb01c pattern, introducing an ensemble effect. However, note that\nthe resulting gain in accuracy comes at the cost of increased computational cost (cf. Table 3).\nFigure 2: Clause feedback probability for T\u201c4.\nIn the following, we \ufb01rst de\ufb01ne the Type I and Type II feedback operations for clauses with positive polarity. As\nopposed to the feedback tables in [12], the representation here is in a more compact matrix form."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c616a-934e-11ee-8912-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 4, "chroma:document": "Type I: For training output y\u201c1, TAs belonging to positive clauses are given Type I feedback to make vapproach T.\nA vector R`\n1\u201cpr`\nj,1qPt0,1um\n2picks out the positive clauses selected for feedback (the lower index of R`\n1\nrefers to the output y\u201c1):\nr`\nj,1\u201c#\n1with probabilityT\u00b4clamppv,\u00b4T,Tq\n2T,\n0otherwise .(6)\nHere, the clamp operation restricts vto lie between \u00b4TandT. Further, the lower index of r`\nj,1refers to the"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c616b-934e-11ee-b247-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 4, "chroma:document": "j,1refers to the\nclause jand the output y\u201c1. As illustrated by plot y\u201c1in Figure 2, clauses are randomly selected for\nfeedback, with a larger chance of being selected for lower values of v. In effect, clauses are updated more\naggressively the farther away the voting sum is from T, up to\u00b4T.\nWe now divide the Type I feedback into two parts, Type Ia and Type Ib. Type Ia reinforces Include actions\nto make the patterns \ufb01ner. Only TAs taking part in clauses that output 1and whose associated literal"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c616c-934e-11ee-8b14-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 4, "chroma:document": "takes the value 1are select for Type Ia feedback. We collect the indexes of these TAs in the set IIa\nC`\u201c\u2423\npj, kq|lk\u201c1^c`\nj\u201c1^r`\nj,1\u201c1(\n.\nType Ib feedback is designed to reinforce Exclude actions to combat over-\ufb01tting. Type Ib feedback is handed\nout to the TAs stochastically, using a user set parameter s\u011b1.0(a larger sprovides \ufb01ner patterns). The\n5"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c616d-934e-11ee-9487-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 5, "chroma:document": "APREPRINT - DECEMBER 30, 2019\nstochastic part of the calculation is organized in a matrix Q`\u201cpq`\nj,kqPt0,1um\n2\u02c62owith entries:\nq`\nj,k\u201c\"1with probability1\ns,\n0otherwise .(7)\nHere, the lower index of q`\nj,krefers to the clause jand the TA k, considering the positive clauses (up-\nper index). The indexes of the TAs selected for Type Ib feedback are collected in the set IIb\nC`\u201c!\npj, kq|plk\u201c0_c`\nj\u201c0q^r`\nj,1\u201c1^q`\nj,k\u201c1)\n. That is, TAs taking part in clauses that output 0, or"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c616e-934e-11ee-b953-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 5, "chroma:document": "whose associated literal takes the value 0, are selected for Type Ib feedback, however, only if stochastically\npinpointed by r`\nj,1\u201c1andq`\nj,k\u201c1.\nAfter the TAs has been selected for feedback, their states are updated by two state update operators \u2018anda:\nA`\u00d0`\nA`\u2018IIa\nC`\u02d8\naIIb\nC`These operators add/subtract 1from the states of the singled out TAs, however,\nnot beyond the given state space. In our example, if the TA associated with literal x1in the \ufb01rst clause is"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c616f-934e-11ee-9057-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 5, "chroma:document": "singled out for Type Ia feedback, it would move from state 4to state 5, reinforcing the Include action. If it\ninstead receives Type Ib feedback, it would move to state 3, reinforcing Exclude .\nType II: For training output y\u201c0, TAs belonging to positive clauses are given Type II feedback to suppress clause\noutput 1. This, together with the negative clauses, makes vapproach\u00b4T. A matrix R`\n0\u201cpr`\nj,0qPt0,1um\n2\npicks out the positive clauses selected for feedback:\nr`\nj,0\u201c#"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6170-934e-11ee-96f7-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 5, "chroma:document": "r`\nj,0\u201c#\n1with probabilityT`clamppv,\u00b4T,Tq\n2T,\n0otherwise .(8)\nThe lower index of r`\nj,0refers to the clause jand the output y\u201c0, respectively. Here too, clauses are randomly\nselected for feedback, but now with a larger chance of being selected for higher v(cf. plot y\u201c0in Figure\n2). Next, the TAs selected are the ones that will turn clauses that output 1into clauses that output 0, that is,\nthose that have excluded literals that take the value 0:III\nC`\u201c\u2423\npj, kq|lk\u201c0^c`\nj\u201c1^r`\nj,0\u201c1(\n. Again,"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6171-934e-11ee-bd41-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 5, "chroma:document": "C`\u201c\u2423\npj, kq|lk\u201c0^c`\nj\u201c1^r`\nj,0\u201c1(\n. Again,\nthe states of the selected TAs are updated using the dedicated operators: A`\u00d0A`\u2018III\nC`. Thus, if the TA\nassociated with literal x2in the \ufb01rst clause of our example is selected for Type II feedback, it would change\nstate from 3to4, reinforcing the Include action.\nAll of the above operations are for positive clauses. For negative clauses, Type I feedback is simply replaced with Type\nII feedback and vice versa!"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6172-934e-11ee-add2-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 5, "chroma:document": "II feedback and vice versa!\n1010100113 x 3 input image4 positive clauses4 negative clauses1\n\u2211+1\nxy+10000 < x10y <= 0010 < x11y <= 0000 < x00y <= 0110 < x01y <= 0100 < x10y <= 0010 < x10y <= 001000 < x11y <= 0000 < x00y <= 01100\n(a)\n1010100113 x 3 input image4 positive clauses4 negative clauses\u2211P(Feedback) = (T-1)/(2T) = 0.25\nxyType I Feedback0 < x10y <= 0010 < x11y <= 0000 < x00y <= 0110 < x01y <= 0100 < x10y <= 0010 < x10y <= 0010 < x11y <= 0000 < x00y <= 011Type II Feedback+10000000+1 (b)"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6173-934e-11ee-ab3c-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 5, "chroma:document": "Figure 3: Example of inference (a) and learning (b) for the Noisy 2D XOR Problem.\n6"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6174-934e-11ee-8017-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 6, "chroma:document": "APREPRINT - DECEMBER 30, 2019\n0 < x01y <= 0101010100113 x 3 input image4 positive clauses4 negative clauses1\n\u2211+2\nxy+10000 < x10y <= 0010 < x11y <= 0000 < x00y <= 0110 < x01y <= 0100 < x10y <= 001000 < x11y <= 0000 < x00y <= 0110+1\n(a)\n5/20/2019 m.html\n1/13\n3 (b)\nFigure 4: (a) Goal state for the Noisy 2D XOR Problem. (b) Illustration of image, \ufb01lter and patches.\n2.5 Integer Clause Weighting"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6175-934e-11ee-8395-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 6, "chroma:document": "2.5 Integer Clause Weighting\nIt turns out that introducing clause weighting improves TM performance, both accuracy- and computation-wise [ 31].\nBy weighting the output of the clauses, one clause can replace multiple and the impact of a clause can be \ufb01ne-tuned. In\nall brevity, classi\ufb01cation is then performed as a weighted majority vote:\ns1pxq\u201cm{2\u00ff\nj\u201c1w`\njC`\njpxq\u00b4m{2\u00ff\nj\u201c1w\u00b4\njC\u00b4\njpxq. (9)"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6176-934e-11ee-8e3a-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 6, "chroma:document": "j\u201c1w`\njC`\njpxq\u00b4m{2\u00ff\nj\u201c1w\u00b4\njC\u00b4\njpxq. (9)\nWhereas real-valued weighting was introduced in [ 31], we here address learning of integer weights, based on Stochastic\nSearching on the Line [27]:\nInitialization. First of all, the weights are initialized to 1:\nw`\nj\u00d01, (10)\nw\u00b4\nj\u00d01. (11)\nIn other words, the behaviour of the clauses are identical to those of a standard TM at the start of learning.\nWeight Updating. The TA state updating is unmodi\ufb01ed with weights. The weights, in turn, are updated based on"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6177-934e-11ee-957a-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 6, "chroma:document": "Type I and Type II feedback.\nType I: For Type I feedback, a clause weight is increased by 1, however, only if the clause outputted 1:\nw`\nj\u00d0w`\nj`1,ifC`\njpxq\u201c1, (12)\nw\u00b4\nj\u00d0w\u00b4\nj`1,ifC\u00b4\njpxq\u201c1. (13)\nType II: For Type II feedback, we instead update the weights by subtracting 1, with 1being the minimum weight value:\nw`\nj\u00d0w`\nj\u00b41,ifC`\njpxq\u201c1^w`\nj\u01051, (14)\nw\u00b4\nj\u00d0w\u00b4\nj\u00b41,ifC\u00b4\njpxq\u201c1^w\u00b4\nj\u01051. (15)\nWhen a clause evaluates to 0, its weight remains unchanged:\nw`\nj\u00d0w`\nj,ifC`\njpxq\u201c0, (16)\nw\u00b4\nj\u00d0w\u00b4\nj,ifC\u00b4"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6178-934e-11ee-8b6b-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 6, "chroma:document": "w`\nj\u00d0w`\nj,ifC`\njpxq\u201c0, (16)\nw\u00b4\nj\u00d0w\u00b4\nj,ifC\u00b4\njpxq\u201c0. (17)\n7"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6179-934e-11ee-8f33-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 7, "chroma:document": "APREPRINT - DECEMBER 30, 2019\nAs seen, for Type I feedback, the weights are increased to strengthen the impact of the associated clauses, thus\nreinforcing true positive frequent patterns. For Type II feedback, on the other hand, the weights are decreased instead.\nThis is to diminish the impact of the associated clauses, thus combating false positives, increasing discrimination power.\n3 The Convolutional Tsetlin Machine"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c617a-934e-11ee-bbb9-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 7, "chroma:document": "3 The Convolutional Tsetlin Machine\nConsider a set of images X\u201ctXe|1\u010fe\u010fEu, where eis the index of the images. Each image is of size X\u02c6Y, and\nconsists of Zbinary layers (which together encode the pixel colors using thresholding [ 8], one-hot encoding, or any\nother appropriate binary encoding). A classic TM models such an image with an input vector X\u201cpxkqPt0,1uX\u02c6Y\u02c6Z\nthat contains X\u02c6Y\u02c6Zpropositional variables. Further, each clause is composed from X\u02c6Y\u02c6Z\u02c62literals."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c617b-934e-11ee-b7a3-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 7, "chroma:document": "Inspired by the impact convolution has had on deep neural networks, we here introduce the Convolutional Tsetlin\nMachine (CTM).\nInterpretable Rule-based Filters. The CTM uses \ufb01lters with spatial dimensions W\u02c6W, again with Zbinary layers.\nFurther, the clauses of the CTM take the role of \ufb01lters. Each clause is accordingly composed from W\u02c6W\u02c6Z\u02c62\nliterals. Additionally, to make the clauses location-aware [ 23], we augment each clause with binary encoded coordinates."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c617c-934e-11ee-a579-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 7, "chroma:document": "Location awareness may prove useful in applications where both patterns and their location are distinguishing features,\ne.g. recognition of facial features such as eyes, eyebrows, nose, mouth, etc. in facial expression recognition. In\nall brevity, when applying a \ufb01lter of size W\u02c6Won an imagepxkqPt0,1uX\u02c6Y\u02c6Z, the \ufb01lter will be evaluated on\nB\u201cBX\u02c6BYimage patches. Here, BX\u201cPX\u00b4W\ndT\n`1andBY\u201cPY\u00b4W\ndT\n`1, with dbeing the step size of the"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c617d-934e-11ee-9af3-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 7, "chroma:document": "dT\n`1, with dbeing the step size of the\nconvolution. Each image patch thus has a certain location within the image, and we augment the input vector with the\ncoordinates of this location. We denote the resulting augmented input vector Xb:Xb\u201cpxkqPt0,1uW\u02c6W\u02c6Z`BX`BY.\nAs seen, the input vector is extended with one propositional variable per position along each dimension, with the\nposition being encoded using thresholding [ 8] or one-hot encoding. Figure 4b illustrates an example of the image,"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c617e-934e-11ee-9369-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 7, "chroma:document": "patches, and a \ufb01lter for X\u201cY\u201c6,W\u201c3, andd\u201c2. In this example, the 3 \u02c63 \ufb01lter moves from left to right, from\ntop to bottom, 2pixels per step.\nRecognition. The CTM uses the classic TM procedure for recognition (see Sect. 2). However, for the CTM each clause\noutputs Bvalues per image (one value per patch), as opposed to a single output for the TM (Eq. 5). We denote the\noutput of a positive clause jon patch bbycb,`\nj. To turn the multiple outputs c1,`\nj, . . . , cB,`\njof clause jinto a single"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c617f-934e-11ee-b957-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 7, "chroma:document": "j, . . . , cB,`\njof clause jinto a single\noutput denoted by c`\nj, we simply OR the individual outputs:\nc`\nj\u201cB\u0142\nb\u201c1cb,`\nj. (18)\nLearning. Learning in the CTM leverages the TM learning procedure. As seen in Sect. 2, Type Ia, Type Ib, and Type II\nfeedback are in\ufb02uencing each clause jbased on the literals of the input vector X. For the CTM, the input vector is an\nimage patch, and there are Bpatches in an image. There is thus Bliteral inputs Lb,1\u010fb\u010fB, per clause. Therefore,"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6180-934e-11ee-b434-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 7, "chroma:document": "to decide which patch to use when updating a clause, the CTM randomly selects a single patch among the patches that\nmade the clause evaluate to 1. The clause is then updated according to this patch. That is, the input Xbis drawn from\nthe set:tXb|cb,`\nj\u201c1,1\u010fb\u010fBu. Observe that if the set is empty, only Type Ib feedback is applicable, and then\nthe input vector is not needed. For non-empty sets, the TAs to be updated are \ufb01nally singled out using the randomly\nselected patch:\nIIa\nC`\u201c\u2423\npj, kq|lb"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6181-934e-11ee-ba1b-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 7, "chroma:document": "selected patch:\nIIa\nC`\u201c\u2423\npj, kq|lb\nk\u201c1^c`\nj\u201c1^r`\nj,1\u201c1(\n, (19)\nIIb\nC`\u201c!\npj, kq|plb\nk\u201c0_c`\nj\u201c0q^r`\nj,1\u201c1^q`\nj,k\u201c1)\n, (20)\nIII\nC`\u201c\u2423\npj, kq|lb\nk\u201c0^c`\nj\u201c1^r`\nj,0\u201c1(\n. (21)\nThe reason for randomly selecting a patch is to have each clause extract a certain sub-pattern, and the randomness of\nthe uniform distribution statistically spreads the clauses for different sub-patterns in the target image. Finally, observe"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6182-934e-11ee-8820-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 7, "chroma:document": "that the computational complexity of the CTM grows linearly with the number of clauses m, and with the number of\npatches B. However, the computations can be easily parallelized due to their decentralized nature.\nStep-by-step Walk-through of Inference on Noisy 2D XOR. Rather than providing hand-crafted features which can\nbe used for image classi\ufb01cation, the CTM learns feature detectors. We will explain the workings of the CTM by an"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6183-934e-11ee-88b2-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 7, "chroma:document": "illustrative example of noisy 2D XOR recognition and learning (see Figure 4 and Sect. 4). Consider the CTM depicted\nin Figure 3a. It consists of four positive clauses which represent XOR patterns that must be present in a positive\nexample image (positive features) and four negative clauses which represent patterns that will not trigger a positive\n8"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6184-934e-11ee-9bce-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 8, "chroma:document": "APREPRINT - DECEMBER 30, 2019\nimage classi\ufb01cation (negative features). The number of positive and negative clauses is a user-de\ufb01ned parameter. The\nbit patterns inside each clause are represented by the output of eight TAs, two for each bit in a 2\u02c62\ufb01lter.\nConsider the 3\u02c63image shown in Figure 3b. The \ufb01lter represented by the second positive clause matches the patch in\nthe top-right corner of the image and it is the only clause with output 1; similarly, none of the negative clauses respond"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6185-934e-11ee-be33-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 8, "chroma:document": "since their patterns do not match the pattern found in the current patch (Figure 3b). Thus, the TM\u2019s combined output is\nv\u201c1. Learning of feature detectors proceeds as follows: with the CTM\u2019s voting target set to T\u201c2, the probability of\nfeedback isT\u00b4v\n2T\u201c1\n4, and thus learning takes place, which pushes the CTM\u2019s output vtowards T\u201c2. Note that Type\nI feedback reinforces true positive output and reduces false negative output whereas Type II feedback reduces false\npositive output."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6186-934e-11ee-9d41-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 8, "chroma:document": "positive output.\nA subsequent state of the CTM is shown in Figure 4a. There are now two positive clauses which detect their pattern\nin the top-right corner patch. The combined output of all clauses is 2; thus, no further learning is necessary for the\ndetection of the XOR pattern in this patch. Also, the location of the occurrence of each pattern is included. The location\ninformation uses a bit representation as follows: Suppose an XOR pattern occurs at the three X-coordinates 1,4, and6."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6187-934e-11ee-8f66-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 8, "chroma:document": "For the corresponding binary location representation, these coordinates are considered as thresholds: If a coordinate is\ngreater than a threshold, then the corresponding bit in the binary representation will be 0; otherwise, it is set to 1. Thus,\nthe representation of the X-coordinates 1,4, and6will be \u201c111\", \u201c011\" and \u201c001\", respectively. These representations\nof the location of 2\u02c62patterns are also learned by TAs.\nSearch Range 2D Noisy XOR MNIST K-MNIST Fashion-MNIST"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6188-934e-11ee-94ad-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 8, "chroma:document": "#Class Clauses 1\u00b48 000 40 8 000 8 000 8 000\nT 1\u00b420 000 60 10 000 10 000 10 000\ns 1.0\u00b420.0 3.9 5.0 10.0 10.0\nW 2\u00b420 2 10 10 10\u02c7\u02c7Z\u02c7\u02c7 1 1 1 1 1\nClause Weighting Yes/No No Yes Yes Yes\nTable 1: CTM con\ufb01gurations.\n4 Empirical Results\nIn this section, we evaluate the CTM on four different datasets.\n2D Noisy XOR. The 2D Noisy XOR dataset contains 4\u02c64binary images, 2500 training examples and 10 000 test"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6189-934e-11ee-8169-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 8, "chroma:document": "examples. The image bits have been set randomly, except for the 2\u02c62patch in the upper right corner, which reveals\nthe class of the image. A diagonal line is associated with class 1, while a horizontal or vertical line is associated with\nclass0. Thus the dataset models a 2D version of the XOR-relation. Furthermore, the dataset contains a large number of\nrandom non-informative features to measure susceptibility towards the curse of dimensionality. To examine robustness"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c618a-934e-11ee-978f-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 8, "chroma:document": "towards noise we have further randomly inverted 40% of the outputs in the training data.\nMNIST. The MNIST dataset has been used extensively to benchmark machine learning algorithms, consisting of\n28\u02c628grey scale images of handwritten digits [21].\nKuzushiji-MNIST. This dataset contains 28\u02c628grayscale images of Kuzushiji characters, cursive Japanese. Kuzushiji-\nMNIST is more challenging than MNIST because there are multiple distinct ways to write some of the characters\n[5]."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c618b-934e-11ee-af68-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 8, "chroma:document": "[5].\nFashion-MNIST. This dataset contains 28\u02c628grayscale images of articles from the Zalando catalogue, such as\nt-shirts, sandals, and pullovers [41]. This dataset is quite challenging, with a human accuracy of 83.50%.\nThe latter three datasets contain 60 000 training examples and 10 000 test examples. We binarize these datasets using\nan adaptive Gaussian thresholding procedure with window size 11and threshold value 2. Accordingly, the CTM"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c618c-934e-11ee-8521-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 8, "chroma:document": "operates on images with merely 1 bit per pixel. Table 4 reports test accuracy for the CTM, while Table 1 contains the\ncorresponding con\ufb01gurations. The results are based on single-run averages, obtained from the last 100epochs of 250.\nAll of the experiments were run on a NVIDIA DGX-2 server. Note that these datasets are rather simple to solve for\ndeep CNNs, and have been selected to facilitate our study of interpretability."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c618d-934e-11ee-b448-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 8, "chroma:document": "The hyperparameters were set using a light manual binary search. One particularly critical hyperparameter is the\nnumber of clauses employed per class. Table 3 reports execution time per epoch as well as mean test accuracy for an\nincreasing number of class clauses. As seen, test accuracy increases steadily with the number of clauses employed,\nwhile execution time increases sub-linearly due to parallelization.\n9"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c618e-934e-11ee-b731-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 9, "chroma:document": "APREPRINT - DECEMBER 30, 2019\n0: U L 0: U R 9: U L 9: U R 4: L L\n00*000*000\n*000*0*000\n**00*00000\n00000000**\n00*000****\n000000***1\n000**0*111\n0*00**111*\n*****111*0\n00**11**00\n0\u0103X\u010f6\n5\u0103Y\u010f80*********\n0******0**\n********00\n*111111**0\n*111*11**0\n*1*1*11***\n111**11**0\n1****111**\n11***111**\n*****111**\n8\u0103X\u010f17\n0\u0103Y\u010f60*0*****1*\n00000**1**\n000*******\n00***1**00\n000**1**00\n00**1*00*0\n00****00**\n0*******11\n0*********\n000*******\n2\u0103X\u010f7\n5\u0103Y\u010f100**0*****0\n*00*0*****\n**0*******\n*******0**\n*11****0*0\n****0**000"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c618f-934e-11ee-874e-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 9, "chroma:document": "**0*******\n*******0**\n*11****0*0\n****0**000\n****1**00*\n****1***0*\n****11**00\n********0*\n12\u0103X\u010f18\n2\u0103Y\u010f8******1***\n*11*1*1***\n***111****\n*****11***\n*000**1***\n000**1****\n0000*1*0**\n0*00*1**0*\n0**0***0**\n0000****0*\n7\u0103X\u010f11\n12\u0103Y\u010f17\n0: L L 0: L R 9: L L 9: L R 3: U R\n*000**1***\n**********\n**0******0\n*00****110\n*********0\n*0*0***1*0\n******11**\n***0******\n**000**1*1\n0*0****11*\n0\u0103X\u010f5\n10\u0103Y\u010f16*******1**\n******1***\n******1***\n*****1**1*\n****1*1***\n****11****\n*1*11*1***\n1**11*****\n*11*11****\n*1*1******"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6190-934e-11ee-a868-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 9, "chroma:document": "*1*11*1***\n1**11*****\n*11*11****\n*1*1******\n4\u0103X\u010f18\n13\u0103Y\u010f180000000***\n00000001**\n0000000110\n0000000*1*\n000000*0*1\n00000000**\n0000000000\n0000*00000\n0000000000\n0000000000\n0\u0103X\u010f3\n8\u0103Y\u010f14******00**\n*****000*0\n**11*0000*\n**11*00000\n1*11000*00\n11**0000*0\n111****00*\n1**0000000\n1**00*00**\n1*0**00*00\n12\u0103X\u010f16\n9\u0103Y\u010f15**0000*000\n00000*0000\n***0000000\n*11**00000\n*1*1**0000\n0**1*00*00\n0*1**0***0\n**1*0000*0\n*1***0*000\n***0000000\n12\u0103X\u010f18\n0\u0103Y\u010f3"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6191-934e-11ee-a1e5-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 9, "chroma:document": "**1*0000*0\n*1***0*000\n***0000000\n12\u0103X\u010f18\n0\u0103Y\u010f3\nTable 2: Example 10 \u02c610 bit patterns produced by CTM for MNIST, including valid convolution positions. Here \u201c0:\nUL\" means \u201cupper left\" of the image for digit \u201c0\". We can see clearly that \u201c0: UL\", \u201c0: UR\", \u201c0: LL\" and \u201c0: LR\"\njointly construct the shape \u201c0\u201d. The clauses for the other digits behave similarly, and we thus just illustrate selected\npatch positions for each digit.\n#Clauses per class 250 500 1000 2000 4000 8000"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6192-934e-11ee-8364-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 9, "chroma:document": "#Clauses per class 250 500 1000 2000 4000 8000\nMNIST accuracy (%) 98.82 98.98 99.14 99.22 99.28 99.33\nMNIST execution time (s) 15.6 15.8 18.9 20.4 32.4 39.0\nK-MNIST accuracy (%) 92.75 93.86 94.89 95.40 95.85 96.08\nK-MNIST execution time (s) 15.5 17.2 19.7 21.1 33.5 40.5\nF-MNIST accuracy (%) 88.25 88.79 89.42 89.89 90.65 91.18\nF-MNIST execution time (s) 16.9 17.2 17.8 25.0 27.8 52.2\nTable 3: CTM mean test accuracy and execution time per epoch for an increasing number of clauses."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6193-934e-11ee-ab36-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 9, "chroma:document": "The CTM performs rather robustly, providing tight 95% con\ufb01dence intervals for the mean performance. As seen in\nTable 4, we have also included results for selected popular algorithms, as points of reference. Note that the CTM is\nan interpretable approach that does not employ multiple layers at this stage. Therefore, we believe a fair comparison\nshould target traditional/simple CNNs. Results listed in italic are reported in the corresponding papers. Results for"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6194-934e-11ee-ac46-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 9, "chroma:document": "BinaryConnect and FPGA-accelerated BNNs on K-MNIST and Fashion-MNIST were not available, so are not reported.\nNotice that the CTM outperforms the binary CNNs for all the datasets, as well several simple baseline con\ufb01gurations,\nincluding 4-layer CNNs, Random Forests, Gradient Boosting, SVMs, and a 4-nearest neighbour classi\ufb01er. Further\nobserve that both the TM and the CTM obtain higher accuracy than Logistic Circuits [ 22] with binary data. Thus,"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6195-934e-11ee-a959-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 9, "chroma:document": "in our experiments, the TM learning paradigm outperforms the probabilistic circuits paradigm [ 22,30] at extracting\ninformation from binary representations. However, only the CTM performs competitively with Logistic Circuits\nwhen the Logistic Circuits are given the advantage of real-valued inputs. Note that the CTM supports using multiple\nbits to encode the color of each pixel, however, in the present paper, we only investigate single bit representations."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6196-934e-11ee-bfd9-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 9, "chroma:document": "Finally, the CTM is outperformed by the more advanced deep learning network architectures PreActResNet-18 and\nResNET18+VGG.\nFigure 5 depicts test accuracy for the CTM on MNIST, K-MNIST, and F-MNIST, epoch-by-epoch. As seen, test\naccuracy climbs quickly in the \ufb01rst epochs, e.g., passing 99% already in epoch 8for MNIST. MNIST test accuracy\n10"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6197-934e-11ee-9ea7-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 10, "chroma:document": "APREPRINT - DECEMBER 30, 2019\nModel 2D N-XOR MNIST K-MNIST F-MNIST\n4-Nearest Neighbour [5, 41] 61.62 97.14 91.56 85.40\nSVM [5] 94.63 98.57 92.82 89.7\nRandom Forest [22] 70.73 97.3 - 81.6\nGradient Boosting Classi\ufb01er [41] 87.15 96.9 - 88.0\nSimple CNN [5, 22] 91.05 99.06 95.12 90.7\nBinaryConnect [6] - 98.99 - -\nFPGA-accelerated BNN [20] - 98.70 - -\nLogistic Circuit (binary) [22] - 97.4 - 87.6\nLogistic Circuit (real-valued) [22] - 99.4 - 91.3\nPreActResNet-18 [5] - 99.56 97.82 92.00"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6198-934e-11ee-bcfc-ac198e74a6f7
encoding: FLOAT32
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{"source": "source_documents\\1905.09688.pdf", "page": 10, "chroma:document": "PreActResNet-18 [5] - 99.56 97.82 92.00\nResNet18 + VGG Ensemble [5] - 99.60 98.90 -\nTM 99.12 98.57 92.03 90.09\nCTM (Mean) 99.99\u02d80.099.33\u02d80.096.08\u02d80.01 91.18\u02d80.01\nCTM (95 %ile) 100.0 99.38 96.25 91.39\nCTM (Peak) 100.0 99.40 96.31 91.50\nTable 4: Empirical results - test accuracy in percent.\nModel MNIST F-MNIST\nLogistic Circuit (binary) [22] 1 072 kB 2 456 kB\nLogistic Circuit (real-valued) [22] 728kB 1 768 kB\nCNN w/3 conv. layers [22] 8 784 kB 8 784 kB\nResNet [22] 19 352 kB 19 352 kB"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c6199-934e-11ee-b520-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 10, "chroma:document": "ResNet [22] 19 352 kB 19 352 kB\nTM w/ 4 000 class clauses 7 657 kB 7 657 kB\nCTM w/ 250class clauses 127kB 127kB\nCTM w/ 8 000 class clauses 2 109 kB 2 109 kB\nTable 5: Model size in kilobytes (kB), assuming 32-bit real-valued weights.\npeaks at 99.4% after 234epochs, while K-MNIST peaks at 96.31% after 169epochs. For F-MNIST, test accuracy\nsurpasses 90.0% in epoch 9and peaks at 91.5% in epoch 170."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c619a-934e-11ee-803e-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 10, "chroma:document": "In Table 5, the size of the trained models are listed for MNIST and F-MNIST. Size is measured in kilobytes of memory\nused. The memory usage of CTM is similar to Logistic Circuits, which both use signi\ufb01cantly less memory than the\nneural network architectures. A potential advantage of CTM is the ability to trade off accuracy against computation\ntime and memory usage, by reducing the number of clauses employed. E.g., a CTM with 250 clauses per class reduces"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c619b-934e-11ee-be27-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 10, "chroma:document": "memory usage by more than an order of magnitude at a relatively small loss in test accuracy (cf. Table 3).\nTable 2 contains example patterns produced by CTM for MNIST (with one bit per pixel using 8000 clauses). The \u201c*\"\nsymbol can either take the value \u201c0\" or \u201c1\". The remaining bit values require strict matching. The examples have been\nselected to illustrate how several patterns together form complete numbers. As seen, the patterns are relatively easy to"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c619c-934e-11ee-90cf-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 10, "chroma:document": "interpret for humans compared to, e.g., a neural network. They are also ef\ufb01cient to evaluate for computers, involving\nonly logical operators, followed by summation.\n5 Conclusion and Further Work\nThis paper introduced the Convolutional Tsetlin Machine (CTM), leveraging the learning mechanism of the Tsetlin\nMachine (TM). Whereas the TM categorizes images by employing each clause once per X\u02c6Yinput, the CTM"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c619d-934e-11ee-a684-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 10, "chroma:document": "uses each clause as a W\u02c6Wconvolution \ufb01lter. The \ufb01lters learned by the CTM are interpretable, being formulated\nusing propositional formulae. To make the clauses location-aware, each patch is further enhanced with its coordinates\nwithin the image. Location awareness may prove useful in applications where both patterns and their location are\ndistinguishing features. By randomly selecting which patch to learn from, the standard Type I and Type II feedback"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c619e-934e-11ee-8393-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 10, "chroma:document": "of the classic TM can be employed directly. In this manner, the CTM obtains results on MNIST, Kuzushiji-MNIST,\nFashion-MNIST, and the 2D Noisy XOR Problem that compare favorably with simple 4-layer CNNs, Logistic Circuits,\nas well as two binary neural network architectures.\n11"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c619f-934e-11ee-9483-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 11, "chroma:document": "APREPRINT - DECEMBER 30, 2019\n0 20 40 60 80 100 120 140 160 180 200 220 240767880828486889092949698100\nEpochAccuracy (%)\nMNIST\nK-MNIST\nF-MNIST\nFigure 5: Single-run test accuracy per epoch for CTM on MNIST, K-MNIST, and F-MNIST.\nIn our further work, we intend to investigate more advanced binary encoding schemes, to go beyond grey-scale images\n(e.g., addressing CIFAR-10 and ImageNet). We further intend to develop schemes for deeper CTMs, with the \ufb01rst step"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61a0-934e-11ee-a9ff-ac198e74a6f7
encoding: FLOAT32
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{"source": "source_documents\\1905.09688.pdf", "page": 11, "chroma:document": "being a two-layer CTM, to introduce more compact and expressive patterns with nested propositional formulae.\nReferences\n[1]K. D. Abeyrathna, O.-C. Granmo, X. Zhang, L. Jiao, and M. Goodwin. The Regression Tsetlin Machine - A Novel\nApproach to Interpretable Non-Linear Regression. Philosophical Transactions of the Royal Society A , 378, 2019.\n[2]R. Agrawal, T. Imieli \u00b4nski, and A. Swami. Mining association rules between sets of items in large databases.\nSIGMOD Rec. , 22(2):207\u2013216, 1993."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61a1-934e-11ee-b769-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 11, "chroma:document": "SIGMOD Rec. , 22(2):207\u2013216, 1993.\n[3]G. T. Berge, O.-C. Granmo, T. O. Tveit, M. Goodwin, L. Jiao, and B. V . Matheussen. Using the Tsetlin Machine\nto Learn Human-Interpretable Rules for High-Accuracy Text Categorization with Medical Applications. IEEE\nAccess , 7:115134\u2013115146, 2019.\n[4]N. Bouhmala and O.-C. Granmo. Stochastic Learning for SAT-Encoded Graph Coloring Problems. International\nJournal of Applied Metaheuristic Computing , 1(3):1\u201319, 2010."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61a2-934e-11ee-bc64-ac198e74a6f7
encoding: FLOAT32
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{"source": "source_documents\\1905.09688.pdf", "page": 11, "chroma:document": "[5]T. Clanuwat, M. Bober-Irizar, A. Kitamoto, A. Lamb, K. Yamamoto, and D. Ha. Deep Learning for Classical\nJapanese Literature. arXiv:1812.01718 , Dec 2018.\n[6]M. Courbariaux, Y . Bengio, and J.-P. David. Binaryconnect: Training deep neural networks with binary weights\nduring propagations. In Advances in neural information processing systems , pages 3123\u20133131, 2015.\n[7]S. Darabi, M. Belbahri, M. Courbariaux, and V . Partovi Nia. BNN+: Improved Binary Network Training."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61a3-934e-11ee-95ba-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 11, "chroma:document": "arXiv:1812.11800 , Dec 2018.\n[8]K. Darshana Abeyrathna, O.-C. Granmo, X. Zhang, and M. Goodwin. A Scheme for Continuous Input to the\nTsetlin Machine with Applications to Forecasting Disease Outbreaks. arXiv:1905.04199 , May 2019.\n[9]V . Feldman. Hardness of Approximate Two-Level Logic Minimization and PAC Learning with Membership\nQueries. Journal of Computer and System Sciences , 75(1):13\u201326, 2009."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61a4-934e-11ee-af76-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 11, "chroma:document": "[10] M. Ghavipour and M. R. Meybodi. A streaming sampling algorithm for social activity networks using \ufb01xed\nstructure learning automata. Applied Intelligence , 2018.\n12"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61a5-934e-11ee-8cdd-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 12, "chroma:document": "APREPRINT - DECEMBER 30, 2019\n[11] J. Gittins. Bandit processes and dynamic allocation indices. Journal of the Royal Statistical Society, Series B\n(Methodological) , 41(2):148\u2013177, 1979.\n[12] O.-C. Granmo. The Tsetlin Machine - A Game Theoretic Bandit Driven Approach to Optimal Pattern Recognition\nwith Propositional Logic. arXiv:1804.01508 , Apr 2018.\n[13] O.-C. Granmo and N. Bouhmala. Solving the Satis\ufb01ability Problem Using Finite Learning Automata. International"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61a6-934e-11ee-b419-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 12, "chroma:document": "Journal of Computer Science and Applications , 4(3):15\u201329, 2007.\n[14] O. C. Granmo and B. J. Oommen. Optimal sampling for estimation with constrained resources using a learning\nautomaton-based solution for the nonlinear fractional knapsack problem. Applied Intelligence , 33(1):3\u201320, 2010.\n[15] O.-C. Granmo and B. J. Oommen. Solving Stochastic Nonlinear Resource Allocation Problems Using a Hierarchy\nof Twofold Resource Allocation Automata. IEEE Transactions on Computers , 59(4):545\u2013560, 2010."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61a7-934e-11ee-b833-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 12, "chroma:document": "[16] O.-C. Granmo, B. J. Oommen, S. A. Myrer, and M. G. Olsen. Learning Automata-based Solutions to the Nonlinear\nFractional Knapsack Problem with Applications to Optimal Resource Allocation. IEEE Transactions on Systems,\nMan, and Cybernetics, Part B , 37(1):166\u2013175, 2007.\n[17] V . Haugland, M. Kj\u00f8lleberg, S.-E. Larsen, and O.-C. Granmo. A two-armed bandit collective for hierarchical ex-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61a8-934e-11ee-9999-ac198e74a6f7
encoding: FLOAT32
metadata:
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id: 152c61a9-934e-11ee-83dc-ac198e74a6f7
encoding: FLOAT32
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topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61aa-934e-11ee-9c98-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.09688.pdf", "page": 12, "chroma:document": "Proceedings of the IEEE , 86(11):2278\u20132324, 1998.\n[22] Y . Liang and G. Van den Broeck. Learning logistic circuits. In Proceedings of the 33rd Conference on Arti\ufb01cial\nIntelligence (AAAI) , jan 2019.\n[23] R. Liu, J. Lehman, P. Molino, F. P. Such, E. Frank, A. Sergeev, and J. Yosinski. An intriguing failing of\nconvolutional neural networks and the coordconv solution. In Proceedings of the 32Nd International Conference\non Neural Information Processing Systems , NIPS\u201918, pages 9628\u20139639, 2018."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61ab-934e-11ee-a074-ac198e74a6f7
encoding: FLOAT32
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topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61ac-934e-11ee-8885-ac198e74a6f7
encoding: FLOAT32
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id: 152c61ad-934e-11ee-8c04-ac198e74a6f7
encoding: FLOAT32
metadata:
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id: 152c61ae-934e-11ee-ab4b-ac198e74a6f7
encoding: FLOAT32
metadata:
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topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61af-934e-11ee-8b3e-ac198e74a6f7
encoding: FLOAT32
metadata:
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topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61b0-934e-11ee-bf83-ac198e74a6f7
encoding: FLOAT32
metadata:
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topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61b1-934e-11ee-9a11-ac198e74a6f7
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topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61b2-934e-11ee-913f-ac198e74a6f7
encoding: FLOAT32
metadata:
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created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61b3-934e-11ee-b255-ac198e74a6f7
encoding: FLOAT32
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created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61b4-934e-11ee-8807-ac198e74a6f7
encoding: FLOAT32
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created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61b5-934e-11ee-b975-ac198e74a6f7
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{"source": "source_documents\\1905.09688.pdf", "page": 13, "chroma:document": "computer vision , pages 818\u2013833. Springer, 2014.\n[46] J. Zhang, Y . Wang, C. Wang, and M. Zhou. Symmetrical Hierarchical Stochastic Searching on the Line in\nInformative and Deceptive Environments. IEEE Transactions on Cybernetics , 47(3):626 \u2013 635, Jul 2016.\n14"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61b6-934e-11ee-b5bf-ac198e74a6f7
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{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 0, "chroma:document": "Proceedings of the 13th Conference on Language Resources and Evaluation (LREC 2022) , pages 3761\u20133770\nMarseille, 20-25 June 2022\n\u00a9 European Language Resources Association (ELRA), licensed under CC-BY-NC-4.0\n3761ConvTextTM: An Explainable Convolutional Tsetlin Machine Framework\nfor Text Classification\nBimal Bhattarai, Ole-Christoffer Granmo, Lei Jiao\nUniversity of Agder\nNorway\n{bimal.bhattarai, ole.granmo, lei.jiao }@uia.no\nAbstract"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61b7-934e-11ee-a9ce-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 0, "chroma:document": "Abstract\nRecent advancements in natural language processing (NLP) have reshaped the industry, with powerful language models such\nas GPT-3 achieving superhuman performance on various tasks. However, the increasing complexity of such models turns\nthem into \u201cblack boxes\u201d, creating uncertainty about their internal operation and decision-making. Tsetlin Machine (TM)\nemploys human-interpretable conjunctive clauses in propositional logic to solve complex pattern recognition problems and has"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61b8-934e-11ee-9b21-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 0, "chroma:document": "demonstrated competitive performance in various NLP tasks. In this paper, we propose ConvTextTM, a novel convolutional\nTM architecture for text classification. While legacy TM solutions treat the whole text as a corpus-specific set-of-words\n(SOW), ConvTextTM breaks down the text into a sequence of text fragments. The convolution over the text fragments\nopens up for local position-aware analysis. Further, ConvTextTM eliminates the dependency on a corpus-specific vocabulary."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61b9-934e-11ee-a66e-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 0, "chroma:document": "Instead, it employs a generic SOW formed by the tokenization scheme of the Bidirectional Encoder Representations from\nTransformers (BERT) (Devlin et al., 2019a). The convolution binds together the tokens, allowing ConvTextTM to address\nthe out-of-vocabulary problem as well as spelling errors. We investigate the local explainability of our proposed method\nusing clause-based features. Extensive experiments are conducted on seven datasets, to demonstrate that the accuracy of"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61ba-934e-11ee-af85-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 0, "chroma:document": "ConvTextTM is either superior or comparable to state-of-the-art baselines.\nKeywords: Set-Of-Word (SOW), Convolutional Tsetlin Machine (CTM), Explainable, Human-Interpretable, Language\nModel, Text Classification, Tsetlin Machine (TM).\n1. Introduction\nRecent advances in Artificial Intelligence (AI) have\nbrought increasingly accurate learning algorithms and\npowerful computation platforms. However, the ac-\ncuracy gains come with escalating computation costs,"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61bb-934e-11ee-8abf-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 0, "chroma:document": "and models are getting too complicated for humans\nto comprehend. Prohibitive computation costs hinder\nthe training of state-of-the-art models, while a lack of\nmodel transparency reduces trust. When end-users can-\nnot understand model decisions and researchers report\non how susceptible the models are to data bias, confi-\ndence in machine learning models declines.\nMounting computation costs are problematic because\nof the long-term environmental impact. The obscurity"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61bc-934e-11ee-8b26-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 0, "chroma:document": "of AI-driven decisions, however, raises immediate eth-\nical concerns. Indeed, many decision errors can be fa-\ntal in high-risk application domains, including bank-\ning (Le and Viviani, 2018), medicine (Esteva et al.,\n2019), bioinformatics (Freitas et al., 2008), and self-\ndriving cars (Badue et al., 2020). Transparency is re-\nquired to ensure fair and safe decisions. AI model inter-\npretability is thus a research area of increasing interest,\ncrucial for further advancement of the AI field."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61bd-934e-11ee-bd84-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 0, "chroma:document": "crucial for further advancement of the AI field.\nThe field of Natural Language Processing (NLP) man-\nifests all of the above concerns. With the develop-\nment of powerful language models such as Transform-\ners (Vaswani et al., 2017), the prediction accuracy al-\nready peaks for several NLP tasks, such as sentiment\nanalysis and text classification. However, model com-\nplexity is immense, and only approximate interpreta-tion techniques are available. On the other side of"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61be-934e-11ee-96f9-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 0, "chroma:document": "the spectrum, traditional models like Linear Regres-\nsion, Logistic Regression, and Decision Trees can be\nhighly interpretable but are far from achieving state-of-\nart accuracy. As such, they demonstrate the challeng-\ning accuracy-interpretability trade-off researchers must\nresolve.\nThe Tsetlin Machine (TM) (Granmo, 2018) is a rule-\nbased pattern recognition approach that aims to bridge\nthe gap between accuracy and interpretability. It uses\na majority vote among multiple rules for decision-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61bf-934e-11ee-90ec-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 0, "chroma:document": "making. As such, TMs unify summation-based (cf.\nlogistic regression) and rule-based (cf. decision trees)\napproaches. TMs further employ three powerful strate-\ngies for learning patterns: (i) Frequent pattern mining\nwith so-called Type I Feedback ; (ii) Pattern discrimi-\nnation with so-called Type II Feedback ; and (iii) Data\ndissection utilizing a vote margin .\nRecent papers report TM accuracy results that are com-\nparable to or surpass the accuracy of contemporary"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61c0-934e-11ee-8650-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 0, "chroma:document": "interpretable methods. These results cover sentiment\nanalysis (Yadav et al., 2021a), novelty detection (Bhat-\ntarai et al., 2021a)(Bhattarai et al., 2022), fake news\ndetection (Bhattarai et al., 2021b), and semantic re-\nlation analysis (Saha et al., 2020). Indeed, in some\ncases, the TM outperforms state-of-the-art deep learn-\ning baselines (Bhattarai et al., 2021b). Based on propo-\nsitional logic and bitwise operations for learning, TMs\noffer an alternative approach to deep learning models."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61c1-934e-11ee-bc77-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 0, "chroma:document": "The advantages are interpretable learning, minimalist"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61c2-934e-11ee-b36b-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 1, "chroma:document": "3762complexity, and comparable or better prediction accu-\nracy in an increasing number of cases.\nTMs achieve human-level interpretability through\nAND rules with negation that uses set-of-words (SOW)\nbased features. In SOW, each word is one-hot encoded\nand then ORed into a document bit vector. One can also\nview each AND-rule as a conjunctive clause in propo-\nsitional logic. A propositional variable represents each\nword. As reported by Blakely et al., clauses learned"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61c3-934e-11ee-b2c6-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 1, "chroma:document": "by a TM are highly discriminative, while being easy to\ninterpret (Blakely and Granmo, 2020). Because each\nclause is self-contained, one can interpret the TM glob-\nally simply by inspecting each clause.\nWith increasing vocabulary size, however, the SOW\nrepresentation becomes increasingly sparse. The\nsparseness affects both the preprocessing time, train-\ning time, and accuracy. Yadav et al. were able\nto reduce sparsity by boosting the SOW with GloVe\nsynonyms (Yadav et al., 2021b). However, reduc-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61c4-934e-11ee-8f24-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 1, "chroma:document": "synonyms (Yadav et al., 2021b). However, reduc-\ning pre-trained word embeddings to synonyms re-\nmoves information from the embeddings. A main\nproblem is that pre-trained word embeddings such as\nword2vec (Mikolov et al., 2013), GloVe (Pennington\net al., 2014), and FastText (Bojanowski et al., 2017),\nare real-valued. TMs, however, require binary input.\nHow to produce binary embeddings that are suitable\nfor TMs is an open problem. Additionally, using non-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61c5-934e-11ee-a594-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 1, "chroma:document": "interpretable word embeddings would impact TM in-\nterpretability.\nContributions: In this paper, we propose Conv-\nTextTM, a novel convolutional TM (CTM) (Granmo\net al., 2019) architecture for text classification. While\nlegacy TM solutions treat the whole text as a corpus-\nspecific SOW, ConvTextTM breaks down the text into\na sequence of text fragments. The convolution over\nthe text fragments opens up for local position-aware\nanalysis. Further, ConvTextTM eliminates the depen-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61c6-934e-11ee-be7f-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 1, "chroma:document": "dency on a corpus-specific vocabulary. Instead, it\nemploys a generic SOW formed by the tokenization\nscheme of the Bidirectional Encoder Representations\nfrom Transformers (BERT). The convolution binds to-\ngether the tokens, allowing ConvTextTM to address the\nout-of-vocabulary problem as well as spelling errors.\nWe investigate the local explainability of our proposed\nmethod using clause-based features. To our knowledge,\nthis is the first time CTM has been used in a text-based\napplication."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61c7-934e-11ee-bcc8-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 1, "chroma:document": "application.\n2. Related Work\nHuman interpretable machine learning models have a\nlong history, with Breiman\u2019s research on decision trees\nand random forests being an early example (Breiman,\n2001)(Li et al., 1984). Since then, several approaches\nfor explaining the prediction of models have appeared.\nHowever, only a few studies focus on model inter-\npretability (Lipton, 2018)(Lage et al., 2019). Some of\nthese address local interpretability, i.e., they study how"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61c8-934e-11ee-bbe7-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 1, "chroma:document": "to understand single outputs (Ribeiro et al., 2016). Oth-ers try to interpret the entire model, providing global\ninterpretability (Ustun and Rudin, 2016).\nGilpin et al. define interpretability of deep learning in\nterms of three categories (Gilpin et al., 2018): (1) mod-\nels that map an input to output, focusing on connec-\ntivity, (2) models that explain latent variables for an\nexplanation, and (3) models that explain themselves.\nBased on these categories, Agarwal et al. (Agarwal et"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61c9-934e-11ee-a7b9-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 1, "chroma:document": "al., 2020) proposed a deep learning-based interpretable\nmodel inspired by the family of Neural Additive Mod-\nels (NAMs). However, their model was not able to\nsurpass regular deep learning models accuracy-wise.\nAs recent advances have demonstrated, interpretable\nrule-based approaches may provide a better trade-off\nbetween interpretability and accuracy. Numerous ap-\nproaches, such as frequent itemset mining for associ-\nation rule learning (Agrawal et al., 1993), and Prob-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61ca-934e-11ee-bba8-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 1, "chroma:document": "ably Approximately Correct (PAC) (Feldman, 2009)\nhave provided insights into how data patterns can be\nrepresented in Disjunctive Normal Form (DNF) using\npropositional formula. These techniques, however, are\ngenerally not scalable and robust to noise, and cannot\ncompete with deep learning models.\nTMs are a recent approach to rule-based machine learn-\ning that extracts human-interpretable patterns from data\nusing propositional reasoning. Berge et al. (Berge"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61cb-934e-11ee-9d54-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 1, "chroma:document": "et al., 2019) employed TM for categorizing medical\nrecords, with an emphasis on the interpretability of the\nrules generated by TM. They demonstrated that TMs\nare interpretable, yet provide competitive accuracy in\ncomparison with other machine learning techniques,\nincluding Convolutional Neural Networks (CNN) and\nLong Short-Term Memory (LSTM) Neural Networks.\nOther researchers report similar findings, for example\nwithin regression (Darshana Abeyrathna et al., 2020),"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61cc-934e-11ee-aa0c-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 1, "chroma:document": "natural language understanding (Yadav et al., 2021a;\nBhattarai et al., 2021b; Saha et al., 2020; Yadav et al.,\n2021c), and speech understanding (Lei et al., 2021).\nAdditionally, the Convolutional TM performs com-\npetitively on MNIST, Fashion-MNIST, and Kuzushiji-\nMNIST, compared with several other contemporary\nmethods including CNNs (Granmo et al., 2019).\nMethods for global and local model interpretation are\ngaining increasing attention in the NLP research com-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61cd-934e-11ee-aee1-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 1, "chroma:document": "munity. (Jacovi et al., 2018) examined how CNN net-\nworks process and categorize text. They demonstrate,\nby employing various alternative activation patterns,\nhow filters may capture several semantic classes of\nn-grams. They compute word-level scores in two\nways: locally and globally. Both techniques, however,\nneed a specific input and employ leave-one-out evalu-\nations. The authors of (Xiong et al., 2018) conclude\nthat Layer-wise Relevance Propagation (LRP) extracts"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61ce-934e-11ee-b6e5-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 1, "chroma:document": "more relevant features and argue that a single word\ndoes not adequately explain any given outcome. For\ninstance, a single word can be a component of a signif-\nicant n-gram. However, their method requires knowl-\nedge of the model parameters, which cannot be consid-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c61cf-934e-11ee-9f4e-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 2, "chroma:document": "3763\nSentence\nwindow window \nwindow BER T Vocabulary\nList\nwindow \nwindow SOW features Figure 1: Preprocessing text for Convolutional TM.\nered an explanation for the black-box nature of the neu-\nral network. (Chen and Ji, 2020) use masks over word\nembedding named variational word mask (VMASK)\nand provide an interpretable architecture for text clas-\nsification to learn task-specific important words. They\ndemonstrate the model\u2019s interpretability by compar-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c840c-934e-11ee-8393-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 2, "chroma:document": "ing it to LIME and SampleShapley (Strumbelj and\nKononenko, 2010). Similarly, (Nguyen, 2018) pre-\nsented a robust technique for text categorization that\nrelies on local explanation. They demonstrate through\ncrowdsourcing experiments that automatic evaluation\nmetrics based on word elimination, such as LIME, are\nreasonably consistent with human evaluations.\nDespite these advances in NLP interpretability, strong\ntransformer-based language models such as BERT (De-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c840d-934e-11ee-b8f1-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 2, "chroma:document": "vlin et al., 2019a) and XLNet (Yang et al., 2019a) out-\nperform alternative approaches that rely on pre-trained\nembeddings. In summary, previous work report that\nas the complexity of the model increases, the interpre-\ntation becomes more ambiguous (Lipton, 2018). For\nexample, it is possible that the small neural network\nmodels may be more interpretable than large decision\ntrees. One can argue that some models employ an at-\ntention mechanism that can be interpreted based on the"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c840e-934e-11ee-8919-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 2, "chroma:document": "weighting of the input features. Still, other researchers\nreport that attention weights do not provide a meaning-\nful explanation (Bai et al., 2020)(Serrano and Smith,\n2019). To overcome these shortcomings, the interest\nin rule-based interpretable techniques is rising, with\nTM being a promising approach. However, as dis-\ncussed, the SOW sparsity introduced by large vocab-\nularies is significantly limiting TMs. Yadav et al. were\nable to partially mitigate increasing sparsity by boost-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c840f-934e-11ee-8381-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 2, "chroma:document": "ing TM SOWs with GloVe synonyms, significantly in-\ncreasing accuracy (Yadav et al., 2021b). The work we\npresent here, however, attempts to address this issue by\nemploying a fixed-sized pre-trained BERT embedding\nvocabulary. Accordingly, we establish a general TM\nSOW of manageable size.\n3. ConvTextTM Architecture\n3.1. Tsetlin Machine Basics\nA basic TM consists of two-action Tsetlin Au-\ntomata (TAs) with 2Nstates. Each TA performs anaction associated with its current state, which is either"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8410-934e-11ee-b5f2-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 2, "chroma:document": "an \u201cInclude\u201d action (in State 1toN) or an \u201cExclude\u201d\naction ( N+ 1to2N). The state updates are based on\niterative feedback, i.e., rewards and penalties. Rewards\nreinforce the action performed by the TA, while penal-\nties suppress the action. In this way, the TA progres-\nsively shifts toward the optimal action (Tsetlin, 1961).\nTo address the pattern recognition problem, the collec-\ntion of TAs construct conjunctive clauses in proposi-\ntional logic. The input to a TM consists of proposi-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8411-934e-11ee-9028-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 2, "chroma:document": "tional values, i.e., the input is Boolean. A TM uses\nboth the non-negated and negated version of each input\nwhen forming the clauses, each of which is handled by\nan individual TA. Accordingly, each TM clause cap-\ntures a specific sub-pattern. The output, in turn, is de-\ntermined based on votes for the available classes. It\nis the class with the largest number of matching sub-\npatterns that wins the round of voting and is output by\nthe TM.\nThe TM takes a Boolean input vector, X="}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8412-934e-11ee-9556-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 2, "chroma:document": "the TM.\nThe TM takes a Boolean input vector, X=\n(x1, . . . , x o),xk\u2208 {0,1},k\u2208 {1, . . . , o}to be clas-\nsified into one of the Clclasses, Y= (y1, . . . , y Cl),\nwhere Clis total number of classes. From the in-\nput vector, we obtain 2oliterals L= (l1, l2, . . . , l 2o).\nThe literals consist of the inputs xkand their negated\ncounterparts \u00afxk=\u00acxk= 1\u2212xk, i.e., L=\n(x1, . . . , x o,\u00acx1, . . . ,\u00acxo). The TM patterns are\nformed using mconjunctive clauses. Subscript j="}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8413-934e-11ee-9965-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 2, "chroma:document": "formed using mconjunctive clauses. Subscript j=\n1, . . . , m/ 2denotes the clause index, while the super-\nscript describes the polarity of a clause. In brief, half\nof the clauses are assigned positive polarity, i.e., C+\nj,\nand the other half are assigned negative polarity, i.e.,\nC\u2212\nj. A clause C\u03be\nj,\u03be\u2208 {\u2212 ,+},is formed by ANDing\na subset of the literals, i.e., the ones that are \u201cincluded\u201d\nby the corresponding TAs, L\u03be\nj\u2286L, as:\nC\u03be\nj(X) =^\nlk\u2208L\u03be\njlk=Y\nlk\u2208L\u03be\njlk. (1)"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8414-934e-11ee-8443-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 2, "chroma:document": "j\u2286L, as:\nC\u03be\nj(X) =^\nlk\u2208L\u03be\njlk=Y\nlk\u2208L\u03be\njlk. (1)\nThe final classification output is obtained by subtract-\ning the negative votes from the positive votes, and then\nthresholding the resulting sum via the unit step function\nu:\n\u02c6y=u\uf8eb\n\uf8edm/2X\nj=1C+\nj(X)\u2212m/2X\nj=1C\u2212\nj(X)\uf8f6\n\uf8f8. (2)\nThe TM learning process carefully guides the TAs to\nmake optimal decisions. The reinforcement is chan-\nneled directly to the conjunctive clauses. Each clause,\nin turn, forwards the feedback to its individual TAs ran-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8415-934e-11ee-b7fd-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 2, "chroma:document": "domly. To this end, the TM employs Type I and Type\nII feedback. These feedback types control how rewards\nand penalties are distributed to the TAs. The distribu-\ntion depends on six factors: (1) target output ( y= 0or\ny= 1), (2) clause polarity, (3) clause output ( Cj= 0or\n1), (4) literals value ( x= 1, or\u00acx= 1), (5) vote sum,\nand (6) the current state of the TA. Type I feedback is\nintended to generate frequent patterns, eliminate false"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8416-934e-11ee-9051-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 3, "chroma:document": "3764\nwindow \nwindow Sentence\nArgmaxFeedbackPreprocessed text\nDivide into\nwindowsFigure 2: ConvTextTM Architecture.\nnegatives, and make clauses evaluate to 1. Positive po-\nlarity clauses receive Type I input when y= 1, while\nnegative polarity clauses receive it when y= 0. Type II\nfeedback, on the other hand, improves pattern discrim-\nination, suppresses false positives, and spurs clauses to\nevaluate to 0. Type II feedback is given to positive\npolarity clauses when y= 0 and to negative polarity"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8417-934e-11ee-8fc1-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 3, "chroma:document": "clauses when y= 1.\nThe feedback is further regulated by the sum of votes\nvfor each output class. That is, the voting sum is\ncompared against a voting margin T, which is em-\nployed to guide distinct clauses to learn different sub-\npatterns. The details of the learning process can be\nfound in (Granmo, 2018).\n3.2. Convolutional Tsetlin Machine and\nPre-processing for Text\nThe CTM is a variation of TM developed for image\nclassification. The CTM takes an image X= (xk)\u2208"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8418-934e-11ee-8fd3-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 3, "chroma:document": "classification. The CTM takes an image X= (xk)\u2208\n{0,1}A\u00d7B\u00d7Cas input. Here, A\u00d7B specifies the image\ndimension and Cdenotes the depth of the binary layers.\nBecause CTM is designed for fixed-sized images, we\nmust preprocess our text data prior to feeding it to the\nCTM. To begin with, each input instance is segmented\ninto a number of equal-sized windows. To make the\nwindow size equal, we append \u201cPAD\u201d tokens at the\nend of the instances. Because the average lengths of"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8419-934e-11ee-a851-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 3, "chroma:document": "instances in different datasets can be quite different,\nthe number of windows generated for different datasets\nmay vary.\nTo integrate the information from BERT, we create a\ndictionary that indexes all of the tokens in the BERT\nvocabulary. The words in each window are then one-\nhot encoded using their indices in the dictionary and\nthe window number in which they appear. That is, each\nword is denoted by a 2DSOW representation. For ex-\nample, suppose a word present in the second window of"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c841a-934e-11ee-a258-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 3, "chroma:document": "the first input instance is assigned the 500thindex in the\ndictionary of BERT. Then, position (2, 500) of the input\nis set to 1. After preprocessing, each input text is repre-\nsented as a Boolean 2DSOW. Now, the complete input\ndataset can be represented by (xk)\u2208 {0,1}A\u00d7B\u00d7C.\nHereAdenotes the total number of input instances, B\ndenotes the total number of windows, and Crepresents\nthe total number of tokens in the BERT vocabulary list.\nFigure 1 depicts the full preprocessing pipeline."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c841b-934e-11ee-abc7-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 3, "chroma:document": "Figure 1 depicts the full preprocessing pipeline.\nThe CTM for text uses clauses with spatial dimension\n1\u00d71as filters to perform convolution over the prepro-Dataset name Train set size Test set size Label\nPolitiFact 716 238 2\nGossipCop 15,175 5,058 2\nBBCSports 517 220 5\nTwitter 2,176 932 3\nQuery 17,500 3,850 2\nR8 5,478 2,189 8\nWOS-5736 4,588 1,148 11\nTable 1: Dataset Statistics.\ncessed input text. The filter evaluates P=B\u22121\nq+ 1\npatches of dimensionality C, with qbeing the step"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c841c-934e-11ee-bc21-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 3, "chroma:document": "patches of dimensionality C, with qbeing the step\nsize of the convolution. Additionally, each clause can\nspecify binary encoded coordinates for location aware-\nness (visualized as red boxes in Figure 2). The coor-\ndinates are encoded by augmenting each patch input\nvector xp= [xp\nk]\u2208 {0,1}C,p\u2208 {1,2, . . . , P }, with a\ncoordinate vector. The coordinate vector lp= [lp\nk]\u2208\n{0,1}P\u00d72of each patch is threshold-encoded (Dar-\nshana Abeyrathna et al., 2020). That is, the input vec-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c841d-934e-11ee-9dbb-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 3, "chroma:document": "tor is extended with one propositional variable per po-\nsition. The resulting augmented vector is denoted by\nxp:xp= [xp\nk]\u2208 {0,1}C+P. The overall ConvTextTM\narchitecture is depicted in Figure 2.\nClassification in CTM is similar to that of vanilla TM,\nas shown in Eq. 2. However, because we have Pinput\nvectors xpfor CTM, each clause produces Poutput\nvalues. The final output is obtained by OR ingthe indi-\nvidual outputs from each patch, specified as follows:\n\u02c6y=u\uf8ee\n\uf8ef\uf8f0m/2X\nj=1P_\np=1\uf8eb\n\uf8ec\uf8ed^\nlk\u2208L+\njlp"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c841e-934e-11ee-9a21-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 3, "chroma:document": "\u02c6y=u\uf8ee\n\uf8ef\uf8f0m/2X\nj=1P_\np=1\uf8eb\n\uf8ec\uf8ed^\nlk\u2208L+\njlp\nk\uf8f6\n\uf8f7\uf8f8\u2212m/2X\nj=1P_\np=1\uf8eb\n\uf8ec\uf8ed^\nlk\u2208L\u2212\njlp\nk\uf8f6\n\uf8f7\uf8f8\uf8f9\n\uf8fa\uf8fb.\n(3)\nCTM learning leverages the TM learning, with clauses\nreceiving the feedback based on the input vector and\nlabel. However, for CTM, there are Pinput patches in\nan input. Therefore, when a clause is updated, CTM\nrandomly selects one of the patch input vector xpthat\nmade the clause evaluate to 1:\nxp\nj=Random\uf8eb\n\uf8ec\uf8ed\uf8f1\n\uf8f4\uf8f2\n\uf8f4\uf8f3xp\f\f\f\f\f\f\f\uf8eb\n\uf8ec\uf8ed^\nlk\u2208L\u03be\njlp\nk\uf8f6\n\uf8f7\uf8f8= 1,1\u2264p\u2264P\uf8fc\n\uf8f4\uf8fd\n\uf8f4\uf8fe\uf8f6\n\uf8f7\uf8f8.\n(4)"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c841f-934e-11ee-959c-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 3, "chroma:document": "\uf8ec\uf8ed^\nlk\u2208L\u03be\njlp\nk\uf8f6\n\uf8f7\uf8f8= 1,1\u2264p\u2264P\uf8fc\n\uf8f4\uf8fd\n\uf8f4\uf8fe\uf8f6\n\uf8f7\uf8f8.\n(4)\nThe randomly chosen patch input xpenables each\nclause to extract a specific sub-pattern, and the unpre-\ndictability of the uniform distribution statistically scat-\nters the clauses for various sub-patterns in the target\ntext.\n4. Experiments\n4.1. Datasets\nTable 1 provides an overview of the publicly available\ndatasets used in our experiment. The goal of this study\nis to assess our framework across a variety of datasets"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8420-934e-11ee-84f3-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 3, "chroma:document": "with varying semantic content, sentence lengths, and"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8421-934e-11ee-a8aa-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 4, "chroma:document": "3765Datasets Epochs #clauses Threshold (T) Sensitivity (s) Window\nPolitiFact 200 10,000 100*100 10.0 3\nGossipCop 200 15,000 100*100 20.0 3\nBBCSports 100 10,000 150*150 10.0 2\nTwitter 100 10,000 50*50 10.0 2\nQuery 100 5,000 150*150 10.0 2\nR8 150 10,000 100*100 10.0 2\nWOS-5736 150 10,000 150*150 10.0 2\nTable 2: Hyperparameter configurations.\nlinguistic patterns. To this end, we employ datasets\nrelated to fact-checking, document classification, aca-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8422-934e-11ee-acf2-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 4, "chroma:document": "demic text classification, and short text classification.\nWe organize the datasets as follows:\n\u2022Fact Checking : We here utilize a publicly avail-\nable data repository for fake news detection,\nFakeNewsNet (Shu et al., 2020a). The labels\nare provided by professional journalists from the\nfact-checking websites PolitiFact andGossipCop .\nPolitiFact focuses on U.S. political news, whereas\nGossipCop focuses on entertainment news from\nvarious media.\n\u2022Topic Classification : For topic classification, we"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8423-934e-11ee-b5af-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 4, "chroma:document": "use BBC Sports and a Twitter dataset. BBC Sports\nconsists of 737documents from the BBC Sports\nwebsite, collected between 2004 and 2005, la-\nbeled according to five sports categories. Further-\nmore, the Twitter dataset consists of a collection\nof5,513 tweets that have been hand-classified\ninto one of the four topics: Apple, Google, Twit-\nter, and Microsoft. The tweets are further labeled\nwith sentiments positive, negative, or neutral.\n\u2022Short text classification : These datasets in-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8424-934e-11ee-beea-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 4, "chroma:document": "\u2022Short text classification : These datasets in-\nvolve short text sentences. We explore perfor-\nmance using the Query (Faruqui and Das, 2018)\nand R8 (Debole and Sebastiani, 2005) datasets.\nGoogle\u2019s query dataset was created by crowd-\nsourcing well-formedness annotations for 25,100\nqueries from the Paralex corpus. Each query\nwas binary annotated by five raters regarding\nwhether the query was well-formed. R8 is a subset\nof the Reuters-21578 corpus that contains news"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8425-934e-11ee-bbd8-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 4, "chroma:document": "of the Reuters-21578 corpus that contains news\ndocuments classified into the eight most popular\nclasses. Note that the document distribution in R8\nis severely skewed, with the smallest class holding\njust 51 documents.\n\u2022Academic text classification : We utilize the Web\nof Science (WoS)-5736 datset (Kowsari et al.,\n2017a), which comprises 5,736published papers\nwith eleven categories organized under three main\ncategories.\n4.2. Baselines\nWe begin by summarizing the baseline methods."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8426-934e-11ee-bdf3-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 4, "chroma:document": "We begin by summarizing the baseline methods.\n\u2022 FastText (Joulin et al., 2017) uses a linear classi-\nfier to input a document embedding, which is cre-\nated by the average of word/n-grams embeddings.\u2022 Rhetorical Structure Theory (RST) (Rubin et al.,\n2015) uses a tree structure to depict the relation-\nship between words in a document. It extracts the\nnews style features from a bag of words by map-\nping them into a latent feature representation.\n\u2022 Linguistic Inquiry and Word Count (LIWC) (Pen-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8427-934e-11ee-83dc-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 4, "chroma:document": "\u2022 Linguistic Inquiry and Word Count (LIWC) (Pen-\nnebaker et al., 2015) is used to extract and learn\nfeatures from psycholinguistic and deception cat-\negories.\n\u2022 Hierarchical attention neural net-\nwork (HAN) (Yang et al., 2016) is employed for\nembedding word-level attention on each sentence\nand sentence-level attention on news content for\nfake news detection.\n\u2022 CNN-text (Kim, 2014) utilizes a convolutional\nneural network (CNN) with pre-trained word vec-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8428-934e-11ee-9e0e-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 4, "chroma:document": "neural network (CNN) with pre-trained word vec-\ntors to perform sentence-level classification. Mul-\ntiple convolutional filters enable the model to col-\nlect various granularities of text features from\nnews articles.\n\u2022 LSTM-ATT (Lin et al., 2019a) employs long short\nterm memory (LSTM) in conjunction with an at-\ntention mechanism. The model feeds a two-layer\nLSTM with a 300-dimensional vector representa-\ntion of news items as input for fake news detec-\ntion."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8429-934e-11ee-a815-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 4, "chroma:document": "tion.\n\u2022 Hierarchical Deep Learning for Text Classifica-\ntion (HDLTex) (Kowsari et al., 2017b) performs\nhierarchical classification by stacking deep learn-\ning architectures to give specialized comprehen-\nsion at each level of the document hierarchy.\n\u2022 RoBERTa-MWSS was proposed in (Shu et al.,\n2020b), which employs the Multiple Sources of\nWeak Social Supervision (MWSS) approach built\nupon RoBERTa (Liu et al., 2019).\n\u2022 Bidirectional Encoder Representations from"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c842a-934e-11ee-9b88-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 4, "chroma:document": "\u2022 Bidirectional Encoder Representations from\nTransformers (BERT) (Devlin et al., 2019b) is\na Transformer-based model which contains an\nencoder with 12 transformer blocks, self-attention\nheads, and a hidden shape size of 768.\n\u2022 XLNet (Yang et al., 2019b) is a generalized auto-\nregressive pretraining model that integrates au-\ntoencoding and a segment recurrence mechanism\nfrom transformers.\nOther approaches include Word Mover\u2019s Dis-\ntance (WMD), which defines the distance between"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c842b-934e-11ee-9970-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 4, "chroma:document": "tance (WMD), which defines the distance between\ntwo documents as the minimum cost of converting\nthe words of one document into words of the other.\nDeepsets adopt objective functions defined on sets\nthat are invariant to permutations, allowing for the\nbuilding of a deep network architecture that operates\non sets. Similarly, NNattention and Set-Transformer\nare variants of Deepsets that substitutes an attention\nmechanism for the sum operator."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c842c-934e-11ee-ba27-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 5, "chroma:document": "3766Datasets RST LIWC HAN CNN-text LSTM-ATT RoBERTa-MWSS BERT XLNet TM TMconv TMconv(max)\nPolitiFact 60.7 76.9 83.7 65.3 83.3 82.5 88 89.5 87.1\u00b10.24 90.27\u00b10.33 91.21\nGossipCop 53.1 73.6 74.2 73.9 79.3 80.3 85 85.5 84.2\u00b10.03 85.82\u00b10.27 86.28\nTable 3: Performance comparison of our model with other baseline models for fact checking.\nDatasets WMD Deepsets NNattention Transformer LSTM BERT XLNet TM TMconv TMconv(max)"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c842d-934e-11ee-b189-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 5, "chroma:document": "BBCSports 95.40\u00b10.70 74.55\u00b120.1 95.28\u00b10.97 95.82\u00b11.23 95.52 99 98 96.91 96.78 \u00b10.32 97.97\nTwitter 71.3\u00b10.70 70\u00b11.62 70.91\u00b10.62 72.21\u00b10.47 72.1 74.71 78 71.13 70.67\u00b10.27 71.91\nTable 4: Performance comparison of our model with other baseline models for topic classification.\n0 2 4 6 8 10\nWindow86878889909192Accuracy (%)\nFigure 3: Accuracy vsWindow.\n4.3. Training and Testing\nWe use a random train-test split of 70% /30% for all\ndatasets except R8 and query as they have predefined"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c842e-934e-11ee-bf19-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 5, "chroma:document": "train and test sets. The process is repeated five times,\nand the average accuracy and F1 scores are reported.\nTo provide robust results, we calculated an ensemble\naverage by first taking the average of 50stable epochs,\nfollowed by taking the average of the resulting five av-\nerages. The experiments were conducted on the server\n- NVIDIA DGX-2 with dual Intel Xeon Platinum 8168,\n2.7 GHz, 16 \u00d7NVIDIA Tesla V100 (32 GB), and\nUbuntu 18.04 LTS x64. The hyperparameter config-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c842f-934e-11ee-9a6c-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 5, "chroma:document": "Ubuntu 18.04 LTS x64. The hyperparameter config-\nurations of the experiment for each dataset are listed in\nTable 2.\n5. Results and Discussions\nIn this section, we evaluate the performance of our\nframework with the aforementioned baselines for each\nclassification task, including seven datasets.\nFor fact-checking (i.e., PolitiFact and GossipCop), we\nsee that HAN outperforms LIWC, CNN-text, and RST\non both datasets. This is arguable because HAN can"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8430-934e-11ee-b3a2-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 5, "chroma:document": "capture the syntactic and semantic rules required to de-\ntect fake news via hierarchical attention. Similarly, the\nLIWC performs better than RST. One possible reason\nfor this is that LIWC is able to extract the linguistic\nfeatures from news articles based on words that de-\nnote psycholinguistic characteristics. The LSTM-ATT,\nwhich incorporates substantial preprocessing utilizing\ncount features and sentiment features, as well as hyper-\nparameter tweaking (Lin et al., 2019b), performs sim-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8431-934e-11ee-838b-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 5, "chroma:document": "ilarly to HAN in PolitiFact but exceeds it on Gossip-Cop. One possible explanation for this can be that the\nattention mechanism is able to capture the relevant rep-\nresentation of the input. Our model outperforms all the\nbaselines, including transformer-based models such as\nRoBERTa-MWSS, BERT, and XLNet. Indeed, Con-\nvTextTM achieves maximum accuracy of 91.21% for\nPolitiFact and 86.28% for GossipCop. Besides, our\nmodel is significantly simpler than the deep learning"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8432-934e-11ee-8bbc-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 5, "chroma:document": "models since we do not use any pre-trained embed-\ndings in preprocessing. This also contributes to the\ntransparency, interpretability, and explainability of our\nmodel. Table 3 illustrates the comparison outcomes.\nFor topic classification (i.e., BBC Sports and Twit-\nter), Table 4 shows the classification accuracy of our\nproposed model and those of the baselines. The\nset-transformer outperforms other deep learning algo-\nrithms including Deepsets, NNattention, and LSTM,"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8433-934e-11ee-ba4b-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 5, "chroma:document": "rithms including Deepsets, NNattention, and LSTM,\nmarginally. The disparate performance of LSTM might\nbe explained by the fact that bidirectional LSTMs are\nineffective in modeling ungrammatical text. However,\nBERT and XLNet surpass all other approaches, with\nBERT achieving the accuracy of 99% in BBC Sports.\nAs the prior knowledge in the pre-trained BERT and\nXLNet is not particular to any domain, fine-tuning is\nrequired to unleash the actual potential of BERT and"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8434-934e-11ee-83ad-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 5, "chroma:document": "XLNet. Our proposed CTM method outperforms the\nvanilla TM and all other techniques except BERT and\nXLNet, and obtains an accuracy close to those of BERT\nand XLNet. The low accuracy of our model in the Twit-\nter dataset is most probably because our model, by rely-\ning entirely on the SOW approach, overlooks important\nword orders that are useful in sentiment classification.\nFor short text classification (i.e., Query and R8), Ta-\nble 5 compares the accuracy of ConvTextTM against"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8435-934e-11ee-9b03-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 5, "chroma:document": "ble 5 compares the accuracy of ConvTextTM against\nstate-of-the-art methods. As previously stated, with\nlarge-scale pretraining and fine-tuning on small-data\ntasks, BERT achieves 80% on Query and XLNet ob-\ntains98% on R8, surpassing other approaches signifi-\ncantly. Human evaluation was conducted on the query\ndataset by submitting 1,000queries to a human profi-\ncient in English, who were able to match the label with\n88.4%accuracy, indicating an estimated upper bound."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8436-934e-11ee-aa85-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 5, "chroma:document": "For academic text classification (i.e., WOS-5736), Ta-\nble 6 compares the accuracy of our model with other\ntechniques. While the RNN outperforms DNN and\nCNN, HDLTex with stacked deep learning CNN ar-\nchitecture performed surprisingly well, outperforming"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8437-934e-11ee-b716-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 6, "chroma:document": "3767Datasets CNN Fasttext LSTM HAN BERT XLNet Human TM TMconv TMconv(max)\nQuery 67.38 62.1 65.8 64.64 80 77 88.4 53.87 67.43\u00b10.22 67.94\nR8 95.71 96.13 96.09 - 97.8 98 - 96.16 96.32\u00b10.11 96.43\nTable 5: Performance comparison of our model with other baseline models for short text classification.\nDataset DNN CNN RNN Stacking SVM HDLTex-CNN BERT XLNet TM TMconv TMconv(max)\nWOS-5736 86.15 88.68 89.46 85.68 90.93 90.24 90 89.47 90.73\u00b10.27 91.28"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8438-934e-11ee-9731-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 6, "chroma:document": "Table 6: Performance comparison of our model with other baseline models for academic classification.\nBERT, XLNet, and TM. However, the maximum accu-\nracy from our proposed model outperformed HDLTex-\nCNN by a slight margin.\n5.1. Accuracy vs Window Size\nWe now use the PolitiFact dataset to investigate the\neffect of increasing the window size Won accuracy.\nAs PolitiFact contains long sentences per example, our\nmodel is able to achieve very high accuracy by utiliz-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8439-934e-11ee-ba85-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 6, "chroma:document": "ing clauses to capture linguistic patterns in each win-\ndow. However, for datasets with short sentences such\nas Query and R8, it is not feasible to use more than two\nwindows since each window would contain only a few\nwords, rendering it useless for classification. Figure 3\nillustrates the trade-off between window size and accu-\nracy. We notice that as the window size increases, the\naccuracy decreases. The highest accuracy is attained\nwhenW= 1, which means that the input text sentence"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c843a-934e-11ee-b325-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 6, "chroma:document": "has not been divided into any windows. The maximum\naccuracy obtained for each dataset using W= 1 is\nshown in Table 8. Because we are investigating the\nlocal interpretability using parts of a text sentence, we\nhave to break the text sentence into windows. As a re-\nsult,W= 2 andW= 3 are most suitable for us, as\ntheir accuracy is comparable to that of W= 1, with\nthe added benefit of local interpretation. From this ex-\nperiment, we can conclude that the length of the text"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c843b-934e-11ee-bc68-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 6, "chroma:document": "sentence determines the window size. That is, if the\ndataset contains lengthy sentences, we may increase\nthe window size without compromising accuracy.\n6. Interpretability Analysis\nWe examine the interpretability of our framework using\nthe R8 dataset. Here, we consider both global and lo-\ncal interpretability. We define global interpretability as\nidentifying global features from the trained model that\ncontribute significantly to classification. In contrast, lo-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c843c-934e-11ee-afec-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 6, "chroma:document": "cal interpretability refers to identifying significant fea-\ntures inside a particular window. For example, consider\nthe following input sentence from the R8 dataset, \u201cTai-\nwan shipbuilder looks for Japanese ventures Taiwan\u2019s\nstate-owned China shipbuilding corp csbc plans to seek\njoint production agreements with Japan and further di-\nversify into ship repairing. \u201d with the classification label\n\u201cship\u201d. We divide the sentence into windows. Using a"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c843d-934e-11ee-8feb-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 6, "chroma:document": "window size of two, the sentence can be separated into\ntwo phrases: Window 1 :[Taiwan shipbuilder looks forJapanese ventures Taiwan\u2019s state-owned China ship-\nbuilding corp] andWindow 2 :[csbc plans to seek joint\nproduction agreements with Japan and further diversify\ninto ship repairing] . As a result, we can observe that\nthe first window is sufficient to classify the text. There-\nfore, through local interpretability, our proposed model\ndetermines which section of the sentence is relevant for"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c843e-934e-11ee-b20a-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 6, "chroma:document": "classification. Additionally, global interpretability can\nbe used to highlight the relevant features inside the win-\ndow as seen in Table 7.\nWe split the R8 dataset into two windows for our exper-\niment, given the dataset contains short sentences. That\nis, as seen in Figure 1, each example sentence is split\ninto two local parts. The model is trained on the pre-\nprocessed dataset, and clause-specific features are ex-\ntracted. We note that certain clauses capture features"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c843f-934e-11ee-835a-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 6, "chroma:document": "of all the windows, whereas others capture features of\na particular window. This suggests that we can distin-\nguish between features that have a global impact and\nthe ones that are responsible for a particular classifi-\ncation on a local location-aware level. To demonstrate\nthe local interpretability, we visualize the features from\ntwo windows for \u201c acq\u201d class in Figure 4. The fea-\ntures in each window signify the classification decision\nbased on the corresponding part of the sentence. That"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8440-934e-11ee-a0ab-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 6, "chroma:document": "is, we can know which part of the sentence is essential\nfor the classification.\n7. Conclusion\nIn this paper, we introduce an explainable Convolu-\ntion Tsetlin Machine (CTM) architecture for text clas-\nsification. Due to the fact that CTM is optimized for\nimage-based tasks, we preprocess the text document\ninto various windows. Thus, the clauses from the CTM\ncan capture the semantic features associated with each\nparticular window\u2019s word patterns. We propose us-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8441-934e-11ee-8fbd-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 6, "chroma:document": "particular window\u2019s word patterns. We propose us-\ning predefined fixed-length vocabulary features derived\nfrom the standard Bidirectional Encoder Representa-\ntions from Transformers (BERT) tokens. This allows\nus to mitigate the TM dependency on vocabulary for\neach dataset and the out-of-vocabulary problem. We\nillustrate the effectiveness of our model on four clas-\nsification tasks using seven different datasets. Our ex-\nperimental findings demonstrate that our approach is"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8442-934e-11ee-af4e-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 6, "chroma:document": "superior to or competitive with more sophisticated and\nnon-transparent approaches, including BERT and XL-\nNet. We then investigate the effect of different window"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8443-934e-11ee-a1d0-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 7, "chroma:document": "3768acq crude earn grain interest money-fx ship trade\npointing ##connect accomplish island tesla kruger farmhouse ##ities\ndoping thorns ##sby treating ##oko ashton road harlow\n##rified notably looting surface linux tonight agency pianos\nevergreen ##enter ##osed facebook bed ##sitor ##voking sanskrit\nphone dramatic endelle trail slams becker ##met plunged\npremiere chloride confrontation ##emia photo bed rockies ##cured\ndemonstrated racers temporarily summer mural burning trafficking script"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8444-934e-11ee-b6fe-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 7, "chroma:document": "collections fountain werewolf road vaccines handicap likeness theories\nunwilling ##lon segregation garbage families lightning flaming ineffective\n##liest safety presiding ##nity bronze patent gesellschaft extensive\nTable 7: Significant features captured by our model for each class in R8 dataset.\n(a) Window 0.\n (b) Window 1.\nFigure 4: Wordcloud visualization of local interpretability for \u201c acq\u201d.\nDataset Accuracy (max)\nPolitiFact 92.46\nGossipCop 85.94\nBBCSports 99.54\nTwitter 73.67\nQuery 68.25"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8445-934e-11ee-8300-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 7, "chroma:document": "BBCSports 99.54\nTwitter 73.67\nQuery 68.25\nR8 96.93\nWOS-5736 92.42\nTable 8: Maximum accuracy obtained using window\nsize 1 (i.e., W= 1).\nsizes on our model\u2019s performance. Additionally, we\nillustrate the global and local interpretability provided\nby the CTM depending on the significance of features\ncaptured by clauses in separate windows.\n8. Bibliographical References\nAgarwal, R., Frosst, N., Zhang, X., Caruana, R., and\nHinton, G. E. (2020). Neural additive models: In-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8446-934e-11ee-a8ec-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 7, "chroma:document": "Hinton, G. E. (2020). Neural additive models: In-\nterpretable machine learning with neural nets. arXiv\npreprint:2004.13912 .\nAgrawal, R., Imieli \u00b4nski, T., and Swami, A. (1993).\nMining association rules between sets of items in\nlarge databases. In Proceedings of ACM SIGMOD\ninternational conference on Management of data ,\npages 207\u2013216.\nBadue, C., Guidolini, R., Carneiro, R. V ., Azevedo, P.,\nCardoso, V . B., Forechi, A., Jesus, L., Berriel, R.,"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8447-934e-11ee-94a2-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 7, "chroma:document": "Paixao, T. M., Mutz, F., et al. (2020). Self-driving\ncars: A survey. Expert Systems with Applications ,\npage 113816.\nBai, B., Liang, J., Zhang, G., Li, H., Bai, K., and Wang,F. (2020). Why is attention not so attentive? arXiv\npreprint:2006.05656 .\nBerge, G. T., Granmo, O.-C., Tveit, T. O., Goodwin,\nM., Jiao, L., and Matheussen, B. V . (2019). Us-\ning the tsetlin machine to learn human-interpretable\nrules for high-accuracy text categorization with med-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8448-934e-11ee-864b-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 7, "chroma:document": "ical applications. IEEE Access , 7:115134\u2013115146.\nBhattarai, B., Granmo, O.-C., and Jiao, L. (2021a).\nMeasuring the novelty of natural language text us-\ning the conjunctive clauses of a Tsetlin machine text\nclassifier. In Proceedings of ICAART .\nBhattarai, B., Granmo, O.-C., and Jiao, L. (2021b).\nExplainable tsetlin machine framework for fake\nnews detection with credibility score assessment.\narXiv preprint:2105.09114 .\nBhattarai, B., Granmo, O.-C., and Jiao, L. (2022)."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8449-934e-11ee-b1d9-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 7, "chroma:document": "Word-level human interpretable scoring mechanism\nfor novel text detection using tsetlin machines. Ap-\nplied Intelligence .\nBlakely, C. D. and Granmo, O.-C. (2020). Closed-\nform expressions for global and local interpretation\nof tsetlin machines with applications to explaining\nhigh-dimensional data. arXiv preprint:2007.13885 .\nBojanowski, P., Grave, E., Joulin, A., and Mikolov, T.\n(2017). Enriching word vectors with subword infor-\nmation. Transactions of the ACL , 5:135\u2013146."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c844a-934e-11ee-8e0f-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 7, "chroma:document": "mation. Transactions of the ACL , 5:135\u2013146.\nBreiman, L. (2001). Random forests. Machine learn-\ning, 45(1):5\u201332.\nChen, H. and Ji, Y . (2020). Learning variational word\nmasks to improve the interpretability of neural text\nclassifiers. In Proceedings of EMNLP .\nDarshana Abeyrathna, K., Granmo, O.-C., Zhang, X.,\nJiao, L., and Goodwin, M. (2020). The regression\ntsetlin machine: a novel approach to interpretable"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c844b-934e-11ee-810a-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 8, "chroma:document": "3769nonlinear regression. Philosophical Transactions of\nthe Royal Society A , 378(2164):20190165.\nDebole, F. and Sebastiani, F. (2005). An analysis of the\nrelative hardness of reuters-21578 subsets. Journal\nof the American Society for Information Science and\ntechnology , 56(6):584\u2013596.\nDevlin, J., Chang, M.-W., Lee, K., and Toutanova,\nK. (2019a). Bert: Pre-training of deep bidirectional\ntransformers for language understanding. In Pro-\nceedings of NAACL-HLT ."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c844c-934e-11ee-af2c-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 8, "chroma:document": "ceedings of NAACL-HLT .\nDevlin, J., Chang, M.-W., Lee, K., and Toutanova,\nK. (2019b). Bert: Pre-training of deep bidirectional\ntransformers for language understanding. In Pro-\nceedings of NAACL-HLT .\nEsteva, A., Robicquet, A., Ramsundar, B., Kuleshov,\nV ., DePristo, M., Chou, K., Cui, C., Corrado, G.,\nThrun, S., and Dean, J. (2019). A guide to deep\nlearning in healthcare. Nature medicine , 25(1):24\u2013\n29.\nFaruqui, M. and Das, D. (2018). Identifying well-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c844d-934e-11ee-82c3-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 8, "chroma:document": "Faruqui, M. and Das, D. (2018). Identifying well-\nformed natural language questions. In Proceedings\nof EMNLP , pages 798\u2013803.\nFeldman, V . (2009). Hardness of approximate two-\nlevel logic minimization and pac learning with mem-\nbership queries. Journal of Computer and System\nSciences , 75(1):13\u201326.\nFreitas, A. A., Wieser, D. C., and Apweiler, R. (2008).\nOn the importance of comprehensible classification\nmodels for protein function prediction. IEEE/ACM"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c844e-934e-11ee-a529-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 8, "chroma:document": "models for protein function prediction. IEEE/ACM\nTransactions on Computational Biology and Bioin-\nformatics , 7(1):172\u2013182.\nGilpin, L. H., Bau, D., Yuan, B. Z., Bajwa, A., Specter,\nM., and Kagal, L. (2018). Explaining explanations:\nAn overview of interpretability of machine learning.\nInProceedings of IEEE DSAA , pages 80\u201389. IEEE.\nGranmo, O.-C., Glimsdal, S., Jiao, L., Goodwin, M.,\nOmlin, C. W., and Berge, G. T. (2019). The convo-\nlutional tsetlin machine. arXiv preprint:1905.09688 ."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c844f-934e-11ee-8acf-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 8, "chroma:document": "Granmo, O.-C. (2018). The Tsetlin machine - a\ngame theoretic bandit driven approach to optimal\npattern recognition with propositional logic. arXiv\npreprint:1804.01508 .\nJacovi, A., Shalom, O. S., and Goldberg, Y . (2018).\nUnderstanding convolutional neural networks for\ntext classification. In Proceedings of EMNLP Work-\nshop BlackboxNLP .\nJoulin, A., Grave, \u00b4E., Bojanowski, P., and Mikolov, T.\n(2017). Bag of tricks for efficient text classification.\nInProceedings of EACL , pages 427\u2013431."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8450-934e-11ee-a6cd-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 8, "chroma:document": "InProceedings of EACL , pages 427\u2013431.\nKim, Y . (2014). Convolutional neural networks for\nsentence classification. In Proceedings of EMNLP .\nKowsari, K., Brown, D. E., Heidarysafa, M.,\nMeimandi, K. J., Gerber, M. S., and Barnes, L. E.\n(2017a). Hdltex: Hierarchical deep learning for\ntext classification. In Proceedings of IEEE ICMLA ,\npages 364\u2013371.\nKowsari, K., Brown, D. E., Heidarysafa, M.,\nMeimandi, K. J., Gerber, M. S., and Barnes, L. E.(2017b). Hdltex: Hierarchical deep learning for"}


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topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8451-934e-11ee-ad1f-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 8, "chroma:document": "text classification. In Proceedings of IEEE ICMLA ,\npages 364\u2013371.\nLage, I., Chen, E., He, J., Narayanan, M., Kim, B.,\nGershman, S., and Doshi-Velez, F. (2019). An eval-\nuation of the human-interpretability of explanation.\nCoRR , abs/1902.00006.\nLe, H. H. and Viviani, J.-L. (2018). Predicting\nbank failure: An improvement by implementing a\nmachine-learning approach to classical financial ra-\ntios. Research in International Business and Fi-\nnance , 44:16\u201325."}


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topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8452-934e-11ee-8c87-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 8, "chroma:document": "nance , 44:16\u201325.\nLei, J., Rahman, T., Shafik, R., Wheeldon, A.,\nYakovlev, A., Granmo, O.-C., Kawsar, F., and\nMathur, A. (2021). Low-power audio keyword spot-\nting using tsetlin machines. Journal of Low Power\nElectronics and Applications , 11(2):18.\nLi, B., Friedman, J., Olshen, R., and Stone, C. (1984).\nClassification and regression trees (cart). Biomet-\nrics, 40(3):358\u2013361.\nLin, J., Tremblay-Taylor, G., Mou, G., You, D., and\nLee, K. (2019a). Detecting fake news articles. In"}


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topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8453-934e-11ee-a680-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 8, "chroma:document": "Lee, K. (2019a). Detecting fake news articles. In\nProceedings of 2019 IEEE International Conference\non Big Data .\nLin, J., Tremblay-Taylor, G., Mou, G., You, D., and\nLee, K. (2019b). Detecting fake news articles. In\nProceedings of 2019 IEEE International Conference\non Big Data .\nLipton, Z. C. (2018). The mythos of model inter-\npretability: In machine learning, the concept of in-\nterpretability is both important and slippery. Queue ,\n16(3):31\u201357."}


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topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8454-934e-11ee-8e3a-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 8, "chroma:document": "16(3):31\u201357.\nLiu, Y ., Ott, M., Goyal, N., Du, J., Joshi, M., Chen, D.,\nLevy, O., Lewis, M., Zettlemoyer, L., and Stoyanov,\nV . (2019). Roberta: A robustly optimized BERT\npretraining approach. CoRR , abs/1907.11692.\nMikolov, T., Sutskever, I., Chen, K., Corrado, G.,\nand Dean, J. (2013). Distributed representations of\nwords and phrases and their compositionality. In\nProceedings of NIPS .\nNguyen, D. (2018). Comparing automatic and human\nevaluation of local explanations for text classifica-"}


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topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8455-934e-11ee-ac1e-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 8, "chroma:document": "tion. In Proceedings of NAACL-HLT (Long Papers) ,\npages 1069\u20131078.\nPennebaker, J., Boyd, R. L., Jordan, K., and Blackburn,\nK. G. (2015). The development and psychometric\nproperties of liwc2015. Technical report.\nPennington, J., Socher, R., and Manning, C. D. (2014).\nGlove: Global vectors for word representation. In\nProceedings of EMNLP , pages 1532\u20131543.\nRibeiro, M. T., Singh, S., and Guestrin, C. (2016). \u201d\nwhy should i trust you?\u201d explaining the predictions"}


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topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8456-934e-11ee-ad70-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 8, "chroma:document": "of any classifier. In Proceedings of ACM SIGKDD .\nRubin, V . L., Conroy, N., and Chen, Y . (2015). To-\nwards news verification: Deception detection meth-\nods for news discourse. In Proceedings of the Rapid\nScreening Technologies, Deception Detection and\nCredibility Assessment Symposium, at the 48th An-"}


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topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8457-934e-11ee-b9db-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 9, "chroma:document": "3770nual Hawaii International Conference on System\nSciences .\nSaha, R., Granmo, O.-C., and Goodwin, M. (2020).\nMining interpretable rules for sentiment and seman-\ntic relation analysis using tsetlin machines. In Pro-\nceedings of International Conference on Innova-\ntive Techniques and Applications of Artificial Intel-\nligence .\nSerrano, S. and Smith, N. A. (2019). Is attention inter-\npretable? In Proceedings of ACL , pages 2931\u20132951.\nShu, K., Mahudeswaran, D., Wang, S., Lee, D., and"}


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topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8458-934e-11ee-8f70-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 9, "chroma:document": "Shu, K., Mahudeswaran, D., Wang, S., Lee, D., and\nLiu, H. (2020a). Fakenewsnet: A data repository\nwith news content, social context, and spatiotempo-\nral information for studying fake news on social me-\ndia.Big data , 83:171\u2013188.\nShu, K., Zheng, G., Li, Y ., Mukherjee, S., Awadallah,\nA. H., Ruston, S. W., and Liu, H. (2020b). Lever-\naging multi-source weak social supervision for early\ndetection of fake news. arXiv preprint:2004.01732 .\nStrumbelj, E. and Kononenko, I. (2010). An efficient"}


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id: 152c8459-934e-11ee-b62c-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 9, "chroma:document": "explanation of individual classifications using game\ntheory. The Journal of Machine Learning Research ,\n11:1\u201318.\nTsetlin, M. L. (1961). On behaviour of finite au-\ntomata in random medium. Avtomat. i Telemekh ,\n22(10):1345\u20131354.\nUstun, B. and Rudin, C. (2016). Supersparse linear in-\nteger models for optimized medical scoring systems.\nMachine Learning , 102(3):349\u2013391.\nVaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J.,\nJones, L., Gomez, A. N., Kaiser, \u0141., and Polosukhin,"}


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topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c845a-934e-11ee-8ea6-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 9, "chroma:document": "I. (2017). Attention is all you need. In Proceedings\nof NIPS , pages 6000\u20136010.\nXiong, W., Ni\u2019mah, I., Huesca, J. M., van Ipenburg, W.,\nVeldsink, J., and Pechenizkiy, M. (2018). Looking\ndeeper into deep learning model: attribution-based\nexplanations of textcnn. In Proceedings of NIPS\n2018 Workshop on Challenges and Opportunities for\nAI in Financial Services: the Impact of Fairness, Ex-\nplainability, Accuracy, and Privacy .\nYadav, R., Jiao, L., Granmo, O.-C., and Goodwin,"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c845b-934e-11ee-b72b-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 9, "chroma:document": "Yadav, R., Jiao, L., Granmo, O.-C., and Goodwin,\nM. (2021a). Human-level interpretable learning for\naspect-based sentiment analysis. In Proceedings of\nAAAI .\nYadav, R. K., Jiao, L., Granmo, O.-C., and Good-\nwin, M. (2021b). Distributed word representation\nin tsetlin machine. arXiv preprint:2104.06901 .\nYadav, R. K., Jiao, L., Granmo, O.-C., and Goodwin,\nM. (2021c). Interpretability in word sense disam-\nbiguation using tsetlin machine. In Proceedings of\nICAART , pages 402\u2013409."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c845c-934e-11ee-bbbe-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 9, "chroma:document": "ICAART , pages 402\u2013409.\nYang, Z., Yang, D., Dyer, C., He, X., Smola, A., and\nHovy, E. (2016). Hierarchical attention networks\nfor document classification. In Proceedings of HLT-\nNAACL .\nYang, Z., Dai, Z., Yang, Y ., Carbonell, J., Salakhutdi-\nnov, R., and Le, Q. V . (2019a). Xlnet: Generalizedautoregressive pretraining for language understand-\ning. In Proceedings of NIPS .\nYang, Z., Dai, Z., Yang, Y ., Carbonell, J., Salakhutdi-\nnov, R., and Le, Q. V . (2019b). Xlnet: Generalized"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c845d-934e-11ee-be94-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2022.lrec-1.401.pdf", "page": 9, "chroma:document": "autoregressive pretraining for language understand-\ning. In Proceedings of NIPS ."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c845e-934e-11ee-aec2-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 0, "chroma:document": "The Regression Tsetlin Machine: A Tsetlin\nMachine for Continuous Output Problems\nK. Darshana Abeyrathna, Ole-Christo\ufb00er Granmo, Lei Jiao, and\nMorten Goodwin\nCentre for Arti\ufb01cial Intelligence Research, University of Agder, Grimstad, Norway\n{darshana.abeyrathna, ole.granmo, lei.jiao, morten.goodwin }@uia.no\nAbstract. The recently introduced Tsetlin Machine (TM) has provided\ncompetitive pattern classi\ufb01cation accuracy in several benchmarks, com-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c845f-934e-11ee-988e-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 0, "chroma:document": "posing patterns with easy-to-interpret conjunctive clauses in proposi-\ntional logic. In this paper, we go beyond pattern classi\ufb01cation by in-\ntroducing a new type of TMs, namely, the Regression Tsetlin Machine\n(RTM). In all brevity, we modify the inner inference mechanism of the\nTM so that input patterns are transformed into a single continuous out-\nput, rather than to distinct categories. We achieve this by: (1) using the\nconjunctive clauses of the TM to capture arbitrarily complex patterns;"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8460-934e-11ee-b27d-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 0, "chroma:document": "(2) mapping these patterns to a continuous output through a novel vot-\ning and normalization mechanism; and (3) employing a feedback scheme\nthat updates the TM clauses to minimize the regression error. The feed-\nback scheme uses a new activation probability function that stabilizes\nthe updating of clauses, while the overall system converges towards an\naccurate input-output mapping. The performance of the RTM is eval-\nuated using six di\ufb00erent arti\ufb01cial datasets with and without noise, in"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8461-934e-11ee-b7ba-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 0, "chroma:document": "comparison with the Classic Tsetlin Machine (CTM) and the Multiclass\nTsetlin Machine (MTM). Our empirical results indicate that the RTM\nobtains the best training and testing results for both noisy and noise-\nfree datasets, with a smaller number of clauses. This, in turn, translates\nto higher regression accuracy, using signi\ufb01cantly less computational re-\nsources.\nKeywords: Tsetlin Machine, Regression Tsetlin Machine, Tsetlin Automata,\nRegression, Pattern Recognition, Propositional Logic."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8462-934e-11ee-89ef-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 0, "chroma:document": "1 Introduction\nComputational simplicity, ease of interpretation, along with competitive pattern\nrecognition accuracy, make the recently introduced Tsetlin Machine (TM) [1] a\npromising new paradigm for machine learning. Indeed, the TM has outperformed\nwell-known machine learning algorithms such as Logistic Regression, Neural Net-\nworks, and Support Vector Machine (SVM) in several benchmarks, including Iris\nData Classi\ufb01cation, Handwritten Digits Classi\ufb01cation (MNIST), Predicting Op-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8463-934e-11ee-adec-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 0, "chroma:document": "timum Moves in the Axis and Allies Board Game, and Classi\ufb01cation of Noisy\nXOR Data with Non-Informative Features [1].arXiv:1905.04206v2  [cs.LG]  21 Jun 2019"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8464-934e-11ee-a66e-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 1, "chroma:document": "Tsetlin Automata and the Tsetlin Machine. The core of the TM is built\non Tsetlin Automata (TAs), developed by M. L. Tsetlin in the early 1960s [2].\nThis powerful, yet simple, leaning mechanism has been used to solve a number\nof machine learning and stochastic optimization problems, such as resource allo-\ncation [3], stochastic searching on the line [4], distributed coordination [5], graph\ncoloring [6], and forecasting disease outbreaks [7]. In the TM, TAs represent lit-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8465-934e-11ee-bd33-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 1, "chroma:document": "erals \u2013 input features and their negations. The literals, in turn, form conjunctive\nclauses in propositional logic, as decided by the TAs. The \ufb01nal TM output is\na disjunction of all the speci\ufb01ed clauses. In this manner, the pattern composi-\ntion and learning procedure of the TM is fully transparent and understandable,\nfacilitating human interpretation. In addition, the TM has an inherent compu-\ntational advantage. That is, the inputs and outputs of the TM can naturally be"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8466-934e-11ee-ba60-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 1, "chroma:document": "represented as bits, and recognition and learning is performed by manipulating\nthose bits. The operation of the TM thus demands relatively small computa-\ntional resources, and supports hardware-near and parallel computation e.g. on\nGPUs.\nLately, the TM has provided state-of-the-art performance in several real-life\napplications. Berge et al. have for instance successfully used the TM for medi-\ncal text categorization [8]. They used the TM to provide interpretable pattern"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8467-934e-11ee-a475-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 1, "chroma:document": "recognition for the analysis of electronic health records. The authors demon-\nstrated that the TM can outperform established machine learning algorithms\nsuch as k-nearest neighbors (kNN), SVM, Random Forest, Decision Trees, Mul-\ntilayer Perceptron (MLP), Long Short-Term Memory (LSTM) Neural Networks,\nand Convolutional Neural Networks (CNNs), in terms of precision, recall, and\nF-measure. Furthermore, Darshana et al. have shown that the TM can outper-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8468-934e-11ee-90f1-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 1, "chroma:document": "form MLPs, Decision Trees, and SVMs in dengue fever outbreak prediction. The\nlatter result was achieved by making the TM capable of expressing thresholds\nand intervals that capture patterns formed by continuous features. By carefully\nselecting thresholds and intervals, the TM avoided losing information due to\nbinarization [9].\nResearch Question and Paper Contributions. The TM has been de-\nsigned for classi\ufb01cation, not for producing continuous output. How to best pro-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8469-934e-11ee-92a3-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 1, "chroma:document": "duce continuous output is unclear, with the existing binarization schemes being\nincapable of fully leveraging the natural ranking of numbers. In this paper, we\nintroduce the Regression Tsetlin Machine (RTM) to overcome above limitation\nof the TM. The RTM is a novel variant of the Classic Tsetlin Machine (CTM),\nspeci\ufb01cally addressing the unique properties of regression. The novel modi\ufb01ca-\ntions that we introduce are subtle, but crucial. First of all, the clause polarities"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c846a-934e-11ee-ae7b-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 1, "chroma:document": "the CTM uses to discriminate patterns, using positive and negative examples,\nare eliminated. Instead, the objective of the RTM is to use the clauses to map\nthe sum of the clause outputs into one single continuous output. The discrep-\nancy between predicted and target output is minimized with a new feedback\nscheme tailored for regression, including a modi\ufb01ed stochastic activation proba-\nbility function."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c846b-934e-11ee-a75d-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 2, "chroma:document": "Paper Organization. The remainder of the paper is organized as follows. In\nSection 2, we present the main contribution of this paper, which is the RTM, and\nhow we build it upon the CTM. We then investigate the behavior of the RTM\nusing six di\ufb00erent arti\ufb01cial datasets in Section 3. We demonstrate empirically\nthat the RTM is superior both to the CTM as well as its multiclass version when\nit comes to predicting continuous output. We conclude our work in Section 4."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c846c-934e-11ee-be9f-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 2, "chroma:document": "2 The Regression Tsetlin Machine (RTM)\nThe RTM is a novel variant of the CTM. To highlight the unique properties of\nthe RTM, we start this section with \ufb01rst reviewing the TM in more detail, and\nthen discuss how it can be modi\ufb01ed to support continuous output.\n2.1 The Classic Tsetlin Machine (CTM)\nAt the heart of the TM, we \ufb01nd multiple teams of TAs that build conjunctive\nclauses in propositional logic. The purpose is to capture hidden patterns in the\ndata."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c846d-934e-11ee-8ff7-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 2, "chroma:document": "data.\nLearning with TAs. Each Tsetlin Automaton (TA) learns the optimal\naction in an environment by sequentially performing the actions that the envi-\nronment o\ufb00ers. To identify the optimal actions, the TAs adjust their states based\non the feedback they receive from the environment, which can be penalties or\nrewards. Asymptotically, a TA identi\ufb01es the action that provides the highest\nprobability of reward [10, 11]. These simple learning devices are capable of on-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c846e-934e-11ee-a8f2-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 2, "chroma:document": "line learning, have a simple structure, and require modest computational power.\nYet, they are able to learn accurately with relatively few interactions with the\nenvironment [12,13].\nClause Formation and the TA Team. The TM bases its operations on\nthe simplest form of TAs, namely, the two action one, with \ufb01nite memory depth.\nAs illustrated in Table 1, a team of TAs cooperates to form a clause. The table\ndepicts the steps leading to a clause being formed. Consider an input feature"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c846f-934e-11ee-a0f8-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 2, "chroma:document": "Table 1. The steps used to form a clause based on the input features and the actions\nof the TAs.\nPhase  Operations  Comment s \n1 \ud835\udc651 \ud835\udc652 \u2026\u2026\u2026\u2026\u2026  \ud835\udc65\ud835\udc5c Input Features, \ud835\udc7f \n2 \ud835\udc651 \u00ac\ud835\udc651 \ud835\udc652  \u00ac\ud835\udc652  \ud835\udc65\ud835\udc5c \u00ac\ud835\udc65\ud835\udc5c Literals  \n3 TA11 TA12 TA21 TA22 \u2026\u2026\u2026 \u2026\u2026.  TA \ud835\udc5c1 TA \ud835\udc5c2 TA \n4 in ex ex in \u2026\u2026\u2026\u2026\u2026\u2026.  ex in Actions  = {in, ex} \n5 \ud835\udc651 \u0245 \u00ac\ud835\udc652 \u0245\u2026\u2026\u2026\u0245  \u00ac\ud835\udc65\ud835\udc5c c1 = \u22c0 \ud835\udc65\ud835\udc58\ud835\udc5c\n\ud835\udc58=1 ,    \u2200 TA\ud835\udc581 = in  \n \nc2 = \u22c0 \u00ac\ud835\udc65\ud835\udc58\ud835\udc5c\n\ud835\udc58=1 ,   \u2200 TA\ud835\udc582 = in \nC = c1 \u0245 c2 \n \nPhase  Operations  Comments  \n1 x1 x2 \u2026\u2026\u2026\u2026\u2026  Xn X = [x1, x2, x3, \u2026\u2026. Xn] \n2 x1 \u00ac x1 x2  \u00ac x2"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8470-934e-11ee-89c5-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 2, "chroma:document": "2 x1 \u00ac x1 x2  \u00ac x2  \nxn \u00ac xn Literals  \n3 TA11 TA12 TA21 TA22 \u2026\u2026\u2026\u2026\u2026.  TA \ud835\udc5b1 TA \ud835\udc5b2 TA \n4 in ex ex in \u2026\u2026\u2026\u2026\u2026\u2026.  ex in Actions = { in, ex} \n5 x1 \u0245 \u00ac x2 \u0245\u2026\u2026\u2026\u0245  \u00ac xo c1 = \u22c0 \ud835\udc65\ud835\udc58\ud835\udc5b\n\ud835\udc58=1,    \u2200 TA\ud835\udc581 = in  \n \nc2 = \u22c0 \u00ac\ud835\udc65\ud835\udc58\ud835\udc5b\n\ud835\udc58=1 ,   \u2200 TA\ud835\udc582 = in \n \nC = c1 \u0245 c2 \n \n \n \n\u2200 \n1 0 0  0 1 0  \n0 0 1  0 1 1  1 0 1 1 1 0  \n1 1 1  0 0 0"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8471-934e-11ee-af27-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 3, "chroma:document": "vectorX= [x1, x2, . . . , x o]. Each TA represents either an input feature xkor\nits negation\u00acxk(jointly referred to as literals). Further, each TA in the team\ndecides whether to include or exclude its assigned literal in the clause that the\nteam is forming. Accordingly, when there are oinput features, 2 \u00d7oTAs are\nneeded to form the clause. The two actions available to each TA are {in,ex}.\nHere, inrefers to including the literal controlled by the TA and exrefers to"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8472-934e-11ee-a80e-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 3, "chroma:document": "excluding it. As seen in the \ufb01nal step in the table, the included literals form a\nconjunctive clause, while the excluded ones are ignored.\nClauses and Voting. The number of clauses, m, needed for a particular\nproblem depends on the complexity of the dataset. It should at least be su\ufb03-\ncient to cover the full range of sub-patterns associated with each output {0, 1}.\nHowever, with hidden and unknown sub-patterns, a grid search is required to\n\ufb01nd the best m."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8473-934e-11ee-85c6-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 3, "chroma:document": "\ufb01nd the best m.\nThemclauses are assigned either a positive or negative polarity, and they\nvote separately to decide the \ufb01nal output of the TM. Clauses with odd index\nare assigned positive polarity ( C+) and they vote for the \ufb01nal output 1. Clauses\nwith even index are assigned negative polarity ( C\u2212) and they vote for the \ufb01nal\noutput 0. For both categories, a vote is submitted when the clause recognizes\na sub-pattern. If the clause is unable to \ufb01nd a sub-pattern, it declines to vote."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8474-934e-11ee-884b-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 3, "chroma:document": "Finally, the output, y, is decided based on the number of votes gained by each\ncategory{0, 1}as given in the Eq. (1):\ny=\uf8f1\n\uf8f4\uf8f2\n\uf8f4\uf8f31, if\u2211\nj=1,3,m\u22121C+\nj>\u2211\nj=2,4,mC\u2212\nj\n0, if\u2211\nj=1,3,m\u22121C+\nj<\u2211\nj=2,4,mC\u2212\nj.(1)\nLearning Procedure. Learning in the TM is based on reinforcement learn-\ning. The reward, penalty, and inaction probabilities that guide the TAs in all\nof the clauses depend on several factors, namely, the actual output, the clause"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8475-934e-11ee-88d4-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 3, "chroma:document": "output, the literal value, and the current state of the TA. The basic idea is to\nalter the number of votes belong to each output category when the output is a\nfalse negative or a false positive. In the TM, this is done by two types of feed-\nback \u2013 Type I and Type II. Type I feedback eliminates false negative output and\nreinforces true positive output, while Type II feedback eliminates false positive\noutput. Both of these kinds of feedback are summarized in Table 2."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8476-934e-11ee-807e-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 3, "chroma:document": "Type I feedback is given to clauses with positive polarity when the actual out-\nput, \u02c6y, is 1 and clauses with negative polarity when the actual output, \u02c6 y, is 0. The\nprobability of activation of Type I feedback is [ T\u2212max(\u2212T,min(T,\u2211m\nj=1Cj))]/2T.\nType II feedback is given to clauses with positive polarity when the actual out-\nput, \u02c6y, is 0 and clauses with negative polarity when the actual output, \u02c6 y, is 1. The\nprobability of activation of Type II feedback is [ T+max(\u2212T,min(T,\u2211m\nj=1Cj))]/2T."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8477-934e-11ee-a6b0-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 3, "chroma:document": "j=1Cj))]/2T.\nTAs remain unchanged if the vote di\ufb00erence,\u2211m\nj=1Cj, is higher than or equal\ntoTwhen \u02c6 y= 1 and lower than or equal to - Twhen \u02c6 y= 0, according to the\nactivation probabilities of each type of feedback.\nIn all brevity, when the target output for a training instance \u02c6Xis \u02c6y= 1, the\nvotes from the clauses with negative polarity must not outnumber the votes from"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8478-934e-11ee-88d7-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 4, "chroma:document": "the clauses with positive polarity (in order to correctly classify the instance).\nTherefore, clauses with positive polarity receive Type I feedback (the activation\nprobability increases with the number of voting clauses with negative polarity)\nsince this reinforces clauses which output 1. Similarly, clauses with negative\npolarity receive Type II feedback (the activation probability increases with the\nnumber of voting clauses with positive polarity) since this suppresses voting"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8479-934e-11ee-a716-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 4, "chroma:document": "activity by making clauses of negative polarity evaluate to 0. The procedure\nis similar when the target output is \u02c6 y= 0. The TM then needs to make sure\nthat more clauses with negative polarity provide votes compared to those with\npositive polarity. Eventually, the above feedback reduces the number of false\npositives and false negatives to make the TM learn the propositional formulae\nthat provide high accuracy output.\n2.2 The Multiclass Tsetlin Machine (MTM)"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c847a-934e-11ee-97e6-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 4, "chroma:document": "2.2 The Multiclass Tsetlin Machine (MTM)\nFor the CTM, the \ufb01nal summation operator aggregates all of the clause outputs\ninto one of the two available outputs: 0 or 1. However, for categorization tasks\nwith more classes than two, another design is needed. In the Multiclass Tsetlin\nMachine (MTM), clauses are partitioned equally among the classes. The clauses\nof each individual class then act separately, similarly to a single TM. However,"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c847b-934e-11ee-9a62-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 4, "chroma:document": "the votes output for each class then form the basis for classi\ufb01cation. That is, an\nargmax operator arbitrates the \ufb01nal class, based on the votes collected for each\nclass. When there are nclasses, the output ycan thus be expressed as:\ny= argmaxi=1,...,n{(\u2211\nj=1,3,...(m\nn)\u22121Ci\nj\u2212\u2211\nj=2,4,...(m\nn)Ci\nj)}\n. (2)\nThe training procedure is similar to the CTM training procedure. However,\nin the MTM, the clauses of the class being the target of the current training"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c847c-934e-11ee-ba3e-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 4, "chroma:document": "sample are treated as if \u02c6 y= 1, while the clauses of a randomly selected class\nfrom the remaining classes is treated as if \u02c6 y= 0. In each class, clauses with\npositive polarity vote to say that the output belongs to the considered class.\nTable 2. Type I and Type II feedback designed to eliminate false negative and false\npositive output.\nFeedback Type I II\nClause Output 1 0 1 0\nLiteral Value 1 0 1 0 1 0 1 0Current StateIncludeReward Probability (s-1)/s NA 0 0 0NA 0 0"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c847d-934e-11ee-a084-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 4, "chroma:document": "Inaction Probability 1/s NA (s-1)/s (s-1)/s 1NA 1 1\nPenalty Probability 0 NA 1/s 1/s 0NA 0 0\nExcludeReward Probability 0 1/s 1/s 1/s 0 0 0 0\nInaction Probability 1/s (s-1)/s (s-1)/s (s-1)/s 1 0 1 1\nPenalty Probability (s-1)/s 0 0 0 0 1 0 0\n\u2020s is the precision and controls the granularity of the sub-patterns captured [1]"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c847e-934e-11ee-ae6f-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 5, "chroma:document": "Similarly, the clauses with negative polarity vote to indicate that the output\ndoes not belong to the considered class.\n2.3 The Regression Tsetlin Machine (RTM)\nWhen the output is continuous, neither the CTM or the MTM above are ideal.\nHowever, we will now show that the CTM can be modi\ufb01ed to produce continuous\noutput by means of three pertinent modi\ufb01cations.\nIn CTM and MTM, the polarity of clauses is used to classify data into dif-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c847f-934e-11ee-9a56-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 5, "chroma:document": "ferent classes. We now remove the polarity of clauses, since we intend to use\nthe clauses as additive building blocks that can be used to calculate continuous\noutput. That is, we intend to map the total vote count into a single continuous\noutput. As a result, the complexity of the RTM is actually reduced.\nWith merely one type of clauses, the summation operator outputs a value\nbetween 0 and T, which is simply the number of clauses that evaluates to 1. This"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8480-934e-11ee-b097-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 5, "chroma:document": "value is then normalized to produce the regression output. Thus, through this\nsimple modi\ufb01cation, the TM can now produce continuous output, with precision\nthat increases with higher T.\nLet \u02c6ymaxdenote the maximum output value \u02c6 yamong the Ntraining samples\nY= [\u02c6y1,\u02c6y2,\u02c6y3, . . . , \u02c6yN]. Then the sum of the votes from the clauses\u2211m\nj=1Cj\nof the TM is normalized to achieve the regression output by dividing by Tand\nmultiplying with \u02c6 ymax. So, for the othtraining sample, ( \u02c6Xo,\u02c6yo), the TM output,"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8481-934e-11ee-b700-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 5, "chroma:document": "yo, is calculated from the input \u02c6Xoas follows:\nyo=\u2211m\nj=1Cj(\u02c6Xo)\u00d7\u02c6ymax\nT. (3)\nFeedback, then, is based on comparing the output, yoof the TM with the\ntarget output \u02c6 yo. The target value \u02c6 yocan be higher or lower than the output\nvalue yo. This is our basis for our new feedback scheme. That is, similarly to other\nmachine learning methods, certain internal operations are needed to minimize\nthe error between the predicted output, yo, and target output, \u02c6 yo. In the RTM,"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8482-934e-11ee-83a4-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 5, "chroma:document": "this is quite simply achieved by providing Type I and Type II feedbacks according\nto the following criteria:\nFeedback =\uf8f1\n\uf8f4\uf8f2\n\uf8f4\uf8f3Type I , ifyo<\u02c6yo,\nType II , ifyo>\u02c6yo.(4)\nAs with the CTM, the idea here is to increase the number of clauses that\noutput 1 when the predicted output is less than the target output ( yo<\u02c6yo). To\nachieve this, we then provide Type I feedback. Conversely, Type II feedback is\napplied to decrease the number of clauses that evaluate to 1 when the predicted"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8483-934e-11ee-84cd-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 5, "chroma:document": "output is higher than the target output ( yo>\u02c6yo).\nTo stabilize learning, we use an activation probability function that makes\nthe probability of giving a clause feedback proportional to the di\ufb00erence between"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8484-934e-11ee-824c-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 6, "chroma:document": "the predicted and target output (the error). That is, in the RTM, feedback to\nclauses is determined stochastically using the following activation probability\nfunction, Pact:\nPact=K\u00d7|yo\u2212\u02c6yo|\n\u02c6ymax. (5)\nAs seen, the magnitude of the function is adjusted with the constant K. The\nresulting activation function reduces the oscillation of the the predicted value\nduring the training process, stabilizing it around the target value."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8485-934e-11ee-8b44-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 6, "chroma:document": "The behavior of the RTM is studied in the following sections, in comparison\nwith the CTM and MTM.\n3 Empirical Results\n3.1 Experiment Setup\nWe study the behavior of the RTM using six di\ufb00erent datasets. These datasets\nhave been constructed to facilitate empirical analysis of the optimality of RTM\nlearning, with the underlying input-output mapping being known. Dataset I\ncontains 2-bit feature input. The output is 100 times larger than the decimal"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8486-934e-11ee-a1c2-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 6, "chroma:document": "value of the binary input (e.g., when the input is [1, 0], the output is 200).\nThe training set consists of 8000 samples while the testing set consists of 2000\nsamples, both without noise. Dataset II contains the same data as Dataset I,\nexcept that the output of the training data is perturbed to introduce noise. For\nDataset III we introduce 3-bit input, without noise, and for Dataset IV we have\n3-bit input with noisy output. Finally, Dataset V has 4-bit input without noise,"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8487-934e-11ee-847c-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 6, "chroma:document": "and Dataset VI has 4-bit input with noisy.\nEach input feature have been generated independently with equal probability\nof 0 and 1 values, leading to a more or less uniform distribution of bit values.\nIn order to increase our understanding of the RTM, we investigate the e\ufb00ect\nthe hyper-parameters Tandshave on learning.\nExperiment I : We \ufb01rst study the e\ufb00ect varying Thas on performance for the\ndi\ufb00erent datasets.\nExperiment II : The e\ufb00ect of di\ufb00erent svalues (controlling the number of"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8488-934e-11ee-8db7-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 6, "chroma:document": "sub-patterns) is further investigated for all of the datasets.\nExperiment III : We \ufb01nally compare the RTM results with what can be\nachieved with CTM and MTM.\n3.2 Results and Discussion\nWe use Mean Absolute Error ( MAE ) to measure performance. Fig. 1 plots error\nacross 200 epochs, with learning in\ufb02uenced by di\ufb00erent Tvalues. Fig. 1(a) shows"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8489-934e-11ee-888c-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 7, "chroma:document": "0102030\n1\n11\n21\n31\n41\n51\n61\n71\n81\n91\n101\n111\n121\n131\n141\n151\n161\n171\n181\n191MAEa: Dataset -I 3-T(0.00) 10-T(7.80)\n30-T(0.00) 100-T(0.78)\n500-T(0.50) 1000-T(0.20)\n4000-T(0.33)\n050100\n1\n11\n21\n31\n41\n51\n61\n71\n81\n91\n101\n111\n121\n131\n141\n151\n161\n171\n181\n191MAEb: Dataset -II3-T(7.15) 10-T(10.96)\n30-T(8.78) 100-T(5.36)\n500-T(5.53) 1000-T(5.23)\n4000-T(5.36)\n050100150\n1\n11\n21\n31\n41\n51\n61\n71\n81\n91\n101\n111\n121\n131\n141\n151\n161\n171\n181\n191MAEc: Dataset -III 7-T(0.00) 20-T(14.63)\n70-T(0.00) 300-T(1.86)"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c848a-934e-11ee-95ef-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 7, "chroma:document": "70-T(0.00) 300-T(1.86)\n700-T(0.96) 2000-T(1.04)\n4000-T(0.90)\n050100150\n1\n11\n21\n31\n41\n51\n61\n71\n81\n91\n101\n111\n121\n131\n141\n151\n161\n171\n181\n191MAEd: Dataset -IV 7-T(7.34) 20-T(13.82)\n70-T(6.60) 300-T(5.83)\n700-T(5.87) 2000-T(5.59)\n4000-T(5.54)\n0102030\n1\n11\n21\n31\n41\n51\n61\n71\n81\n91\n101\n111\n121\n131\n141\n151\n161\n171\n181\n191MAE\nEpoche: Dataset -V 7-T(9.84) 15-T(0.00)\n70-T(1.69) 150-T(0.00)\n700-T(0.24) 1500-T(0.15)\n4000-T(0.16)\n0100200300\n1\n11\n21\n31\n41\n51\n61\n71\n81\n91\n101\n111\n121\n131\n141\n151\n161\n171\n181"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c848b-934e-11ee-90bb-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 7, "chroma:document": "61\n71\n81\n91\n101\n111\n121\n131\n141\n151\n161\n171\n181\n191MAE\nEpochf: Dataset -VI 7-T(79.78) 15-T(51.43)\n50-T(13.11) 150-T(10.26)\n700-T(5.53) 1500-T(5.23)\n4000-T(5.39)Fig. 1. Training error over training epochs. Each dataset is processed with di\ufb00erent T.\nthe results for Dataset I, Fig. 1(b) reports results for Dataset II, and so on. MAE\nafter 200 epochs is also given in brackets for each threshold in the legend.\nFrom Fig. 1, we can observe that just 3 clauses ( T= 3) are enough to reduce"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c848c-934e-11ee-9bac-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 7, "chroma:document": "error to zero for Dataset I, which can be explained by the noise-free data. Because\nthe output value is decided by the number of clauses that output 1, we require\ntwoclauses with TA1\n1={in}, TA2\n1={ex}, TA1\n2={ex}, and TA2\n2={ex}\nto capture the pattern (1 .); see Phase 4 in Table 1. Further, we need one\nclause with TA1\n1={ex}, TA2\n1={ex}, TA1\n2={in}, and TA2\n2={ex}to capture\nthe pattern ( .1). Here, .means an input feature that can take an arbitrary"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c848d-934e-11ee-97d4-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 7, "chroma:document": "value, either 0 or 1. These three clauses can collectively form any outputs for the\nDataset I as shown in Table 3. For instance, input (0 1) only activates the clause\nwith TA1\n1={ex}, TA2\n1={ex}, TA1\n2={in}, and TA2\n2={ex}, which represents\nthe pattern ( .1). Accordingly, the RTM correctly computes the output, 100.\nLikewise, input (1 0) only activates the twoclauses with TA1\n1={in}, TA2\n1=\n{ex}, TA1\n2={ex}, and TA2\n2={ex}, which represent the pattern (1 .). Thus,"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c848e-934e-11ee-ac28-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 7, "chroma:document": "2={ex}, which represent the pattern (1 .). Thus,\nthe output 200 is correctly computed. All the clauses are activated when the\ninput is (1 1) and therefore the output 300 is computed correctly as well."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c848f-934e-11ee-8abb-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 8, "chroma:document": "Table 3. Computing output for di\ufb00erent datasets by activating di\ufb00erent clauses.\nDataset Output Required number of clauses to represent di\ufb00erent patterns\u2020\u2020\nI0 None\n100 1\u00d7(.1)\n200 2\u00d7(1.)\n300 2\u00d7(1.) + 1 \u00d7(.1)\nIII0 None\n100 1\u00d7(. . 1)\n200 2\u00d7(.1.)\n300 2\u00d7(.1.) + 1 \u00d7(. . 1)\n400 4\u00d7(1. .)\n500 4\u00d7(1. .) + 1 \u00d7(. . 1)\n600 4\u00d7(1. .) + 2 \u00d7(.1.)\n700 4\u00d7(1. .) + 2 \u00d7(.1.) + 1 \u00d7(. . 1)\nV0 None\n100 1\u00d7(. . . 1)\n200 2\u00d7(. . 1.)\n300 2\u00d7(. . 1.) + 1 \u00d7(. . . 1)\n400 4\u00d7(.1. .)\n500 4\u00d7(.1. .) + 1 \u00d7(. . . 1)"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8490-934e-11ee-a705-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 8, "chroma:document": "400 4\u00d7(.1. .)\n500 4\u00d7(.1. .) + 1 \u00d7(. . . 1)\n600 4\u00d7(.1. .) + 2 \u00d7(. . 1.)\n700 4\u00d7(.1. .) + 2 \u00d7(. . 1.) + 1 \u00d7(. . . 1)\n800 8\u00d7(1. . . )\n900 8\u00d7(1. . . ) + 1 \u00d7(. . . 1)\n1000 8\u00d7(1. . . ) + 2 \u00d7(. . 1.)\n1100 8\u00d7(1. . . ) + 2 \u00d7(. . 1.) + 1 \u00d7(. . . 1)\n1200 8\u00d7(1. . . ) + 4 \u00d7(.1. .)\n1300 8\u00d7(1. . . ) + 4 \u00d7(.1. .) + 1 \u00d7(. . . 1)\n1400 8\u00d7(1. . . ) + 4 \u00d7(.1. .) + 2 \u00d7(. . 1.)\n1500 8\u00d7(1. . . ) + 4 \u00d7(.1. .) + 2 \u00d7(. . 1.) + 1 \u00d7(. . . 1)\n\u2020\u2020for example, \u201c twoclauses to represent the pattern (1 .)\u201d is written as \u201c2 \u00d7(1.)\u201d"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8491-934e-11ee-a6e2-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 8, "chroma:document": "We observe similar behaviour for Dataset III and Dataset V. More speci\ufb01-\ncally, Dataset III requires seven clauses to represent the three di\ufb00erent patterns\nit contains, namely, (4 \u00d7(1. .), 2\u00d7(.1.), 1\u00d7(. .1))1. Further, Dataset\nV requires \ufb01fteen clauses to represent four di\ufb00erent patterns it contains (8 \u00d7\n(1. . . ), 4\u00d7(.1. .), 2\u00d7(. . 1.), 1\u00d7(. . . 1)). As we can see\nfrom these 3 datasets, RTM can reach 0.00 for the training MAE when Tis a"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8492-934e-11ee-9332-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 8, "chroma:document": "multiplier of the minimum required clauses. For example, Dataset I can also be\nperfectly learned when there are 30 clauses.\nHowever, when Tis not a multiplier of the minimum required clauses, RTM\ncannot align its output yoto the target output \u02c6 yoduring the training phase.\nFor instance, by assigning four clauses for Dataset I, the training will end up\nwith e.g. allocating three clauses to represent the pattern (1 .) or twoclauses"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8493-934e-11ee-8982-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 8, "chroma:document": "to represent the pattern ( .1). As a result, one or more output values cannot\nbe computed correctly. For example, if there are three clauses for the pattern (1\n.) and oneclause for the pattern ( .1) after training, input (1 0) activates the\n1In this expression, \u201c four clauses to represent the pattern (1 . .)\u201d is written as \u201c4\n\u00d7(1. .)\u201d"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8494-934e-11ee-90d7-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 9, "chroma:document": "0100200300400500600700\n1 2 3 4 5 6 7 8 9 10MAE\nsDataset-II (30-T)\nDataset-IV (70-T)\nDataset-VI (150-T)Fig. 2. Variation of MAE over di\ufb00erent sfor \ufb01xed T.\nPhase  Operations  Comment s \n1 x1 x2 \u2026\u2026\u2026\u2026\u2026  xr X = [x1, x2, x3, \u2026\u2026. x r] \n2 x1 \u00ac x1 x2  \u00ac x2  \nxr \u00ac xr Literals  \n3 TA11 TA12 TA21 TA22 \u2026\u2026\u2026 \u2026\u2026.  TA\ud835\udc5f1 TA\ud835\udc5f2 TA \n4 in ex ex in \u2026\u2026\u2026\u2026\u2026\u2026.  ex in Actions = { in, ex} \n5 x1 \u0245 \u00ac x2 \u0245\u2026\u2026\u2026\u0245  \u00ac xr c1 = \u22c0\ud835\udc65\ud835\udc56\ud835\udc5f\n\ud835\udc56=1,    \u2200 TA\ud835\udc561 = in  \n \nc2 = \u22c0\u00ac\ud835\udc65\ud835\udc56\ud835\udc5f\n\ud835\udc56=1 ,   \u2200 TA\ud835\udc562 = in \n \nC = c1 \u0245 c2 \n \n \n\u2200 \n1 0 0  0 1 0"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8495-934e-11ee-96af-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 9, "chroma:document": "C = c1 \u0245 c2 \n \n \n\u2200 \n1 0 0  0 1 0  \n0 0 1  0 1 1  1 0 1 1 1 0  \n1 1 1  0 0 0  \nFig. 3. Pattern distribution for the 3-bits input datasets.\nclauses that represent the pattern (1 .), producing an incorrect output that is\n300. Likewise, input (1 1) activates all four clauses to incorrectly compute the\noutput 400.\nAs a strategy for problems where the number of clauses is unknown, and\nfor real-world applications where noise plays a signi\ufb01cant role, the RTM can be"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8496-934e-11ee-aa3e-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 9, "chroma:document": "initialized with a much larger T. Then, since the output, yo, is a fraction of the\nthreshold, T, the error decreases. This behaviour is veri\ufb01ed empirically in Fig. 1,\nshowing how increasing Tleads to reduced error.\nThe e\ufb00ect of sis studied by increasing it from 1 .0 to 10 .0 for Dataset II,\nDataset IV, and Dataset VI, with \ufb01xed T. Fig. 2 shows the variation of MAE\nover various svalues for noisy data. The MAE decreases when sincreases from"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8497-934e-11ee-875f-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 9, "chroma:document": "1.0 to 2 .0. After 2 .0,MAE increases, and then stabilizes after a while.\nFor all of the datasets considered here, the optimum s, where the RTM learns\nthe datasets with minimum MAE , is equal to 2 .0. The reason can be explained\nwith the aid of Fig. 3, where one sees the distribution of patterns when the\ndataset has 3 input bits.\nThe occurrence probability of any of the 3-bit patterns is1\n8since there are\noverall 8 unique patterns. However, to capture the pattern (1 . .) (shaded"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8498-934e-11ee-ac62-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 9, "chroma:document": "area), according to the TM dynamics [1],1\nsshould be equal to the probability\nof the considered pattern, which is4\n8(=1\n2). Hence, sshould be 2. For instance,\nif someone assigns s= 4, clauses will start to learn much \ufb01ner patterns, such"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8499-934e-11ee-8879-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 10, "chroma:document": "as (1 0 .), (1 1 .), and (0 1 .). This signi\ufb01cantly increases the number of\nclauses needed to capture the sub-patterns. This is also the case for Dataset\nII and Dataset VI. Then, the probability that (1 .) occurs is2\n4(=1\n2) and the\nprobability that (1 . . . ) occurs is7\n14(=1\n2).\nTo compare the performance of the RTM with CTM and MTM, each model\nis tested with di\ufb00erent Tvalues. The training and testing MAE for all the cases\nare summarized in Table 4 and 5, respectively."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c849a-934e-11ee-8115-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 10, "chroma:document": "are summarized in Table 4 and 5, respectively.\nTable 4. Training MAE after 200 training epochs with di\ufb00erent Ton various methods.\nRTM CTM MTM\nT 3 10 30 100 500 1000 4000 68000 1000 10000 16000Dataset1MAE 0.0 7.8 0.0 0.8 0.5 0.2 0.3 7.7 0.0 0.0 0.0 0.0\n2MAE 7.2 11.0 8.8 5.4 5.5 5.2 5.4 11.1 24.1 8.4 7.1 7.9\nT 7 20 70 300 700 2000 5000 14 8000 2000 10000 16000\n3MAE 0.0 14.6 0.0 1.9 1.00 1.0 0.9 0.0 0.0 18.3 0.0 0.0\n4MAE 7.4 13.8 6.6 5.8 5.9 5.6 5.5 111.3 13.3 14.2 8.8 8.4"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c849b-934e-11ee-a69f-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 10, "chroma:document": "T 7 15 70 150 700 1500 4000 30 8000 4000 10000 16000\n5MAE 9.8 0.0 1.7 0.0 0.2 0.2 0.2 149.7 158.7 373.1 0.0 0.0\n6MAE 79.8 51.4 13.1 10.3 5.5 5.3 5.4 181.5 96.4 449.9 8.0 7.8\nTable 5. Testing MAE for di\ufb00erent Ton various methods.\nRTM CTM MTM\nT 3 10 30 100 500 1000 4000 68000 1000 10000 16000Dataset1MAE 0.0 7.6 0.0 0.8 0.5 0.2 0.3 9.0 0.0 0.0 0.0 0.0\n2MAE 5.0 10.6 7.1 1.2 2.7 1.6 1.8 9.4 25.3 7.5 5.4 7.0\nT 7 20 70 300 700 2000 5000 14 8000 2000 10000 16000"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c849c-934e-11ee-8509-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 10, "chroma:document": "3MAE 0.0 14.2 0.0 2.1 1.0 1.2 1.0 0.0 0.0 22.0 0.0 0.0\n4MAE 5.0 14.5 4.2 3.3 3.4 1.9 2.7 98.5 12.5 16.0 8.7 8.3\nT 7 15 70 150 700 1500 4000 30 8000 4000 10000 16000\n5MAE 9.9 0.0 1.8 0.0 0.3 0.2 0.2 154.6 155.5 372.9 0.0 0.0\n6MAE 78.0 50.1 12.5 8.5 3.5 2.7 2.8 191.3 102.4 431.3 6.9 6.7\nThe training and testing MAE reach zero when the RTM operates with noise\nfree data and when Tequals the optimum clauses required. When the optimum"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c849d-934e-11ee-832c-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 10, "chroma:document": "Tis unknown, and when data is noisy, applying a higher Tis bene\ufb01cial. As an\nexample, Dataset III, which has 3 bits as inputs, can be perfectly learned with T\nequal to 7 and 70. For the same dataset, RTM acquires training MAE 1.0 with\nTequaling 700, which is better than the MAE of 14.2 obtained when Tequals\n20.\nFor CTM, the outputs are converted to bits and each bit position is then\ntrained and predicted separately. According to the training and testing MAE in"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c849e-934e-11ee-b791-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 10, "chroma:document": "Table 4 and 5, CTM works better with less complex datasets such as Dataset"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c849f-934e-11ee-9003-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 11, "chroma:document": "I and Dataset III. However, with a higher number of inputs and with noisy\ntraining data, performance decreases.\nMTM requires a large number of clauses by nature when it works with con-\ntinuous outputs since it has to consider all possible values from 0 to \u02c6 ymaxas\ndistinct classes (e.g. 300 classes for Dataset I and Dataset II, and 700 classes for\nDataset III and Dataset IV). According to the training and testing MAE in the"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84a0-934e-11ee-a472-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 11, "chroma:document": "Tables 4 and 5, MTM requires roughly 3 clauses or more per class. For instance,\nthe features in Dataset I can be learned with 1000 clauses, yet that amount is\ninsu\ufb03cient for Dataset III and Dataset V. Note that the noise free datasets can\nbe learned perfectly with 10000 or more clauses. However, this accuracy gain is\naccompanied with a larger computational cost.\nOverall, RTM obtains the best training and testing MAE for both noisy"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84a1-934e-11ee-9893-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 11, "chroma:document": "and noise free data with a smaller number of clauses compared with the CTM\nand MTM. Dataset II, Dataset IV, and Dataset VI are more similar to real-\nworld datasets by being noisy. The minimum MAE values obtained by RTM\nfor these three Datasets are 1.6, 1.9, and 2.7, respectively. The average of these\nminimum MAE values (2.07) is approximately 20 and 3.5 times lower than the\naverages obtained with CTM and MTM, respectively. In terms of the number of"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84a2-934e-11ee-93dd-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 11, "chroma:document": "clauses required to achieve the above results, RTM utilizes 1000 clauses, while\nCTM and MTM utilize 8 and 16 times more clauses than that. This di\ufb00erence is\ncharacteristic for RTM \u2013 it provides better MAE with less computational power.\n4 Conclusion\nIn this paper we proposed the Regression Tsetlin Machine (RTM), a novel variant\nof the Classic Tsetlin Machine that supports continuous output in regression\nproblems. In RTM, the polarities in clauses were removed and the total clause"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84a3-934e-11ee-ae1e-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 11, "chroma:document": "output was normalized to produce continuous output predictions. The number of\nclauses to receive the feedback in RTM was decided stochastically using a linear\nactivation probability function. The prediction power of this novel approach was\nstudied using six di\ufb00erent datasets, with noise free and noisy training data. Our\nempirical results showed signi\ufb01cantly better performance of RTM compared with\nCTM and MTM, both in terms of training and the testing error, as well as the"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84a4-934e-11ee-bf05-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 11, "chroma:document": "computational power required.\nPotential applications for RTM can be weather prediction, sales forecasting,\nstock predictions, energy forecasting, and outbreak forecasting, to name a few.\nIn our future work, we will evaluate RTM on the aforementioned applications\nand performance will be compared with conventional machine learning methods.\nReferences\n1. O.-C. Granmo, \u201cThe Tsetlin Machine - A Game Theoretic Bandit Driven Ap-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84a5-934e-11ee-8035-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 11, "chroma:document": "proach to Optimal Pattern Recognition with Propositional Logic,\u201d arXiv e-prints,\np. arXiv:1804.01508 , Apr 2018\n2. M. L. Tsetlin, \u201dOn Behaviour of Finite Automata in Random Medium,\u201d Avtom I\nTelemekhanika , vol. 22, pp. 1345-1354, 1961."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84a6-934e-11ee-a932-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 12, "chroma:document": "3. O.-C. Granmo and B. J. Oommen, \u201dSolving Stochastic Nonlinear Resource Alloca-\ntion Problems Using a Hierarchy of Twofold Resource Allocation Automata,\u201d IEEE\nTransaction on Computers , vol. 59, no. 4, pp. 545-560, 2010.\n4. B. J. Oommen, S.-W. Kim, M. T. Samuel, and O.-C. Granmo, \u201dA Solution to the\nStochastic Point Location Problem in Metalevel Nonstationary Environments,\u201d IEEE\nTransactions on Systems, Man, and Cybernetics, Part B (Cybernetics) , vol. 38, no.\n2, pp. 466-476, 2008."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84a7-934e-11ee-9b86-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 12, "chroma:document": "2, pp. 466-476, 2008.\n5. B. Tung and L. Kleinrock, \u201dUsing Finite State Automata to Produce Self-\nOptimization and Self-Control,\u201d IEEE transactions on parallel and distributed sys-\ntems, vol. 7, no. 4, pp. 439-448, 1996.\n6. N. Bouhmala and O.-C. Granmo, \u201dStochastic Learning for SAT-Encoded Graph\nColoring Problems,\u201d International Journal of Applied Metaheuristic Computing\n(IJAMC) , vol. 1, no. 3, pp. 1-19, 2010.\n7. K. Abeyrathna, O.-C. Granmo, and M. Goodwin, \u201dA Novel Tsetlin Automata"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84a8-934e-11ee-8865-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 12, "chroma:document": "Scheme to Forecast Dengue Outbreaks in the Philippines,\u201d 2018 IEEE 30th Interna-\ntional Conference on Tools with Arti\ufb01cial Intelligence (ICTAI) , pp. 680- 685, IEEE,\n2018.\n8. G. T. Berge, O.-C. Granmo, T. Oddbj\u00f8rn Tveit, M. Goodwin, L. Jiao, and B.\nViggo Matheussen, \u201dUsing the Tsetlin Machine to Learn Human-Interpretable Rules\nfor High-Accuracy Text Categorization with Medical Applications,\u201d arXiv e-prints,\np. arXiv:1809.04547 , Sep 2018."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84a9-934e-11ee-b760-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 12, "chroma:document": "p. arXiv:1809.04547 , Sep 2018.\n9. K. Abeyrathna, O.-C. Granmo, X. Zhang, and M. Goodwin, \u201dA Scheme for Con-\ntinuous Input to the Tsetlin Machine With Applications to Forecasting Disease Out-\nbreaks,\u201d arXiv e-prints, p. arXiv:1905.04199 , May 2019.\n10. S. Misra, P. V. Krishna, and K. I. Abraham, \u201dA Simple Learning Automata-Based\nSolution for Intrusion Detection in Wireless Sensor Networks,\u201d Wireless Communi-\ncations and Mobile Computing , vol. 11, no. 3, pp. 426-441, 2011."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84aa-934e-11ee-985c-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\1905.04206.pdf", "page": 12, "chroma:document": "11. T. A. Tuan, L. C. Tong, and A. Premkumar, \u201dAn Adaptive Learning Automata\nAlgorithm for Channel Selection in Cognitive Radio Network,\u201d 2010 International\nConference on Communications and Mobile Computing , pp. 159-163, IEEE, 2010.\n12. K. S. Narendra and M. A. Thathachar, Learning Automata: An Introduction.\nCourier Corporation , 2012.\n13. K. Narendra and M. Thathachar, \u201dLearning Automata-A Survey,\u201d IEEE Transac-\ntions on systems, man, and cybernetics , no. 4, pp. 323-334, 1974."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84ab-934e-11ee-9692-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 0, "chroma:document": "royalsocietypublishing.org/journal/rsta\nResearch\nCitethisarticle: DarshanaAbeyrathnaK,\nGranmoO-C,ZhangX,JiaoL,GoodwinM.2019\nTheregressionTsetlinmachine:anovelapproachtointerpretablenonlinearregression. P h i l .T r a n s .R .S o c .A 378:20190165.\nhttp://dx.doi.org/10.1098/rsta.2019.0165\nAccepted:30September2019Onecontributionof13toathemeissue\n\u2018Harmonizingenergy-autonomouscomputingandintelligence\u2019.\nSubjectAreas:\nartificialintelligence\nKeywords:"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84ac-934e-11ee-b5f1-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 0, "chroma:document": "SubjectAreas:\nartificialintelligence\nKeywords:\nTsetlinmachine,regressionTsetlinmachine,patternrecognitionwithpropositionallogic,\nInterpretableAI,interpretablemachine\nlearning,nonlinearregression\nAuthorforcorrespondence:\nK.DarshanaAbeyrathna\ne-mail:darshana.abeyrathna@uia.noTheregressionTsetlin\nmachine:anovelapproachtointerpretablenonlinearregression\nK.DarshanaAbeyrathna,Ole-ChristofferGranmo,\nXuanZhang,LeiJiaoandMortenGoodwin\nCentreforArtificialIntelligenceResearch,UniversityofAgder,"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84ad-934e-11ee-bfad-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 0, "chroma:document": "Grimstad,Norway\nKDA,0000-0003-4816-2597\nRelying simply on bitwise operators, the recently\nintroduced Tsetlin machine (TM) has provided\ncompetitive pattern classi\ufb01cation accuracy in several\nbenchmarks, including text understanding. In this\npaper, we introduce the regression Tsetlin machine\n(RTM), a new class of TMs designed for continuous\ninput and output, targeting nonlinear regression\nproblems. In all brevity, we convert continuous inputinto a binary representation based on thresholding,"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84ae-934e-11ee-b532-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 0, "chroma:document": "and transform the propositional formula formed by\nthe TM into an aggregated continuous output. Ourempirical comparison of the RTM with state-of-the-art\nregression techniques reveals either superior or on\npar performance on \ufb01ve datasets.\nThis article is part of the theme issue \u2018Harmonizing\nenergy-autonomous computing and intelligence\u2019.\n1. Introduction\nOver the last few years, there has been tremendous\nprogress in research on predictive models, resulting in"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84af-934e-11ee-bdee-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 0, "chroma:document": "increasingly higher predictive accuracy. However, highpredictive accuracy is not always suf\ufb01cient to trust\na predictive model. For applications where humans\nare making the \ufb01nal decision, the rationale behind a\nprediction can sometimes be essential to the decision-\nmaking process. Therefore, human interpretability of\nresults is of great importance [ 1]. This importance has\nbeen emphasized in many application domains such as\ncredit scoring [ 2,3], medicine [ 4,5], bioinformatics [ 6,7]"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84b0-934e-11ee-9d83-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 0, "chroma:document": "and churn prediction [ 8,9].\n2019TheAuthor(s)PublishedbytheRoyalSociety.Allrightsreserved.\n Downloaded from https://royalsocietypublishing.org/ on 05 December 2023"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84b1-934e-11ee-b856-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 1, "chroma:document": "2royalsocietypublishing.org/journal/rsta P h i l .T r a n s .R .S o c .A 378:20190165................................................................The Tsetlin machine (TM) is a recent pattern recognition approach that attempts to bridge the\ngap between the interpretability of rule-based techniques and the high predictive accuracy of\ndeep learning [ 10].\nThe TM is relatively simple computationally, being based on propositional logic to form the"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84b2-934e-11ee-b70d-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 1, "chroma:document": "classi\ufb01er, and straightforward bitwise operations for recognition and learning. This structuremakes the TM interpretable, yet it achieves competitive accuracy for many pattern recognition\nproblems.\nThe inputs and output of the TM are propositional variables, represented as bits. In the \ufb01rst\nTM layer, the inputs and their negations, referred to as literals, are connected by conjunctions\nto form so-called conjunctive clauses . In the second layer, the output of the TM is decided by a"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84b3-934e-11ee-9429-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 1, "chroma:document": "majority vote among the clauses that have been formed in layer one. For learning patterns, eachclause is assigned one Tsetlin automaton (TA) [ 11] per literal. A literal takes part in a clause if the\ndesignated TA decides to include it. To make this decision, the TA interacts with its environment\n(the rest of the TM) in an iterative manner. It decides the next action based on its current state,which, in turn, is in\ufb02uenced by the feedback it receives. Feedback in the TM is governed by a"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84b4-934e-11ee-ba31-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 1, "chroma:document": "novel game, with each TA trying to learn the optimal action after a series of interactions with the\nenvironment [ 10].\nThe use of TAs to solve complex problems has a long history. Illustrative work includes\nforecasting disease outbreaks [ 12], graph colouring [ 13], distributed coordination [ 14], stochastic\nsearching on the line [ 15], and resource allocation [ 16]. Despite its simplicity, the TM has provided"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84b5-934e-11ee-b39f-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 1, "chroma:document": "competitive results in comparison with traditional machine learning techniques, including\nmultilayer perceptrons, support vector machines, logistic regression and Na\u0131ive Bayes, in well-known benchmarks such as handwritten digits classi\ufb01cation (MNIST), Iris data classi\ufb01cation,\nand classi\ufb01cation of Noisy XOR data with non-informative features [ 10]. Recently, Berge et al."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84b6-934e-11ee-a2c1-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 1, "chroma:document": "also studied the ability of the TM to categorize natural language text simply based on a documentword presence vector [ 17]. They further investigated the interpretability of the produced clauses,\nfor analysing electronic health records. This work demonstrated that the TM in some cases can\noutperform vanilla deep learning techniques, including convolutional neural networks (CNN)and long short-term memory (LSTM) neural networks, while keeping the important property of\ninterpretability."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84b7-934e-11ee-9f2d-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 1, "chroma:document": "interpretability.\nPaper Contributions: The classic TM has been designed for binary inputs and output.\nAlthough continuous input and output can be encoded in bit form, the natural ordering of\nnumbers is lost. We address this limitation in the present paper by introducing the regression\nTsetlin machine (RTM), which consists of three parts:\n(i) For continuous input, we propose a data preprocessing procedure that transforms the"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84b8-934e-11ee-897e-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 1, "chroma:document": "input losslessly into a binary representation that maintains semantic relationship betweennumbers. In brief, the preprocessing procedure considers each unique data sample in each\ncontinuous feature as a potential threshold. The original data samples are then compared\nwith the complete set of thresholds to create a new feature matrix that only contains bits.\n(ii) To produce continuous output that leverages the natural ordering of numbers, we modify"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84b9-934e-11ee-9466-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 1, "chroma:document": "the inner inference mechanism of the TM. That is, the inputs are transformed into a single\ncontinuous output, rather than to distinct categories. We achieve this by eliminating the\npolarities of the clauses, and by summing all the non-polarized votes, mapping the sum\ninto a continuous output.\n(iii) Finally, we propose a new feedback scheme for guiding the TA of the RTM, to support\nregression. This scheme minimizes the discrepancy between the predicted and the target"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84ba-934e-11ee-8151-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 1, "chroma:document": "outputs, with the aid of a modi\ufb01ed stochastic clause activation function.\nPaper Organization: The remainder of the paper is organized as follows. In \u00a72, we discuss\nthe structure and inference mechanisms of the TM, with a particular focus on the parts of thearchitecture that we build upon. Then, in \u00a73 and 4, we present the main contribution of this\npaper, which is the data preprocessing and regression procedures, leading to the RTM. The RTM"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84bb-934e-11ee-a154-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 1, "chroma:document": "Downloaded from https://royalsocietypublishing.org/ on 05 December 2023"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84bc-934e-11ee-a3c3-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 2, "chroma:document": "3royalsocietypublishing.org/journal/rsta P h i l .T r a n s .R .S o c .A 378:20190165................................................................is analysed empirically in \u00a75 by the help of both arti\ufb01cial and real-world datasets, in comparison\nwith selected state-of-the-art regression techniques. We conclude our work in \u00a76.\n2. TheTsetlinmachine\nIn classi\ufb01cation problems, a class can be represented by its constituting sub-patterns. The TM has"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84bd-934e-11ee-86a9-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 2, "chroma:document": "been designed to capture these sub-patterns explicitly by operating upon a series of conjunctiveclauses, how many decided by the user. The structure of the TM as well as the procedures for\nrecognition and learning are described in the following.\nTM structure: Consider an input feature vector X=(x\nk)\u2208{0, 1}oconsisting of opropositional\nvariables xkwith domain {0, 1}. The TM considers both the features xkt h e m s e l v e sa sw e l la s"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84be-934e-11ee-b2e6-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 2, "chroma:document": "their negations \u00acxk(the literals) when forming the clauses. In all brevity, each clause jtakes the\nfollowing form:\ncj=1\u2227\u239b\n\u239c\u239d\u22c0\nk\u2208II\njxk\u239e\n\u239f\u23a0\u2227\u239b\n\u239c\u239d\u22c0\nk\u2208\u00afII\nj\u00acxk\u239e\n\u239f\u23a0. (2.1)\nAbove, II\njand\u00afII\njare non-overlapping subsets of the input variable indexes, II\nj,\u00afII\nj\u2286{1,...,o},II\nj\u2229\n\u00afII\nj=\u2205, that specify which of the literals take part in the clause j. The indexes of the included\noriginal features are found in II\njwhile the indexes of the included negated features are found in \u00afII\nj."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84bf-934e-11ee-9ca9-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 2, "chroma:document": "j.\nThe upper index Isignals that the literals in the subsets are included . Conversely, IE\njand\u00afIE\njspecify\nthe literals that are excluded .\nTo simplify notation, we now introduce an augmented feature vector X\u2032, which can be written\nasX\u2032=[x1,x2,x3,...,xo,\u00acx1,\u00acx2,\u00acx3,...,\u00acxo], after concatenating the original features with the\nnegated features. The elements of the augmented feature vector x\u2032\nkare now the literals, and we\nthen only need to consider II\njand IE"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84c0-934e-11ee-ba67-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 2, "chroma:document": "then only need to consider II\njand IE\nj, however, for the expanded feature index set {1,...,2o}.\nThe TM employs two-action TAs to decide which feature indexes 1, ...,2ogo into II\nj, with one\nteam of TAs per clause j. That is, with ofeatures, we need 2 \u00d7oTAs per clause. Half of them\nrepresent the original features and the remaining represent the negated features.\nThe two actions available to each TA are include and exclude . Here, include refers to including"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84c1-934e-11ee-984c-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 2, "chroma:document": "the literal assigned to the TA and exclude means excluding it. The action that the TA performs is\ndecided by its current state, aj,k\u2208{1,...,2N}. If the state is less than or equal to N, the literal is\nexcluded from the clause. Therefore, the subset of indexes of the excluded literals can be stated\nas,IE\nj={k|aj,k\u2264N,1\u2264k\u22642o}. Conversely, if the state is higher than N, the corresponding literal\nis inserted in the clause. The subset of the indexes of the included literals can be then written asI\nI"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84c2-934e-11ee-ae21-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 2, "chroma:document": "I\nj={k|aj,k>N,1\u2264k\u22642o}. All these states aj,kof all the clauses are organized in an m\u00d72omatrix\nA:A=(aj,k)\u2208{1,...,2N}m\u00d72o.\nFigure 1 illustrates the above described TM structure. In the \ufb01gure, the upper index tof TAt\nk\ndenotes the type of the feature (1 for the original and 2 for the negated) while the lower index k\ndenotes the original feature index.\nClause output: Since the TM clause is a conjunction of literals, including any literal of value"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84c3-934e-11ee-9e16-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 2, "chroma:document": "0, even a single one, will make the clause output 0. Let the index set I1\nX\u2032be the indexes kof all of\nthe literals of value x\u2032\nk=1 in the input X\u2032. Accordingly, a clause evaluates to 1 if and only if the\nindexes of the included literals II\njis a subset of the indexes I1\nX\u2032of literals of value 1:\ncj={\n1i f II\nj\u2286I1\nX\u2032,\n0 otherwise.(2.2)\nClause voting: The above clause outputs are then organized in a vector C=(cj)\u2208{0, 1}m."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84c4-934e-11ee-aaab-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 2, "chroma:document": "To increase the expressiveness of the TM, clauses are assigned positive or negative polarity.\nClauses with positive polarity ( C+) vote for the class y=1 and clauses with negative polarity\n(C\u2212) vote for the class y=0. To avoid bias, the clauses are equally divided among class 0\n Downloaded from https://royalsocietypublishing.org/ on 05 December 2023"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84c5-934e-11ee-98c6-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 3, "chroma:document": "4royalsocietypublishing.org/journal/rsta P h i l .T r a n s .R .S o c .A 378:20190165................................................................\nx1\nx2\nxox1\nx2\n.\n.\nxo\n\u00acx1\n.\n.\n\u00acxo\u20131\n\u00acxoTA2\no\u22121inputs\nliterals\nTA\nTA \ndecisions  \nclause\nconjunction\noperatorTA1\n2\n.\n.\nTA1\no\n.\n.\nTA2\noTA1\n1\nTA21\ninclude/exclude \u00acxo\u20131\ninclude/exclude \u00acxoinclude/exclude x2include/exclude x1\ninclude/exclude \u00acx1include/exclude xo Cj\nFigure1.FormingaclauseusinginputfeaturesandtheactionsoftheTAs.\nTA team 1\nTA team 2"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84c6-934e-11ee-a559-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 3, "chroma:document": "TA team 1\nTA team 2\nTA team m+\n_\n_\noutput\nyC1\nC2\nCmCjm\nj=1TM 1\nTM qTM 2youtput\nargmax\noperatorCj1\nCj2\nCjq\nj=1j=1j=1m\u2014q\nm\u2014q\nm\u2014q(a)( b)\nFigure2.(a)ThebasicTMfortwoclassproblems.( b)Multi-classversionoftheTM.\nand class 1. E.g. clauses with odd indexes can be assigned positive polarity and clauses with\neven indexes can be assigned negative polarity. The TA state matrix Athen has two separate\nsections: A+andA\u2212. The section A+maintains the states of TAs of positive clauses: A+=\n(a+"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84c7-934e-11ee-808e-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 3, "chroma:document": "(a+\nj,k)\u2208{1,...,2N}(m/2)\u00d72o, representing the odd rows of matrix A. The section A\u2212maintains the\nstates of TAs of negative clauses: A\u2212=(a\u2212\nj,k)\u2208{1,...,2N}(m/2)\u00d72o, representing the even rows of\nmatrix A.\nThe resulting two-class architecture is illustrated in \ufb01gure 2 a. The summation operator at the\nend sums the votes for each class separately and considers the difference: v=\u2211\njc+\nj\u2212\u2211\njc\u2212\nj.A t\nlast, the \ufb01nal output is decided as in (2.3).\ny={\n1i f v\u22650\n0i f v<0.(2.3)"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84c8-934e-11ee-a0aa-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 3, "chroma:document": "y={\n1i f v\u22650\n0i f v<0.(2.3)\nNote that for categorization tasks with more classes than two, separate TMs are needed for\neach class as shown in \ufb01gure 2 b. In such situations, clauses are partitioned equally among the\nclasses. Clauses with positive polarity vote in favour of the considered class, and clauses withnegative polarity vote against the considered class. In the end, an argmax operator arbitrates the"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84c9-934e-11ee-8177-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 3, "chroma:document": "class predicted for the input, based on the votes collected for each class. When there are qclasses\nandv\niis the difference between positive and negative votes for class i, the output, y,c a nb e\n Downloaded from https://royalsocietypublishing.org/ on 05 December 2023"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84ca-934e-11ee-abcc-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 4, "chroma:document": "5royalsocietypublishing.org/journal/rsta P h i l .T r a n s .R .S o c .A 378:20190165................................................................expressed as:\ny=argmaxi=1,...,q{\nvi}\n. (2.4)\nLearning procedure: The conjunctive clauses of the TM are formed by the decisions made by\nthe collective of TAs associated with all of the clauses. Hence, training in the TM entails carefulguiding of the TAs so that they as a collective make the optimal include and exclude decisions. We"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84cb-934e-11ee-b81b-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 4, "chroma:document": "achieve this by reinforcement learning, organized as a game between the TAs. In all brevity, the\nTAs adjust their states based on feedback from the game (environment), encompassing rewards,penalties, and inaction feedback. To achieve the learning goal, the probabilities of receiving these\ndifferent types of feedback have been designed to account for critical factors, namely, the actual\noutput, the clause outputs, the literal values, and current state of the TAs."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84cc-934e-11ee-bf8c-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 4, "chroma:document": "In contrast to gradient-based learning, learning in TMs naturally combats false positives and\nfalse negatives. As a consequence, it eludes the issues attached to gradient-based algorithms such\nas vanishing/exploding gradients. In the case of categorization problems with two classes, thebasic idea is to penalize voters when they vote to procure a false positive or false negative and to\nreward voters when they vote to procure a true positive or true negative. In the TM, this is done"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84cd-934e-11ee-ae9d-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 4, "chroma:document": "by two types of feedback\u2014Type I and Type II.\nType I feedback: The clauses that receive Type I feedback is decided stochastically using the\nfollowing conditions:\np\nj,y=\u23a7\n\u23a8\n\u23a91 with probabilityT\u2212max(\u2212T,m i n ( T,v))\n2T,\n0 otherwise.(2.5)\nHere, the lower indexes jand yofprepresent the clause and target class, respectively. A user\nde\ufb01ned target Tdecides the robustness of the learning. Higher Tmakes more clauses get"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84ce-934e-11ee-97a5-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 4, "chroma:document": "involved in learning each sub-pattern, diversifying the representation. However, increasing T\nalso demands more clauses, increasing computational complexity.\nType I feedback is given to clauses with positive polarity when the actual output \u02c6yis 1 and\nto clauses with negative polarity when the actual output \u02c6yis 0. Therefore, the complete matrix,\nPy, that picks the clauses for feedback Type I, is a combination of P+\n1andP\u2212\n0where P+\n1=(p+\nj,1)\u2208\n{0, 1}(m/2)andP\u2212\n0=(p\u2212"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84cf-934e-11ee-8c88-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 4, "chroma:document": "0where P+\n1=(p+\nj,1)\u2208\n{0, 1}(m/2)andP\u2212\n0=(p\u2212\nj,0)\u2208{0, 1}(m/2). Type I feedback does two jobs. Type Ia reinforces include\nactions of TAs whose corresponding literal value is 1 when the clause output is 1. Type Ib combats\nover-\ufb01tting by reinforcing exclude actions of TAs when the corresponding literal is 0 or when the\nclause output is 0. Both Type Ia and Type Ib feedback are provided to TAs stochastically using a\nuser set parameter s(s\u22651)."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84d0-934e-11ee-9bba-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 4, "chroma:document": "user set parameter s(s\u22651).\nType Ia feedback: The matrix R,i . e .R=(rj,k)\u2208{0, 1}m\u00d72ostores the decisions whether the kth\nTA of the jthclause has been selected as candidate for feedback Type Ia. The decisions are made\nstochastically as follows:\nrj,k=\u23a7\n\u23a8\n\u23a91 with probabilitys\u22121\ns,\n0 otherwise.(2.6)\nNow, using the complete set of conditions, the indexes IIa\nCof the TAs which receive Type Ia\nfeedback can be identi\ufb01ed as IIa\nC={(j,k)|x\u2032\nk=1\u2227cj=1\u2227pj,y=1\u2227rj,k=1}."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84d1-934e-11ee-84f7-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 4, "chroma:document": "C={(j,k)|x\u2032\nk=1\u2227cj=1\u2227pj,y=1\u2227rj,k=1}.\nType Ib feedback: Similarly, candidates for receiving Type Ib feedback are decided\nstochastically and decisions are stored in matrix Q,i . e . Q=(qj,k)\u2208{0, 1}m\u00d72o. In this situation,\nthe decision for the kthTA of the jthclause is\nqj,k=\u23a7\n\u23a8\n\u23a91 with probability1\ns,\n0 otherwise.(2.7)\nAgain, considering all other conditions, the indexes IIb\nCof the TAs that receive feedback Type Ib\nare expressed as IIb\nC={(j,k)|(x\u2032\nk=0\u2228cj=0)\u2227pj,y=1\u2227qj,k=1}."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84d2-934e-11ee-9c41-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 4, "chroma:document": "C={(j,k)|(x\u2032\nk=0\u2228cj=0)\u2227pj,y=1\u2227qj,k=1}.\n Downloaded from https://royalsocietypublishing.org/ on 05 December 2023"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84d3-934e-11ee-8fe1-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 5, "chroma:document": "6royalsocietypublishing.org/journal/rsta P h i l .T r a n s .R .S o c .A 378:20190165................................................................The identi\ufb01ed TAs are updated by changing their internal state. The available update\noperations are \u2295and\u2296. The operator \u2295adds 1 to the current state while operator \u2296subtracts\n1 from the current state within the given state space: A\u2190(A\u2295IIa\nC)\u2296IIb\nC.\nIn conclusion, Type I feedback stimulates positive clauses to output 1 when the actual output"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84d4-934e-11ee-89d7-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 5, "chroma:document": "\u02c6yis 1, while it stimulates negative clauses to output 1 when the actual output \u02c6yis 0. Hence, Type\nI feedback reinforces true positive output.\nType II feedback: Type II feedback is given to clauses with positive polarity when the actual\noutput \u02c6yis 0 and clauses with negative polarity when the actual output \u02c6yis 1. Whether the jth\nclause for target output \u02c6yreceives Type II feedback is decided as follows:\npj,y=\u23a7\n\u23a8\n\u23a91 with probabilityT+max(\u2212T,m i n ( T,v))\n2T,\n0 otherwise.(2.8)"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84d5-934e-11ee-a4f1-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 5, "chroma:document": "2T,\n0 otherwise.(2.8)\nSimilar to Type I feedback, Tis a user decided voting target, and decisions are stored in the matrix\nPy. The idea is to alter the clause output of the clauses which output 1. This can be done by\nsimply including literals of value 0. The TAs that match the above conditions can be identi\ufb01edasI\nII\nC={(j,k)|x\u2032\nk=0\u2227cj=1\u2227pj,y=1}. The identi\ufb01ed TAs are updated by changing their internal\nstate: A\u2190A\u2295III\nC."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84d6-934e-11ee-b145-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 5, "chroma:document": "state: A\u2190A\u2295III\nC.\nIn this way, Type II feedback stimulates clauses to output 0. Type II feedback is applied to\nclauses of positive polarity when the actual output \u02c6yis 0 and to clauses of negative polarity when\nthe actual output \u02c6yis 1. In this manner, it combats false positives.\nThe training procedure of the multi-class version of the TM is similar to the above training\nprocedure. Clauses of the class being the target of the current training sample are treated as if"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84d7-934e-11ee-9811-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 5, "chroma:document": "\u02c6y=1, while the clauses of a randomly selected class from the remaining classes are treated as\nif\u02c6y=0. In each class, clauses with positive polarity vote to say that the output belongs to the\nconsidered class. Similarly, the clauses with negative polarity vote to indicate that the output\ndoes not belong to the considered class.\n3. AnencodingschemeforcontinuousinputtotheTsetlinmachine\nThe input feature vector of the TM that we presented in the previous section only had binaryfeatures, i.e. X=[x"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84d8-934e-11ee-8b4f-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 5, "chroma:document": "1,x2,x3,...,xo] with xk,k=1, 2,...,o, being 0 or 1. Clauses are directly\ncomposed by these features or their negations, as decided by the TAs. However, in many real-\nworld applications, one cannot necessarily expect binary features. Instead, the input features are\noften continuous-valued. In order to cope with such applications, we introduce a preprocessing\nprocedure that transforms continuous features into binary ones, while maintaining ranking"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84d9-934e-11ee-b569-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 5, "chroma:document": "relationships among the continuous feature values.\nBy way of example, table 1 shows how two continuous features are binarized. As seen, the\ntwo features are respectively listed in table column 1 and column 2. The preprocessing procedure\nfollows the following steps to convert them into binary form, one feature at a time.\n(i) Identify the unique values {v1,v2,...,vu}of the feature.\n(ii) Sort the identi\ufb01ed unique values from smallest to largest."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84da-934e-11ee-8b2f-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 5, "chroma:document": "(iii) Consider each unique value vi,i=1, 2,...,u, as a threshold \u2018 \u2264vi\u2019, as shown in sorted\norder in the \u2018Thresholds\u2019 row in the table.\n(iv) Compare each original continuous value in the feature with each of the sorted thresholds.\nIf the feature value is greater than the threshold, set the corresponding binary variable to0, otherwise, set the bit to 1.\n(v) Repeat steps (i) to (iv) until all the continuous values are converted into binary form."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84db-934e-11ee-af8d-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 5, "chroma:document": "According to the above procedure, the \ufb01rst feature in the given example has three unique\nvalues, i.e. 5.779, 10.008 and 3.834 (step (i)). These unique values are sorted and considered as\nthresholds, \u22643.834, \u22645.779 and \u226410.008 (step (ii) and (iii)). Note that the number of binary feature\n Downloaded from https://royalsocietypublishing.org/ on 05 December 2023"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84dc-934e-11ee-b992-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 6, "chroma:document": "7royalsocietypublishing.org/journal/rsta P h i l .T r a n s .R .S o c .A 378:20190165................................................................Table1.Preprocessingoftwocontinuousfeatures.\nrawfeature thresholds\n12 \u22643.834 \u22645.779 \u226410.008 \u226411.6 \u226425.7 \u226432.4 \u226456.1\n5.779 25.7 0 1 1 0 1 1 1\n......................................... ............................................ .......................................... ..................................... ......................................"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84dd-934e-11ee-8442-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 6, "chroma:document": "10.008 56.1 0 0 1 0 0 0 1\n......................................... ............................................ .......................................... ..................................... ......................................\n5.779 11.6 0 1 1 1 1 1 1\n......................................... ............................................ .......................................... ..................................... ......................................\n3.834 32.4 1 1 1 0 0 1 1"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84de-934e-11ee-a143-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 6, "chroma:document": "3.834 32.4 1 1 1 0 0 1 1\n......................................... ............................................ .......................................... ..................................... ......................................\nbits we are going to have after converting the continuous inputs equals the number of thresholds.\nIn this case, for Feature 1 in the table (\ufb01rst column), three new binary feature bits are introduced,"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84df-934e-11ee-8dd7-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 6, "chroma:document": "each of which corresponds to its respective threshold. If we compare the \ufb01rst raw continuous\nvalue of Feature 1, namely, 5.779, with the identi\ufb01ed three thresholds, we get a 011 as the rawvalue is greater than 3.834 (resulting in 0), equal to 5.779 (resulting in 1), and less than 10.008\n(resulting in 1) (Step iv). Similarly, the remaining raw continuous values, 10.008 and 3.834, are\nconverted into 001 and 111, respectively."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84e0-934e-11ee-a7ef-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 6, "chroma:document": "converted into 001 and 111, respectively.\nOnce all the raw continuous values of the \ufb01rst feature are converted, conversion of the second\nfeature can start. This procedure is iterated until all the continuous values in all the continuous\nfeatures have been converted to binary form (step (v)).\nNote that the thresholds found in the above procedure are open-ended at the extreme ends.\nThus, arbitrarily low or high feature values can be processed, independent of the actual values in"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84e1-934e-11ee-aedf-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 6, "chroma:document": "the training data.\nThe new binary representation of continuous features becomes particularly powerful because\nit allows the TM to reason about the ordering of the values, forming conjunctive clauses that\nspecify rules based on thresholds, and with negated features, also rules based on intervals.\n4. TheregressionTsetlinmachine\nFor many real-world prediction problems, the target yis continuous valued, referred to as"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84e2-934e-11ee-b364-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 6, "chroma:document": "regression problems. Although continuous output can be encoded in bit form, the inherent\nproperties of continuous values are lost, such as the ordering of values. Thus, the binary output\nof the classic TM shown in \ufb01gure 2 a,bis not ideal for representing continuous output. In order to\naddress this problem, we here propose a new type of TM\u2014the RTM .\nThe structure of the RTM is illustrated in \ufb01gure 3 . As the \ufb01gure shows, we remove the polarity"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84e3-934e-11ee-8251-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 6, "chroma:document": "of the clauses in the vanilla TM structure. Instead, we use clauses as additive building blocksto calculate the continuous outputs. That is, the summation operator in \ufb01gure 3 counts the total\nnumber of clauses that evaluate to 1, and the resulting sum is further mapped into a continuous\nvalue according to equation (4.1):\ny=\u2211\nm\nj=1Cj(\u02c6X)\nT\u00d7\u02c6ymax. (4.1)\nAbove, Tis a user speci\ufb01ed output resolution and \u02c6ymaxis the maximum value of the target output"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84e4-934e-11ee-aa2d-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 6, "chroma:document": "found in the training data, assuming positive output.1This maximum value is merely a reference\npoint, to establish a scale, and should not be considered as an upper bound for the output.\nOnce a continuous output value yhas been calculated, it is compared with the target output\n\u02c6y. Following the convention of regression analysis, we refer to the difference between the output\nyand\u02c6yas the error of the prediction. The output itself and the error are, in turn, fed back to the"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84e5-934e-11ee-ada7-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 6, "chroma:document": "RTM, and in\ufb02uence the decision made by the TAs so that the error can be minimized. The goal is\nfor the RTM to learn patterns appropriate for regression from the training dataset.\n1Our scheme also supports negative output values by employing clauses of negative polarity.\n Downloaded from https://royalsocietypublishing.org/ on 05 December 2023"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84e6-934e-11ee-8ad8-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 7, "chroma:document": "8royalsocietypublishing.org/journal/rsta P h i l .T r a n s .R .S o c .A 378:20190165................................................................TA team 1\nTA team myTA team 2\noutputmappingC1\nC2\nCmCj\nj=1my\u02c6max\ny\u02c6min\nFigure3.TheRTMstructure.\nFeedback for the RTM is derived slightly differently compared to the vanilla TM. That is,\nwhether it is given Type I or Type II feedback is based on the difference between yand\u02c6y,a s\ndetermined by equation (4.2):\nFeedback ={\nType I, if y<\u02c6y,"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84e7-934e-11ee-9a3e-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 7, "chroma:document": "Feedback ={\nType I, if y<\u02c6y,\nType II, if y>\u02c6y.(4.2)\nThe rationale behind equation (4.2) is as follows. We want to increase the number of clauses that\noutput 1 when the predicted output is less than the target output ( y<\u02c6y). To achieve this, Type I\nfeedback is introduced. Conversely, Type II feedback is applied to decrease the number of clausesthat evaluate to 1 when the predicted output is higher than the target output ( y>\u02c6y)."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84e8-934e-11ee-bb6f-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 7, "chroma:document": "If the feedback determined by (4.2) is offered to all the clauses, the predicted value will keep\noscillating around the target output throughout the training process. Hence, we randomly selecta subset of the clauses to receive feedback, with the prediction error controlling the cardinality of\nthe subset. We achieve this by introducing the following feedback activation probability function,\nP\nact, by which the RTM decides stochastically which clauses to be updated:\nPact=K\u00d7|y\u2212\u02c6y|\n\u02c6ymax. (4.3)"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84e9-934e-11ee-a915-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 7, "chroma:document": "Pact=K\u00d7|y\u2212\u02c6y|\n\u02c6ymax. (4.3)\nNote that in equation (4.3), the parameter Kis added to adjust the activation probability according\nto the total number of clauses. In other words, the probability varies proportionally to the error,\nand is reasonably scaled to \ufb01t the total number of clauses.\nThe \ufb02owchart given in \ufb01gure 4 summarizes the complete training procedure of the RTM,\nincluding the data preprocessing step introduced in \u00a73.\n5. Empiricalresultsandanalysis"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84ea-934e-11ee-b5b2-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 7, "chroma:document": "5. Empiricalresultsandanalysis\nWe now study the properties of the RTM empirically, by means of two arti\ufb01cial and \ufb01ve real-world\ndatasets.2\n(a) Artificialdatasets\nThe two arti\ufb01cial datasets have been designed to demonstrate how the RTM form nonlinear\nclauses, which in turn are used as additive components in the regression. The \ufb01rst dataset, Dataset"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84eb-934e-11ee-8f62-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 7, "chroma:document": "I, has 8 distinct outputs, each of which is triggered by a speci\ufb01c 3-bit input. Each input bit has anequal probability of being set to either 0 or 1, leading to a uniform distribution of bit values. The\ncontinuous output is quite simply calculated by multiplying 100 with the decimal representation\nof the input. For example, the continuous output for input (011) becomes 100 \u00d73=300. The"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84ec-934e-11ee-bbb2-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 7, "chroma:document": "2The arti\ufb01cial datasets and RTM code are available to download at https://github.com/cair/regression-tsetlin-machine .\n Downloaded from https://royalsocietypublishing.org/ on 05 December 2023"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84ed-934e-11ee-aa33-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 8, "chroma:document": "9royalsocietypublishing.org/journal/rsta P h i l .T r a n s .R .S o c .A 378:20190165................................................................\ndata\npreprocessing\n(section 3): start regression Tsetlin machine\nset: clauses m, precision s, threshold T\nrandom initialization of TAs:\n2 \u00d7 o TA per clause\nevaluate clauses: eqn (2.2)\nfeedbacks to\nthe clausescompute output y: eqn (4.1)\ntype II feedbacktype I feedback\nstopping\ncriteria\nready to predict unseen datayesnotraining\nsample X\u02c6, y\u02c6\n  data"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84ee-934e-11ee-878f-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 8, "chroma:document": "sample X\u02c6, y\u02c6\n  data\ny<y\u02c6\nsatisfy eqn (4.3)\ny>y\u02c6\nsatisfy eqn (4.3)\nFigure4.Thetrainingwork-flowoftheRTM.\ncomplete dataset consists of 10 000 samples, split into 80% training data and 20% test data. The\nsecond dataset, Dataset II, is built in the same way, except that the output of the training data is\nperturbed by adding a random value in the range [ \u221210, 10] to introduce noise.\nWe train and test the RTM separately on the above two datasets, with mean absolute error"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84ef-934e-11ee-8410-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 8, "chroma:document": "(MAE) used as evaluation criterion. For all of our experiments on arti\ufb01cial data, we use a\nspeci\ufb01city value sof 2. Figures 5and 6depict training MAE across 1000 epochs, examining the\neffect of resolution T. The \ufb01nal training and test MAEs, i.e. the ones obtained after 1000 epochs,\nare provided in the legends. As seen in \ufb01gure 5 , noise-free data can be perfectly learnt by an\nRTM with merely resolution 7, using 7 clauses. However, in general, as seen in \ufb01gure 6 , higher"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84f0-934e-11ee-86a4-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 8, "chroma:document": "resolution progressively reduces MAE under noise.\nLet us now study the case with 7 clauses and noise-free data more carefully to cast further\nlight on how the RTM learns. With 3 uniformly distributed bits, there are 8 unique sub-patterns,\nillustrated in \ufb01gure 7 . Each of these occurs with probability 1 /8. The shaded area in the \ufb01gure\ncontains the pattern (1 \u2733\u2733), whose probability of occurrence is 4 /8. Here, \u2733means either 0 or 1."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84f1-934e-11ee-8e14-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 8, "chroma:document": "Similarly, the probabilities of occurrence for both the pattern ( \u27331\u2733) and the pattern ( \u2733\u2733 1) is 4 /8,\ntoo. According to the TM dynamics explained in [ 10], in order to capture these patterns, speci\ufb01city\nshould be set to s=2.\nWith only 7 clauses available, the clauses need to encode the input in a very compact way,\nshown in table 2 , to produce the correct output. As seen, we need four clauses for the pattern"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84f2-934e-11ee-86a5-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 8, "chroma:document": "(1\u2733\u2733), two clauses for the pattern ( \u27331\u2733), and one clause for the pattern ( \u2733\u2733 1). Now, consider\n Downloaded from https://royalsocietypublishing.org/ on 05 December 2023"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84f3-934e-11ee-a086-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 9, "chroma:document": "10royalsocietypublishing.org/journal/rsta P h i l .T r a n s .R .S o c .A 378:20190165................................................................\n020406080100120\n1\n6\n11\n16\n21\n26\n31\n36\n41\n46\n51\n56\n61\n667176\n81\n86\n91\n96\n101\n106\n111\n116121\n126\n131\n136\n141\n146\n151\n156\n161\n166\n171\n176\n181\n186\n191\n196MAE\niterationDataset I 7-T (train MAE - 0.00, test MAE - 0.00) 20-T (train MAE - 18.60, test MAE - 18.50)\n70-T (train MAE - 0.00, test MAE - 0.00) 500-T (train MAE - 0.40, test MAE - 0.41)"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84f4-934e-11ee-b96b-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 9, "chroma:document": "5000-T (train MAE - 0.07, test MAE - 0.07)\nFigure5.TrainingerrorperepochforDatasetI.Thedatasetisprocessedwithdifferent T.(Onlineversionincolour.)\n020406080100120\n1\n6\n11\n16\n21\n26\n31\n36\n41\n46\n51\n56\n61\n66\n71\n76\n81\n86\n91\n96\n101\n106\n111\n116\n121\n126\n131\n136\n141\n146\n151\n156\n161\n166\n171\n176\n181\n186\n191\n196MAE\niterationDataset II 7-T (train MAE - 7.33, test MAE - 5.64) 20-T (train MAE - 15.49, test MAE - 15.23)\n70-T (train MAE - 7.13, test MAE - 4.81) 500-T (train MAE - 5.40, test MAE - 1.51)"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84f5-934e-11ee-9577-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 9, "chroma:document": "5000-T (train MAE - 5.26, test MAE - 0.26)\nFigure6.TrainingerrorperepochforDatasetII.Thedatasetisprocessedwithdifferent T.(Onlineversionincolour.)\n1 0 0 0 1 0\n0 0 10 1 1 1 0 11 1 0\n1 1 10 0 0\nFigure7.Patterndistributionforthe3-bitsinputdatasets.\ninput (0 1 1) as an example. This input matches both pattern ( \u27331\u2733) and pattern ( \u2733\u2733 1).\nTherefore, it activates three clauses from the table. Consequently, after scaling, output 300 is"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84f6-934e-11ee-974d-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 9, "chroma:document": "correctly computed from (0 1 1). In this manner, the correct output can be calculated for all 3-bit\ninputs from table 2 . Returning to \ufb01gure 5 , we note that the MAE of the RTM is exactly 0 for 7\n Downloaded from https://royalsocietypublishing.org/ on 05 December 2023"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84f7-934e-11ee-9d7c-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 10, "chroma:document": "11royalsocietypublishing.org/journal/rsta P h i l .T r a n s .R .S o c .A 378:20190165................................................................Table2.Computingoutputsfordifferent3bitinputs[ 18].\ninput representedpatterns outputcomputation output\n000 none 4 \u00d7(1\u2733\u2733)\u00d70=00 \u00d7100=0\n2\u00d7(\u27331\u2733)\u00d70=0\n1\u00d7(\u2733\u27331)\u00d70=0"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84f8-934e-11ee-93dd-ac198e74a6f7
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created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
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created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
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created_at: 2023-12-05 09:10:18
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created_at: 2023-12-05 09:10:18
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created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
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created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84fe-934e-11ee-b8de-ac198e74a6f7
encoding: FLOAT32
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{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 10, "chroma:document": "(\u27331\u2733)2 \u00d7(\u27331\u2733)\u00d71=2\n(\u2733\u27331) 1 \u00d7(\u2733\u27331)\u00d71=1\n......................................... ............................................ .......................................... ..................................... ......................................\nclauses/resolution 7, meaning that the RTM has found the structure of table 2 by itself. Hence,\nthe power of the scheme!\nFor real-world cases, however, the exact number of clauses required is generally unknown."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c84ff-934e-11ee-9de5-ac198e74a6f7
encoding: FLOAT32
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created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8500-934e-11ee-9ba5-ac198e74a6f7
encoding: FLOAT32
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{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 10, "chroma:document": "that the testing MAE can be made arbitrarily close to 0 for the present task simply by increasingthe resolution, the number of training examples, and the number of training epochs.\n(b) Real-worlddatasets\nWe now study the behaviour of the RTM on \ufb01ve different real-world datasets:\nDengue Incidences:3This dataset consists of monthly dengue incidences in the Philippines\nper 100 000 population. The Philippines has 17 administrative regions. The department of health"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8501-934e-11ee-a851-ac198e74a6f7
encoding: FLOAT32
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{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 10, "chroma:document": "3Available from https://www.kaggle.com/grosvenpaul/dengue-cases-in-the-philippines .\n Downloaded from https://royalsocietypublishing.org/ on 05 December 2023"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8502-934e-11ee-8b7e-ac198e74a6f7
encoding: FLOAT32
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{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 11, "chroma:document": "12royalsocietypublishing.org/journal/rsta P h i l .T r a n s .R .S o c .A 378:20190165................................................................in the Philippines collected the data from all of these regions separately from 2008 to 2016. In\nthis experiment, the RTM is trained separately for each region using the data from 2008 to 2015.\nDengue incidences from the neighbouring regions are used as input features. More details about"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8503-934e-11ee-80a4-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 11, "chroma:document": "data preprocessing and feature selection can be found in [ 19]. Dengue incidences in 2016 are used\nas testing data.\nEnergy Performance:4In this application, heating load of residential buildings has to be\nestimated using eight input features: glazing area distribution, glazing area, orientation, relative\ncompactness, wall area, surface area, overall height, roof area, and orientation [ 20]. The complete"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8504-934e-11ee-863f-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 11, "chroma:document": "dataset comprises 768 samples. We use 80% of the data samples to train the model and the rest to\nevaluate it.\nStock Selection:5The US historical stock market data was used to simulate the weights of\nthe stock-picking concepts in [ 21]. These weights are employed to build a stock selection decision\nsupport system. The dataset consists of six output variables. Only two of them, i.e. Annual Return"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8505-934e-11ee-9536-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 11, "chroma:document": "and Real Win Rate is used here. Again, 80% of the data samples are used to train the model andthe rest is used for testing.\nReal Estate Valuation:\n6This is a time-series dataset that has been used to estimate the house\nprice per unit area in Taiwan [ 22]. The house price per unit area (Dollars per Ping, 1 Ping = 3.3\nmetre squared) is estimated using six features, namely the transaction date, the house age, the"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8506-934e-11ee-8cd6-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 11, "chroma:document": "distance to the nearest MRT station, the number of convenience stores in the living circle on foot,\nand the geographical coordinates (latitude and longitude). Again we use (80%) of the dataset for\ntraining and (20%) for testing.\nAerofoil Noise:7The dataset comprises different sizes of NACA 0012 aerofoils (an aerofoil\nshape for aircraft wings) at various wind tunnel speeds and angles of attack. The goal is to"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8507-934e-11ee-bb47-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 11, "chroma:document": "predict the self-generated noise of an aerofoil blade in decibels using \ufb01ve attributes, namely,\nFrequency (in Hertzs), Angle of attack (in degrees), Chord length (in metres), Free-stream velocity(in metres per second), and Suction side displacement thickness (in metres). Out of the total 1503\ndata samples, 625 are randomly selected for doing the experiment. The RTM is trained on 80% of\nthe selected data and tested on the rest of them."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8508-934e-11ee-9a8b-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 11, "chroma:document": "the selected data and tested on the rest of them.\nApart from Dengue Incidences, we used the same number of clauses and the same resolution\nfor all of the datasets, respectively, 2 000 000 and 1 000 000. This setting was found by increasing\nthe number of clauses and resolution until the accuracy gain became insigni\ufb01cant. The speci\ufb01citysfor each dataset was found by a manual binary search (4 for Energy Performance, 3 for Annual"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8509-934e-11ee-b8e1-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 11, "chroma:document": "Return, 2.5 for Real Win Rate, 3.8 for Real Estate Valuation, and 2.7 for Aerofoil Noise). For\nforecasting dengue incidences across all the regions in the Philippines, we used 200 000 clauses, aresolution of 100 000, and an s-value of 6.\nTable 3 reports average MAE obtained by replicating each experiment 20 times, together\nwith 95% con\ufb01dence intervals. To evaluate the performance of the RTM, we used three other"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c850a-934e-11ee-880c-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 11, "chroma:document": "state-of-the-art machine learning models as a baseline. These models are regression tree (RT),\nrandom forest (RF) and support vector regression (SVR). Each of these were con\ufb01gured basedon a thorough parameter search in order to facilitate a fair comparison. Each model predicts six\ndifferent data series using their relevant input features. In conclusion, RTM obtained the best"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c850b-934e-11ee-ab4d-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 11, "chroma:document": "MAE for four of the prediction tasks (Dengue Incidences, Energy Performance, Real Win Rate, andReal Estate Valuation). For Annual Return, SVR produced the lowest MAE, while RTM achieved\nthe second best. Finally, RF provided the best MAE for Aerofoil Noise. Here, RTM obtained the\nthird-best result.\nIn order to investigate the ability of the RTM to extrapolate, we cross-validated the model\nusing the Energy Performance dataset. To produce test data with extreme values not found in"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c850c-934e-11ee-ba0c-ac198e74a6f7
encoding: FLOAT32
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{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 11, "chroma:document": "the training data, ten different datasets were created by randomly shuf\ufb02ing the original dataset.\n4Available from https://archive.ics.uci.edu/ml/datasets/Energy+ef\ufb01ciency .\n5Available from https://archive.ics.uci.edu/ml/datasets/Stock+portfolio+performance .\n6Available from https://archive.ics.uci.edu/ml/datasets/Real+estate+valuation+data+set .\n7Available from https://archive.ics.uci.edu/ml/datasets/Airfoil+Self-Noise# .\n Downloaded from https://royalsocietypublishing.org/ on 05 December 2023"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c850d-934e-11ee-ae0b-ac198e74a6f7
encoding: FLOAT32
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{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 12, "chroma:document": "13royalsocietypublishing.org/journal/rsta P h i l .T r a n s .R .S o c .A 378:20190165................................................................Table3.MeanMAEwith95%confidenceintervalsforselectedmodelsonfivedatasets.\nstockselectiondengue energy realestate\nmodel incidences performance annualreturn realwinrate valuation aerofoilnoise\nRTM 5.184 0.503 \u00b10.00 0.077 \u00b10.00 0.089 \u00b10.00 5.218 \u00b10.00 2.244 \u00b10.00"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c850e-934e-11ee-af2c-ac198e74a6f7
encoding: FLOAT32
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{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 12, "chroma:document": "......................................... ............................................ .......................................... ..................................... ......................................\nRT 7.769 0.598 \u00b10.00 0.091 \u00b10.00 0.096 \u00b10.00 6.033 \u00b10.11 2.280 \u00b10.07\n......................................... ............................................ .......................................... ..................................... ......................................"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c850f-934e-11ee-82f5-ac198e74a6f7
encoding: FLOAT32
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{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 12, "chroma:document": "RF 9.122 0.563 \u00b10.00 0.088 \u00b10.00 0.097 \u00b10.00 5.360 \u00b10.00 1.921 \u00b10.00\n......................................... ............................................ .......................................... ..................................... ......................................\nSVR 5.305 1.155 \u00b10.00 0.073 \u00b10.00 0.092 \u00b10.00 5.697 \u00b10.00 2.156 \u00b10.00"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8510-934e-11ee-885f-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 12, "chroma:document": "......................................... ............................................ .......................................... ..................................... ......................................\nCollectively, this procedure created 22 test outcomes outside the minimum and maximum output\nvalues in the training data. The MAE of those 22 testing outputs was 0.516, which is only slightlyhigher than the overall MAE in table 3 , meaning that the RTM extrapolates reasonably well. This"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8511-934e-11ee-ace2-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 12, "chroma:document": "can be explained by the additive nature of RTM regression. By summing the binary output of\nnonlinear clauses, the RTM avoids extreme nonlinear distortions when operating outside thevalue ranges found in the training data.\n6. Conclusion\nIn this paper, we proposed the RTM, a novel variant of the TM that supports continuousoutput in nonlinear regression problems. We also introduced a data preprocessing procedure"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8512-934e-11ee-b414-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 12, "chroma:document": "that converts continuous inputs into a lossless binary feature matrix. In RTM, the polarities in\nclauses are removed and the inner inference mechanism is modi\ufb01ed. That is, the input patterns are\ntransformed into individual continuous outputs, rather than to distinct categories. The activation\nof clauses during RTM learning is based on a linear activation probability function that isgoverned by the magnitude of the regression error. The behaviour of the new algorithm was"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8513-934e-11ee-b5a1-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 12, "chroma:document": "studied by applying it to both arti\ufb01cial and real-world datasets. In brief, RTM demonstrated\nsuperior performance in comparison with Regression Trees, Random Forests, and Support VectorRegression, when predicting Dengue incidences in the Philippines, heating load in the Energy\nPerformance dataset, Real Win Rate in the Stock Selection dataset, and house price per unit"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8514-934e-11ee-98aa-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 12, "chroma:document": "area in the Real Estate Valuation dataset. The RTM also extrapolates reasonably well outside theminimum and maximum output values found in the training data.\nDataaccessibility.\nThis article does not contain any additional data.\nCompetinginterests. We declare we have no competing interests.\nFunding. We received no funding for this study.\nReferences\n1. Freitas AA. 2014 Comprehensible classi\ufb01cation models: a position paper. ACM SIGKDD\nExplor. Newsl. 15, 1\u201310. ( doi:10.1145/2594473.2594475 )"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8515-934e-11ee-aa6c-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 12, "chroma:document": "2. Baesens B, Mues C, De Backer M, Vanthienen J, Setiono R. 2004 Building intelligent credit\nscoring systems using decision tables. In Enterprise Information Systems V , pp. 131\u2013137. Berlin,\nGermany: Springer.\n3. Huysmans J, Dejaeger K, Mues C, Vanthienen J, Baesens B. 2011 An empirical evaluation of\nthe comprehensibility of decision table, tree and rule based predictive models. Decis. Support\nSyst. 51, 141\u2013154. ( doi:10.1016/j.dss.2010.12.003 )"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8516-934e-11ee-9b72-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 12, "chroma:document": "4. Bellazzi R, Zupan B. 2008 Predictive data mining in clinical medicine: current issues and\nguidelines. Int. J. Med. Inform. 77, 81\u201397. ( doi:10.1016/j.ijmedinf.2006.11.006 )\n5. Pazzani MJ, Mani S, Shankle WR. 2001 Acceptance of rules generated by machine learning\namong medical experts. Methods Inf. Med. 40, 380\u2013385. ( doi:10.1055/s-0038-1634196 )\n6. Freitas AA, Wieser DC, Apweiler R. 2010 On the importance of comprehensible classi\ufb01cation"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8517-934e-11ee-b2e5-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 12, "chroma:document": "models for protein function prediction. IEEE/ACM Trans. Comput. Biol. Bioinform. (TCBB) 7,\n172\u2013182. ( doi:10.1109/TCBB.2008.47 )\n Downloaded from https://royalsocietypublishing.org/ on 05 December 2023"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8518-934e-11ee-898d-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 13, "chroma:document": "14royalsocietypublishing.org/journal/rsta P h i l .T r a n s .R .S o c .A 378:20190165................................................................7. Szafron D et al. 2004 Proteome analyst: custom predictions with explanations in a web-\nbased tool for high-throughput proteome annotations. Nucleic Acids Res. 32, W365\u2013W371.\n(doi:10.1093/nar/gkh485 )\n8. Lima E, Mues C, Baesens B. 2009 Domain knowledge integration in data mining using"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8519-934e-11ee-9be5-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 13, "chroma:document": "decision tables: case studies in churn prediction. J. Oper. Res. Soc. 60, 1096\u20131106. ( doi:10.1057/\njors.2008.161 )\n9. Verbeke W, Martens D, Mues C, Baesens B. 2011 Building comprehensible customer churn\nprediction models with advanced rule induction techniques. Expert Syst. Appl. 38, 2354\u20132364.\n(doi:10.1016/j.eswa.2010.08.023 )\n10. Granmo O-C. 2019 The Tsetlin machine - a game theoretic bandit driven approach to optimal"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c851a-934e-11ee-8534-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 13, "chroma:document": "pattern recognition with propositional logic. ( https://arxiv.org/abs/1804.01508 )\n11. Tsetlin ML. 1961 On behaviour of \ufb01nite automata in random medium. Avtom I Telemekhanika\n22, 1345\u20131354.\n12. Abeyrathna. KD, Granmo O-C, Goodwin M. 2018 A novel Tsetlin automata scheme to forecast\ndengue outbreaks in the philippines. In 2018 IEEE 30th Int. Conf. on Tools with Arti\ufb01cial\nIntelligence (ICTAI) , pp. 680\u2013685. IEEE.\n13. Bouhmala N, Granmo O-C. 2010 Stochastic learning for SAT-encoded graph coloring"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c851b-934e-11ee-8689-ac198e74a6f7
encoding: FLOAT32
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{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 13, "chroma:document": "problems. Int. J. Appl. Metaheuristic Comput. (IJAMC) 1, 1\u201319. ( doi:10.4018/jamc.2010070101 )\n14. Tung B, Kleinrock L. 1996 Using \ufb01nite state automata to produce self-optimization and self-\ncontrol. IEEE Trans. Parallel Distrib. Syst. 7, 439\u2013448. ( doi:10.1109/71.494637 )\n15. Oommen BJ, Kim S-W, Samuel MT, Granmo O-C. 2008 A solution to the stochastic point\nlocation problem in metalevel nonstationary environments. IEEE Trans. Syst. Man, Cybern.,"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c851c-934e-11ee-90ac-ac198e74a6f7
encoding: FLOAT32
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{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 13, "chroma:document": "Part B (Cybernetics) 38, 466\u2013476. ( doi:10.1109/TSMCB.2007.913602 )\n16. Granmo O-C, Oommen BJ. 2010 Solving stochastic nonlinear resource allocation problems\nusing a hierarchy of twofold resource allocation automata. IEEE Trans. Comput. 59, 545\u2013560.\n(doi:/10.1109/tc.2009.189 )\n17. Berge GT, Granmo O-C, Oddbj\u00f8rn Tveit T, Goodwin M, Jiao L, Viggo Matheussen B.\n2019 Using the Tsetlin machine to learn human-interpretable rules for high-accuracy text"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c851d-934e-11ee-ad5b-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 13, "chroma:document": "categorization with medical applications. IEEE Access 7, 115 134\u2013115 146. ( doi:10.1109/\nACCESS.2019.2935416 )\n18. Abeyrathna KD, Granmo O-C, Jiao L, Goodwin M. 2019 The regression Tsetlin machine:\na Tsetlin machine for continuous output problems. In EPIA2019: EPIA Conf. on Arti\ufb01cial\nIntelligence , pp. 268\u2013280. Berlin, Germany: Springer.\n19. Abeyrathna KD, Granmo O-C, Zhang X, Goodwin M. 2019 A scheme for continuous input"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c851e-934e-11ee-ad45-ac198e74a6f7
encoding: FLOAT32
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{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 13, "chroma:document": "to the Tsetlin machine with applications to forecasting disease outbreaks. In Int. Conf. on\nIndustrial, Engineering and Other Applications of Applied Intelligent Systems , pp. 564\u2013578. Berlin,\nGermany: Springer.\n20. Tsanas A, Xifara A. 2012 Accurate quantitative estimation of energy performance of residential\nbuildings using statistical machine learning tools. Energy Build. 49, 560\u2013567. ( doi:10.1016/\nj.enbuild.2012.03.003 )"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c851f-934e-11ee-ba2f-ac198e74a6f7
encoding: FLOAT32
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{"source": "source_documents\\darshana-abeyrathna-et-al-2019-the-regression-tsetlin-machine-a-novel-approach-to-interpretable-nonlinear-regression.pdf", "page": 13, "chroma:document": "j.enbuild.2012.03.003 )\n21. Liu Y-C, Yeh I-C. 2017 Using mixture design and neural networks to build stock selection\ndecision support systems. Neural Comput. Appl. 28, 521\u2013535. ( doi:10.1007/s00521-015-2090-x )\n22. Yeh I-C, Hsu T-K. 2018 Building real estate valuation models with comparative approach\nthrough case-based reasoning. Appl. Soft Comput. 65, 260\u2013271. ( doi:10.1016/j.asoc.2018.01.029 )\n Downloaded from https://royalsocietypublishing.org/ on 05 December 2023"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8520-934e-11ee-b878-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 0, "chroma:document": "Massively Parallel and Asynchronous Tsetlin Machine Architecture Supporting\nAlmost Constant-Time Scaling\nKuruge Darshana Abeyrathna* 1Bimal Bhattarai* 1Morten Goodwin* 1Saeed Rahimi Gorji* 1\nOle-Christoffer Granmo* 1Lei Jiao* 1Rupsa Saha* 1Rohan Kumar Yadav* 1\nAbstract\nUsing logical clauses to represent patterns, Tsetlin\nmachines ( TMs) have recently obtained compet-\nitive performance in terms of accuracy, memory\nfootprint, energy, and learning speed on several"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8521-934e-11ee-bd50-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 0, "chroma:document": "footprint, energy, and learning speed on several\nbenchmarks. Each TMclause votes for or against\na particular class, with classi\ufb01cation resolved us-\ning a majority vote. While the evaluation of\nclauses is fast, being based on binary operators,\nthe voting makes it necessary to synchronize the\nclause evaluation, impeding parallelization. In\nthis paper, we propose a novel scheme for desyn-\nchronizing the evaluation of clauses, eliminating\nthe voting bottleneck. In brief, every clause runs"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8522-934e-11ee-affe-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 0, "chroma:document": "in its own thread for massive native parallelism.\nFor each training example, we keep track of the\nclass votes obtained from the clauses in local vot-\ning tallies. The local voting tallies allow us to\ndetach the processing of each clause from the rest\nof the clauses, supporting decentralized learning.\nThis means that the TMmost of the time will op-\nerate on outdated voting tallies. We evaluated the\nproposed parallelization across diverse learning\ntasks and it turns out that our decentralized TM"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8523-934e-11ee-8c43-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 0, "chroma:document": "tasks and it turns out that our decentralized TM\nlearning algorithm copes well with working on\noutdated data, resulting in no signi\ufb01cant loss in\nlearning accuracy. Furthermore, we show that the\nproposed approach provides up to 50times faster\nlearning. Finally, learning time is almost constant\nfor reasonable clause amounts (employing from\n20to7,000clauses on a Tesla V100 GPU). For\nsuf\ufb01ciently large clause numbers, computation\ntime increases approximately proportionally. Our"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8524-934e-11ee-9bd5-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 0, "chroma:document": "time increases approximately proportionally. Our\nparallel and asynchronous architecture thus allows\nprocessing of massive datasets and operating with\nmore clauses for higher accuracy.\n*Equal contribution (The authors are ordered alphabetically by\nlast name.)1Department of Information and Communication Tech-\nnology, Unviersity of Agder, Grimstad, Norway. Correspondence\nto: Ole-Christoffer Granmo <ole.granmo@uia.no >.\nProceedings of the 38thInternational Conference on Machine"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8525-934e-11ee-8547-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 0, "chroma:document": "Learning , PMLR 139, 2021. Copyright 2021 by the author(s).1. Introduction\nTsetlin machines ( TMs) (Granmo, 2018) have recently\ndemonstrated competitive results in terms of accuracy, mem-\nory footprint, energy, and learning speed on diverse bench-\nmarks (image classi\ufb01cation, regression, natural language\nunderstanding, and speech processing) (Berge et al., 2019;\nYadav et al., 2021a; Abeyrathna et al., 2020; Granmo et al.,\n2019; Wheeldon et al., 2020; Abeyrathna et al., 2021; Lei"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8526-934e-11ee-8bae-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 0, "chroma:document": "et al., 2021). They use frequent pattern mining and resource\nallocation principles to extract common patterns in the data,\nrather than relying on minimizing output error, which is\nprone to over\ufb01tting. Unlike the intertwined nature of pat-\ntern representation in neural networks, a TMdecomposes\nproblems into self-contained patterns, expressed as conjunc-\ntive clauses in propositional logic (i.e., in the form ifinput\nXsatis\ufb01es condition Aand not condition Bthen output"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8527-934e-11ee-9f8e-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 0, "chroma:document": "y= 1). The clause outputs, in turn, are combined into a\nclassi\ufb01cation decision through summation and thresholding,\nakin to a logistic regression function, however, with binary\nweights and a unit step output function. Being based on\nthe human-interpretable disjunctive normal form (Valiant,\n1984), like Karnaugh maps (Karnaugh, 1953), a TMcan\nmap an exponential number of input feature value combina-\ntions to an appropriate output (Granmo, 2018)."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8528-934e-11ee-8400-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 0, "chroma:document": "tions to an appropriate output (Granmo, 2018).\nRecent progress on TMs Recent research reports several\ndistinct TM properties. The TM can be used in convolution,\nproviding competitive performance on MNIST, Fashion-\nMNIST, and Kuzushiji-MNIST, in comparison with CNNs,\nK-Nearest Neighbor, Support Vector Machines, Random\nForests, Gradient Boosting, BinaryConnect, Logistic Cir-\ncuits and ResNet (Granmo et al., 2019). The TMhas also\nachieved promising results in text classi\ufb01cation (Berge et al.,"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c8529-934e-11ee-9fc0-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 0, "chroma:document": "2019), word sense disambiguation (Yadav et al., 2021b),\nnovelty detection (Bhattarai et al., 2021c;b), fake news de-\ntection (Bhattarai et al., 2021a), semantic relation analysis\n(Saha et al., 2020), and aspect-based sentiment analysis (Ya-\ndav et al., 2021a) using the conjunctive clauses to capture\ntextual patterns. Recently, regression TMs compared favor-\nably with Regression Trees, Random Forest Regression, and\nSupport Vector Regression (Abeyrathna et al., 2020). The"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c852a-934e-11ee-b2b0-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 0, "chroma:document": "above TMapproaches have further been enhanced by vari-arXiv:2009.04861v4  [cs.AI]  9 Jun 2021"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152c852b-934e-11ee-80b1-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 1, "chroma:document": "Massively Parallel and Asynchronous Tsetlin Machine Architecture\nous techniques. By introducing real-valued clause weights,\nit turns out that the number of clauses can be reduced by\nup to 50\u00d7without loss of accuracy (Phoulady et al., 2020).\nAlso, the logical inference structure of TMs makes it pos-\nsible to index the clauses on the features that falsify them,\nincreasing inference- and learning speed by up to an order of\nmagnitude (Gorji et al., 2020). Multi-granular clauses sim-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab14-934e-11ee-885c-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 1, "chroma:document": "plify the hyper-parameter search by eliminating the pattern\nspeci\ufb01city parameter (Gorji et al., 2019). In (Abeyrathna\net al., 2021), stochastic searching on the line automata (Oom-\nmen, 1997) learn integer clause weights, performing on-par\nor better than Random Forest, Gradient Boosting, Neural\nAdditive Models, StructureBoost and Explainable Boosting\nMachines. Closed form formulas for both local and global\nTMinterpretation, akin to SHAP, was proposed by Blakely"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab15-934e-11ee-8677-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 1, "chroma:document": "& Granmo (2020). From a hardware perspective, energy\nusage can be traded off against accuracy by making infer-\nence deterministic (Abeyrathna et al., 2020). Additionally,\nSha\ufb01k et al. (2020) show that TMs can be fault-tolerant,\ncompletely masking stuck-at faults. Recent theoretical work\nproves convergence to the correct operator for \u201cidentity\u201d and\n\u201cnot\u201d. It is further shown that arbitrarily rare patterns can\nbe recognized, using a quasi-stationary Markov chain-based"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab16-934e-11ee-bceb-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 1, "chroma:document": "analysis. The work \ufb01nally proves that when two patterns are\nincompatible, the most accurate pattern is selected (Zhang\net al., 2021). Convergence for the \u201cXOR\u201d operator has also\nrecently been proven by Jiao et al. (2021).\nPaper Contributions In all of the above mentioned TM\nschemes, the clauses are learnt using Tsetlin automaton\n(TA)-teams (Tsetlin, 1961) that interact to build and in-\ntegrate conjunctive clauses for decision-making. While"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab17-934e-11ee-befd-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 1, "chroma:document": "producing accurate learning, this interaction creates a bottle-\nneck that hinders parallelization. That is, the clauses must\nbe evaluated and compared before feedback can be provided\nto the TAs.\nIn this paper, we \ufb01rst cover the basics of TMs in Section 2.\nThen, we propose a novel parallel and asynchronous archi-\ntecture in Section 3, where every clause runs in its own\nthread for massive parallelism. We eliminate the above\ninteraction bottleneck by introducing local voting tallies"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab18-934e-11ee-8db8-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 1, "chroma:document": "that keep track of the clause outputs, per training exam-\nple. The local voting tallies detach the processing of each\nclause from the rest of the clauses, supporting decentralized\nlearning. Thus, rather than processing training examples\none-by-one as in the original TM, the clauses access the\ntraining examples simultaneously, updating themselves and\nthe local voting tallies in parallel. In Section 4, we investi-\ngate the properties of the new architecture empirically on"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab19-934e-11ee-b1d3-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 1, "chroma:document": "regression, novelty detection, semantic relation analysis and\nword sense disambiguation. We show that our decentralized\nTMarchitecture copes well with working on outdated data,\nwith no measurable loss in learning accuracy. We furtherinvestigate how processing time scales with the number of\nclauses, uncovering almost constant-time processing over\nreasonable clause amounts. Finally, in Section 5, we con-\nclude with pointers to future work, including architectures"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab1a-934e-11ee-b829-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 1, "chroma:document": "for grid-computing and heterogeneous systems spanning the\ncloud and the edge.\nThe main contributions of the proposed architecture can be\nsummarized as follows:\n\u2022 Learning time is made almost constant for reasonable\nclause amounts (employing from 20to7,000clauses\non a Tesla V100 GPU).\n\u2022For suf\ufb01ciently large clause numbers, computation\ntime increases approximately proportionally to the in-\ncrease in number of clauses.\n\u2022The architecture copes remarkably with working on"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab1b-934e-11ee-8e16-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 1, "chroma:document": "outdated data, resulting in no signi\ufb01cant loss in learn-\ning accuracy across diverse learning tasks (regression,\nnovelty detection, semantic relation analysis, and word\nsense disambiguation).\nOur parallel and asynchronous architecture thus allows pro-\ncessing of more massive data sets and operating with more\nclauses for higher accuracy, signi\ufb01cantly increasing the im-\npact of logic-based machine learning.\n2. Tsetlin Machine Basics\n2.1. Classi\ufb01cation"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab1c-934e-11ee-ae6b-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 1, "chroma:document": "2. Tsetlin Machine Basics\n2.1. Classi\ufb01cation\nATMtakes a vector X= [x1, . . . , x o]ofoBoolean features\nas input, to be classi\ufb01ed into one of two classes, y= 0or\ny= 1. These features are then converted into a set of literals\nthat consists of the features themselves as well as their\nnegated counterparts: L={x1, . . . , x o,\u00acx1, . . . ,\u00acxo}.\nIf there are mclasses and nsub-patterns per class, a TM\nemploys m\u00d7nconjunctive clauses to represent the sub-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab1d-934e-11ee-bf60-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 1, "chroma:document": "patterns. For a given class1, we index its clauses by j,\n1\u2264j\u2264n, each clause being a conjunction of literals:\nCj(X) =\u22c0\nlk\u2208Ljlk. (1)\nHere, lk,1\u2264k\u22642o,is a feature or its negation. Further,\nLjis a subset of the literal set L. For example, the particular\nclause Cj(X) =x1\u2227\u00acx2consists of the literals Lj=\n{x1,\u00acx2}and outputs 1ifx1= 1andx2= 0.\nThe number of clauses nassigned to each class is user-\ncon\ufb01gurable. The clauses with odd indexes are assigned pos-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab1e-934e-11ee-aeb7-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 1, "chroma:document": "itive polarity and the clauses with even indexes are assigned\n1Without loss of generality, we consider only one of the classes,\nthus simplifying notation. Any TMclass is modelled and processed\nin the same way."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab1f-934e-11ee-9851-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 2, "chroma:document": "Massively Parallel and Asynchronous Tsetlin Machine Architecture\nnegative polarity. The clause outputs are combined into a\nclassi\ufb01cation decision through summation and thresholding\nusing the unit step function u(v) = 1 ifv\u22650else0:\n\u02c6y=u(\n\u03a3n\u22121\nj=1,3,...Cj(X)\u2212\u03a3n\ni=2,4,...Cj(X))\n.(2)\nNamely, classi\ufb01cation is performed based on a majority\nvote, with the positive clauses voting for y= 1 and the\nnegative for y= 0.\nInput  \nType I feedback Type I feedbackinclude exclude include exclude"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab20-934e-11ee-bd84-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 2, "chroma:document": "1 N N+1 2 N1 N N+1 2 N\nTAstransition\nStep 1Step t\nFigure 1. TMlearning dynamics for an XOR-gate training sample,\nwith input ( x1= 0, x2= 1) and output target y= 1.\n2.2. Learning\nTMlearning is illustrated in Fig. 1. As shown, a clause\nCj(X)is composed by a team of TAs. Each TAhas2N\nstates and decides to Include (from state 1toN) orExclude\n(from state N+1to2N) a speci\ufb01c literal lkin the clause. In\nthe \ufb01gure, TArefers to the TAs that control the original form"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab21-934e-11ee-a806-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 2, "chroma:document": "of a feature ( x1andx2) while TA\u2019 refers to those controlling\nnegated features (\u00acx1and\u00acx2). A TAupdates its state\nbased on the feedback it receives in the form of Reward,\nInaction, and Penalty (illustrated by the features moving in\na given direction in the TA-part of the \ufb01gure). There are\ntwo types of feedback associated with TMlearning: Type I\nfeedback and Type II feedback, which are shown in Table 1\nand Table 2, respectively.\nType I feedback is given stochastically to clauses with odd"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab22-934e-11ee-8433-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 2, "chroma:document": "indexes when y= 1and to clauses with even indexes when\ny= 0. Each clause, in turn, reinforces its TAs based on:\n(1) its output Cj(X); (2) the action of the TA\u2013Include or\nExclude ; and (3) the value of the literal lkassigned to the\nTA. As shown in Table 1, two rules govern Type I feedback:\n\u2022Include is rewarded and Exclude is penalized with prob-\nabilitys\u22121\nsifCj(X) = 1 andlk= 1. This reinforce-\nment is strong2(triggered with high probability) and\n2Note that the probabilitys\u22121"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab23-934e-11ee-8ee2-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 2, "chroma:document": "2Note that the probabilitys\u22121\nsis replaced by 1when boosting\ntrue positives.INPUTCLAUSE 1 0\nLITERAL 1 0 1 0\nINCLUDE LITERALP(R EWARD )s\u22121\nsNA 0 0\nP(INACTION )1\nsNAs\u22121\nss\u22121\ns\nP(P ENALTY ) 0 NA1\ns1\ns\nEXCLUDE LITERALP(R EWARD ) 01\ns1\ns1\ns\nP(INACTION )1\nss\u22121\nss\u22121\nss\u22121\ns\nP(P ENALTY )s\u22121\ns0 0 0\nTable 1. Type I Feedback\nINPUTCLAUSE 1 0\nLITERAL 1 0 1 0\nINCLUDE LITERALP(R EWARD ) 0 NA 0 0\nP(INACTION )1.0 NA 1.0 1.0\nP(P ENALTY ) 0 NA 0 0\nEXCLUDE LITERALP(R EWARD ) 0 0 0 0\nP(INACTION )1.0 0 1.0 1.0"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab24-934e-11ee-86fe-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 2, "chroma:document": "P(INACTION )1.0 0 1.0 1.0\nP(P ENALTY ) 0 1.0 0 0\nTable 2. Type II Feedback\nmakes the clause remember and re\ufb01ne the pattern it\nrecognizes in X.\n\u2022Include is penalized and Exclude is rewarded with prob-\nability1\nsifCj(X) = 0 orlk= 0. This reinforcement\nis weak (triggered with low probability) and coarsens\ninfrequent patterns, making them frequent.\nAbove, parameter scontrols pattern frequency.\nType II feedback is given stochastically to clauses with"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab25-934e-11ee-80d2-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 2, "chroma:document": "odd indexes when y= 0and to clauses with even indexes\nwhen y= 1. As captured by Table 2, it penalizes Exclude\nwith probability 1ifCj(X) = 1 andlk= 0. Thus, this\nfeedback produces literals for discriminating between y= 0\nandy= 1.\nThe \u201cstate\u201d is realized as a simple counter per Tsetlin\nAutomaton. In practice, reinforcing Include (penalizing\nExclude or rewarding Include) is done by increasing the\ncounter, while reinforcing exclude (penalizing Include or"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab26-934e-11ee-b621-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 2, "chroma:document": "rewarding Exclude) is performed by decreasing the counter.\nAs an example of learning, let us consider a dataset with\nXOR-gate sub-patterns. In particular, consider the input\n(x1= 0, x2= 1) and target output y= 1to visualize the\nlearning process (Fig. 1). We further assume that we have\nn= 4clauses per class. Among the 4clauses, the clauses\nC1andC3vote for y= 1and the clauses C0andC2vote for\ny= 0. For clarity, let us only consider how C1andC3learn"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab27-934e-11ee-8850-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 2, "chroma:document": "a sub-pattern from the given sample of XOR-gate input and\noutput. At Step 1 in the \ufb01gure, the clauses have not yet learnt\nthe pattern for the given sample. This leads to the wrong\nclass prediction (\u02c6y= 0) , thereby triggering Type I feedback"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab28-934e-11ee-baab-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 3, "chroma:document": "Massively Parallel and Asynchronous Tsetlin Machine Architecture\nfor the corresponding literals. Looking up clause output\nC1(X) = 0 and literal value x1= 0 in Table 1, we note\nthat the TAcontrolling x1receives either Inaction or Penalty\nfeedback for including x1inC1, with probabilitys\u22121\nsand\n1\ns, respectively. After receiving several penalties, with high\nprobability, the TAchanges its state to selecting Exclude .\nAccordingly, literal x1gets removed from the clause C1."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab29-934e-11ee-9302-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 3, "chroma:document": "After that, the TAthat has excluded literal \u00acx1fromC1also\nobtains penalties, and eventually switches to the Include\nside of its state space. The combined outcome of these\nupdates are shown in Step tforC1. Similarly, the TAthat\nhas included literal \u00acx2in clause C1receives Inaction or\nPenalty feedback with probabilitys\u22121\nsand1\ns, respectively.\nAfter obtaining multiple penalties, with high probability,\n\u00acx2becomes excluded from C1. Simultaneously, the TA"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab2a-934e-11ee-90e9-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 3, "chroma:document": "that controls x2ends up in the Include state, as also shown\nin Step t. At this point, both clause C1andC3outputs 1for\nthe given input, correctly predicting the output \u02c6y= 1.\nResource allocation dynamics ensure that clauses dis-\ntribute themselves across the frequent patterns, rather than\nmissing some and over-concentrating on others. That is,\nfor any input X, the probability of reinforcing a clause\ngradually drops to zero as the clause output sum\nv= \u03a3n\u22121\nj=1,3,...Cj(X)\u2212\u03a3n\ni=2,4,...Cj(X) (3)"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab2b-934e-11ee-93ef-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 3, "chroma:document": "v= \u03a3n\u22121\nj=1,3,...Cj(X)\u2212\u03a3n\ni=2,4,...Cj(X) (3)\napproaches a user-set margin Tfory= 1 (and\u2212Tfor\ny= 0). If a clause is not reinforced, it does not give feed-\nback to its TAs, and these are thus left unchanged. In the\nextreme, when the voting sum vequals or exceeds the mar-\nginT(the TM has successfully recognized the input X),\nno clauses are reinforced. They are then free to learn new\npatterns, naturally balancing the pattern representation re-\nsources (Granmo, 2018)."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab2c-934e-11ee-85a4-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 3, "chroma:document": "sources (Granmo, 2018).\n3. Parallel and Asynchronous Architecture\nEven though CPUs have been traditionally geared to handle\nhigh workloads, they are more suited for sequential process-\ning and their performance is still dependant on the limited\nnumber of cores available. In contrast, since GPUs are pri-\nmarily designed for graphical applications by employing\nmany small processing elements, they offer a large degree\nof parallelism (Owens et al., 2007). As a result, a growing"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab2d-934e-11ee-9bc8-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 3, "chroma:document": "body of research has been focused on performing general\npurpose GPU computation or GPGPU. For ef\ufb01cient use of\nGPU power, it is critical for the algorithm to expose a large\namount of \ufb01ne-grained parallelism (Jiang & Snir, 2005;\nSatish et al., 2009).\nWhile the voting step of the TM(Eq. 3) hinders paral-\nlelization, the remainder of the TMarchitecture is natively\nparallel. In this section, we introduce our decentralized\ninference scheme and the accompanying architecture that"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab2e-934e-11ee-b7b9-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 3, "chroma:document": "makes it possible to have parallel asynchronous learningand classi\ufb01cation, resolving the voting bottleneck by using\nlocal voting tallies.\n3.1. Voting Tally\nA voting tally that tracks the aggregated output of the clauses\nfor each training example is central to our scheme. In a\nstandard TM, each training example (Xi, yi),1\u2264i\u2264q,\nis processed by \ufb01rst evaluating the clauses on Xiand then\nobtaining the majority vote vfrom Eq. (3). Here, qis the\ntotal number of examples. The majority vote vis then"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab2f-934e-11ee-bdf8-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 3, "chroma:document": "compared with the summation margin Twhen y= 1and\n\u2212Twhen y= 0, to produce the feedback to the TAs of each\nclause, explained in the previous section.\nFigure 2. Parallel Tsetlin machine architecture.\nAs illustrated in Fig. 2, to decouple the clauses, we now\nassume that the particular majority vote of example Xihas\nbeen pre-calculated, meaning that each training example\nbecomes a triple (Xi, yi, vi), where viis the pre-calculated\nmajority vote. With viin place, the calculation performed"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab30-934e-11ee-9548-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 3, "chroma:document": "in Eq. (3) can be skipped, and we can go directly to give\nType I or Type II feedback to any clause Cj, without con-\nsidering the other clauses. This opens up for decentralized\nlearning of the clauses, facilitating native parallelization\nat all inference and learning steps. The drawback of this\nscheme, however, is that any time the composition of a\nclause changes after receiving feedback, all voting aggre-\ngates vi,1\u2264i\u2264q,become outdated. Accordingly, the"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab31-934e-11ee-8c38-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 3, "chroma:document": "gates vi,1\u2264i\u2264q,become outdated. Accordingly, the\nstandard learning scheme for updating clauses must be re-\nplaced.\n3.2. Decentralized Clause Learning\nOur decentralized learning scheme is captured by Algo-\nrithm 1. As shown, each clause is trained independently of\nthe other clauses. That is, each clause proceeds with training\nwithout taking other clauses into consideration. Algorithm 1\nthus supports native parallelization because each clause now\ncan run independently in its own thread."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab32-934e-11ee-a046-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 4, "chroma:document": "Massively Parallel and Asynchronous Tsetlin Machine Architecture\nAlgorithm 1 Decentralized updating of clause\nInput: Example pool P, clause Cj, positive polarity\nindicator pj\u2208 {0,1}, batch size b\u2208[1,\u221e), voting\nmargin T\u2208[1,\u221e), pattern speci\ufb01city s\u2208[1,\u221e).\nProcedure: UpdateClause : Cj, pj, P, b, T, s .\nfori= 1tobdo\n(Xi, yi, vi)\u2190ObtainTrainingExample( P)\nvc\ni\u2190clip(vi,\u2212T, T)\ne=T\u2212vc\niifyi= 1elseT+vc\ni\nifrand()\u2264e\n2Tthen\nifyixorpjthen\nCj\u2190TypeIIFeedback( Xi, Cj)\nelse\nCj\u2190TypeIFeedback( Xi, Cj, s)\nend if"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab33-934e-11ee-b728-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 4, "chroma:document": "else\nCj\u2190TypeIFeedback( Xi, Cj, s)\nend if\noij\u2190Cj(Xi)\no\u2217\nij\u2190ObtainPreviousClauseOutput( i, j)\nifoij\u0338=o\u2217\nijthen\nAtomicAdd( vi, oij\u2212o\u2217\nij)\nStorePreviousClauseOutput( i, j, o ij)\nend if\nend if\nend for\nNotice further how the clause in focus \ufb01rst obtains a ref-\nerence to the next training example (Xi, yi, vi)to process,\nincluding the pre-recorded voting sum vi(Line 3). This\nexample is retrieved from an example pool P, which is the\nstorage of the training examples (centralized or decentral-\nized)."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab34-934e-11ee-9cb7-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 4, "chroma:document": "ized).\nThe error of the pre-recorded voting sum viis then calcu-\nlated based on the voting margin T(Line 5). The error, in\nturn, decides the probability of updating the clause. The up-\ndating rule is the standard Type I and Type II TMfeedback,\ngoverned by the polarity pjof the clause and the speci\ufb01city\nhyper-parameter s(Lines 6-11).\nThe moment clause Cjis updated, all recorded voting sums\nin the example pool Pare potentially outdated. This is"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab35-934e-11ee-82ae-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 4, "chroma:document": "because Cjnow captures a different pattern. Thus, to keep\nall of the voting sums viinPconsistent with Cj,Cjshould\nideally have been re-evaluated on all of the examples in P.\nTo partially remedy for outdated voting aggregates, the\nclause only updates the current voting sum vi. This happens\nwhen the calculated clause output oijis different from the\npreviously calculated clause output o\u2217\nij(Lines 12-17). Note\nthat the previously recorded output o\u2217\nijis a single bit that"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab36-934e-11ee-b8a6-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 4, "chroma:document": "ijis a single bit that\nis stored locally together with the clause. In this manner,\nthe algorithm provides eventual consistency . That is, if\nthe clauses stop changing, all the voting sums eventually\nbecome correct.A point to note here is that there is no guarantee that the\nclause outputs in the parallel version will sum up to the\nsame number as in the sequential version. The reason is that\nthe updating of clauses is asynchronous, and the vote sums"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab37-934e-11ee-827c-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 4, "chroma:document": "are not updated immediately when a clause changes. We\nuse the term eventual consistency to refer to the fact that\nif the clauses stop changing, eventually, the tallied voting\nsums become the exact sum of the clause outputs. Although\nnot analytically proven, experimental results show that the\ntwo versions provide consistent \ufb01nal accuracy results after\nclause summation and thresholding.\nEmploying the above algorithm, the clauses access the train-"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab38-934e-11ee-bce5-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 4, "chroma:document": "ing examples simultaneously, updating themselves and the\nlocal voting tallies in parallel. There is no synchronization\namong the clause threads, apart from atomic adds to the\nlocal voting tallies (Line 15).\n4. Empirical Results\nIn this section, we investigate how our new approach to\nTMlearning scales, including effects on training time and\naccuracy. We employ seven different data sets that repre-\nsent diverse learning tasks, including regression, novelty"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab39-934e-11ee-b681-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 4, "chroma:document": "detection, sentiment analysis, semantic relation analysis,\nand word sense disambiguation. The data sets are of var-\nious sizes, spanning from 300to100,000examples, 2to\n20classes, and 6to102,176features. We have striven to\nrecreate TMexperiments reported by various researchers,\nincluding their hyper-parameter settings. For comparison of\nperformance, we contrast with fast single-core TMimple-\nmentations3both with and without clause indexing (Gorji"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab3a-934e-11ee-bd9a-ac198e74a6f7
encoding: FLOAT32
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{"source": "source_documents\\2009.04861.pdf", "page": 4, "chroma:document": "et al., 2020). Our proposed architecture is implemented in\nCUDA and runs on a Tesla V100 GPU (grid size 208and\nblock size 128). The standard implementations run on an\nIntel Xeon Platinum 8168 CPU at 2.70GHz. Code is avail-\nable at https://github.com/cair/ICML-Massively-Parallel-\nand-Asynchronous-Tsetlin-Machine-Architecture.\nWe summarize the obtained performance metrics in Table 3.\nFor better reproducibility, each experiment is repeated \ufb01ve"}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab3b-934e-11ee-9dd6-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 4, "chroma:document": "times and the average accuracy and standard deviation are\nreported. We also report how much faster the CUDA TM\nexecutes compared with the indexed version.\nThe focus in this section is to highlight the speed-ups\nachieved via parallelization of the TM architecture. How-\never, for the sake of completeness, we also include corre-\nsponding results for SVM using ThunderSVM, which is\nan established GPU implementation of SVM (Wen et al.,\n2018). The performance results are compiled in Fig. 44."}


created_at: 2023-12-05 09:10:18
topic: persistent://default/default/a0c119a8-dc6b-46d3-8158-5f41a08fd57f
id: 152cab3c-934e-11ee-a807-ac198e74a6f7
encoding: FLOAT32
metadata:
{"source": "source_documents\\2009.04861.pdf", "page": 4, "chroma:document": "As seen, our TM parallelization is signi\ufb01cantly faster than\n3Retrieved from https://github.com/cair/pyTsetlinMachine.\n4Google\u2019s Colab is used to run the two CUDA models in the\ntable for fair comparison."}


