1Association for the Advancement of Artificial Intelligence
1900 Embarcadero Road, Suite 101
Palo Alto, California 94303-3310 USA
<EMAIL_ADDRESS>
# Any-Way Meta Learning

Written by AAAI Press Staff1
AAAI Style Contributions by Pater Patel Schneider, Sunil Issar,
J. Scott Penberthy, George Ferguson, Hans Guesgen, Francisco Cruz, Marc Pujol-
Gonzalez With help from the AAAI Publications Committee.

###### Abstract

Meta-learning has showcased prowess in rapid adaptability, yet its reliance on
fixed cardinalities contrasts starkly with human learning’s inherent
flexibility. This paper challenges the existing paradigm of meta-learning by
harnessing ‘label equivalence’, emerging from stochastic numeric label
assignments during episodic task sampling. We introduce the “any-way” learning
paradigm, an innovative model training approach free from fixed cardinality
constraints. Surprisingly, this model not only matches but often outperforms
traditional fixed-way models in terms of performance, convergence speed, and
stability, disrupting long-held beliefs about domain generalization. To
address the semantic information gap resulting from label equivalence, we
further propose a mechanism to infuse semantic class information to the model,
enhancing the model’s comprehension and functionality. Experiments on renowned
architectures like MAML and ProtoNet affirm our method’s effectiveness,
pushing the boundaries of what defines “true” meta-learning and setting the
stage for a more versatile and semantically-aware future in the field.

## Introduction

Meta-learning, often referred to as ‘learning to learn’, is a training
strategy designed to enable rapid adaptation to new tasks with only a few
examples. Despite the impressive performance of deep learning models on
extensive datasets, they still fall short of human abilities when it comes to
learning from a small number of instances. Various approaches have been
proposed to tackle this challenge labelequiv:metadefinition.

There are two main meta-learning approaches. The first approach focuses on
creating an effective feature extractor, like ProtoNet episodic:MBML:Protonet,
which can accurately cluster unseen instances from the same class to enable
the model to generalize well to new data. The second approach aims to find a
suitable initialization point for the model, facilitating rapid adaptation to
unseen tasks episodic:GBML:MAML.

To imbue the model with meta-learning ability, both methods involve episodes.
Each episode consists of multiple tasks and tests the model’s meta-learning
ability in the regime of few-shot learning (Fig. 1). This continuous exposure
to new tasks helps the model improve its learning ability from limited data,
which simulates the conditions under which humans learn.

Nonetheless, in contrast to the human’s remarkable flexibility in classifying
varying numbers of classes, the current learning models remain rigid,
restricted to the fixed ‘way’ they were trained on. As evident in Table 1,
when a model trained on 10-way-5-shot tasks from miniImageNet
dataset:miniimagenet is tested on a 3-way-5-shot cars dataset:cars setting,
its performance plunges to a mere 41$\%$. Considering that random sampling
would yield at least 33$\%$, this reveals a glaring deficiency in meta-
learning’s adaptability across different ‘way’ settings.

This sharp decline in performance is more than just a testament to the model’s
inflexibility; it also suggests that different ‘way’ episodes might hail from
different distributions. This variation between distributions touches upon a
deeper, underlying problem: domain generalization. Essentially, to achieve
true ‘any-way’ learning, our models must address the broader challenge of
performing effectively even in disparate, unseen domains.

The core objective of this paper is to highlight and address this challenge,
advocating for an approach where task cardinality agnosticity becomes a
foundational element in meta-learning.

Figure 1: Task sampling procedure of our any-way meta-learning. Meta-learning
learns through episodic learning. It has a mother dataset with a large number
of classes ($M$) where each label represents each semantic class. Each episode
samples $N<M$ classes from this mother dataset and a random numeric class
($\in[N]$) is assigned to each selected class. Note that in our any-way
setting, $N$ is different for different tasks. If $N$ is fixed along episodes,
it becomes conventional sampling procedure.

To deal with this problem, we propose an ‘any-way’ meta-learning method based
on the concept of ‘label equivalence’, which emerges from the task sampling
process, an essential element in few-shot learning including meta-learning.
The task sampling process has a unique characteristic: classes are randomly
sampled and assigned to (typically numeric) class labels within each episode.
These labels are not assigned based on the inherent semantics of the classes;
rather, they are determined by the requirements of the specific tasks in each
episode. As a result, the same class can be assigned different labels in
different tasks and episodes, and the meaning of a label can change from one
task to another. As a result, a numeric class label in a given task does not
necessarily represent a specific class111In this paper, we differentiate the
‘semantic class’ from the ‘numeric class label’ as shown in Fig. 1.. This
distinction introduces a phenomenon we term ‘label equivalence’, which
suggests that all output labels are functionally equivalent to one another.

Table 1: Performance Comparison between different number of ways, a model is trained within miniImageNet. number in paraenthethis indicates number of shots. # of ways (train) | 3 | 10 | 5 | 10
---|---|---|---|---
# of ways (test) | 3 | 5
miniImageNet (5) | 76.27 | 62.45 | 64.92 | 55.2
Cars (5) | 59.95 | 41.47 | 47.73 | 32.38

Examining label equivalence naturally brings up an important question: Given
the equivalence of all labels or output nodes, is it necessary to match the
number of output nodes to the number of classes in each task? For instance, if
a new task consists of three classes, we could select 3 nodes from a pool of,
let’s say, 30 output nodes and designate them as numeric labels, optimizing
solely for this selected path. This implies that there’s no need to rigidly
stick to a fixed number of numeric labels, potentially allowing us to further
generalize the few-shot learning process. It is from this juncture that our
discourse begins.

The primary contribution of this paper is the world-premiere proposition of
‘any-way’ few-shot learning, moving beyond the conventional fixed-way few-shot
learning. Not only do we extend meta-learning to any-way, but we also provide
an efficient, general learning algorithm that achieves performance comparable
to or even better than fixed-way learning. Moreover, label equivalence further
suggests that individual outputs cannot represent the semantic of a class.
This arises from the fact that each few-shot task contains no semantic
information about its class, nor does it recognize or account for the classes
it comprises. From this perspective, we can perceive supervised learning as
solving a given task within an absolute coordinate system (one axis for one
semantic class), while few-shot learning can be viewed as problem-solving
within a relative coordinate system, where the uniqueness of each class is the
only clue for learning.

Our second contribution deals with the challenges arising from the lack of
semantic class information. In this paper, we introduce an algorithm that
compensates for this issue by integrating semantic class information into the
learning process. We show that our algorithm not only improves performance in
environments where the distribution of the test set differs from that of the
training set, but also enables the application of data-augmentation techniques
used in supervised learning to few-shot learning tasks. We demonstrate the
effectiveness of this approach in MAML and ProtoNet, two of the most
representative methods of episode-based meta-learning.

Figure 2: Overall structure of our proposed algorithm. The upper section
delineates the implementation of the any-way meta-learning, while the lower
section highlights the integration of semantic class information. It’s
noteworthy that the encoder $f$ is not updated with $g_{s}$ during the inner
loop.

## Related Works

Meta-learning, briefly described, is about the study of algorithms that learn
from data. As defined in labelequiv:metadefinition, the fundamental concept of
meta-learning is the model’s capability to discern relationships among a
limited number of samples. Furthermore, mechanisms were proposed in
label_equiv:matchingnetwork to continuously verify meta-learning abilities
while simultaneously enhancing performance.

Inspired by the Matching network label_equiv:matchingnetwork, a majority of
current meta-learning models adopt an episode-based training approach. As
summarized by nonepisodic:transferminitocars, these episode-based models
usually consist of two stages: the meta-training stage to acquire meta-
learning capabilities, and the meta-test stage to evaluate their performance.
There are two lines of research in this area:

Gradient-Based Meta Learning (GBML) first introduced by the Model-Agnostic
Meta-learning model (MAML) episodic:GBML:MAML, involves training the support
set in the inner loop through gradient descent. The degree of optimization is
then evaluated on the query set, followed by the outer loop refining the meta-
initialization parameter to enhance learning on the support set. There’s a
growing body of research in GBML such as episodic:GBML:ANIL;
episodic:GBML:imaml; episodic:GBML:warpgrad; episodic:GBML:Reptile. Notably,
due to the computational demands of caluculating the Hessain in the inner
loop, methods that utilize latent vectors to reduce this computation have been
explored episodic:GBML:LEO. Other studies have put forward the idea of
avoiding the use of the Hessian altogether episodic:GBML:ANIL;
episodic:GBML:Reptile; episodic:GBML:MAML.

Metric-Based Meta Learning (MBML) is focused on training an effective encoder
that can perform clustering at the feature level. This approach, which
predates GBML, was established by initiatives such as
label_equiv:matchingnetwork. A foundational architecture for this was proposed
by Protonet episodic:MBML:Protonet. The method involves extracting features
for the inputs in the support set by an encoder, clustering them, and then
minimizing the distance between the query set and the corresponding class.
Although clustering is conventionally conducted in the Euclidean space, it has
been shown to be more effective in other Riemannian spaces like the Hyperbolic
space episodic:MBML:Hyperbolic.

Domain Generalization field focuses on designing models that exhibit
robustness across diverse environments DG:Gunbon0; DG:Gunbon1. Our approach to
“any-way” meta-learning aligns with this objective. As illustrated in Table 1,
episodes of varying cardinality can be perceived as from distinct
distributions. In pursuing a model endowed with a genuine meta-learning
capability— capable of adapting to any task cardinality— we inevitably
confront the challenges posed by domain generalization.

The conventional understanding suggests that while it is possible to enhance
the overall performance on a set of tasks, the performance on individual
datasets might decline when compared to models trained exclusively on a
specific episode DG:wisdom0; DG:wisdom1; DG:wisdom2. In this paper, we
challenge this established notion. Through the integration of label
equivalence, we posit that this trade-off might not be as significant within
the meta-learning realm. Our results exhibit not only the seamless
adaptability to “any-way” tasks but also superior performance compared to
fixed-way training paradigms.

## Method

### Conventional (Fixed-way) Meta-Learning

To evaluate the few-shot learning ability within a given distribution, we
define a process of task sampling. Initially, we select a label set from the
class pool of a larger mother dataset $\mathcal{D}$. In conventional meta-
learning, the cardinality $N$ of the selected label set remains fixed during
the entire training procedure. We then sample data from this set, each
matching the size of the support set (number of shots). Each task $\tau$
consists of a set $\mathcal{X}$ of tuples $\\{(x,y)\\}$ sampled from
$\mathcal{D}$, where $x$ denotes the input data and $y$ represents the numeric
label rather than the semantic class from the dataset (Fig. 1). Moreover,
$\mathcal{X}$ is divided into a support set $\mathcal{X}_{s}$ and a query set
$\mathcal{X}_{q}$ for task learning and performance evaluation, respectively.
To do so, a model with encoder $f$ and $N$-way classifier $g_{f}$222Subscript
$f$ denotes ‘fixed-way’ while $a$ is used for ‘any-way’.  learns from the
support set, then evaluates its performance with the query set.

Algorithm 1 Any-Way Meta-Learning

Output dimension $O$

Trained model $\theta$

Initialize model parameters $\theta$

for episode $=1$ to $K$ do

Sample a random number $N\leq O$

Sample a task $\tau$ with $N$ number of classes and set $J=\lfloor
O/N\rfloor$.

Generate $S=\\{s_{j}\\},j\in[J]$ where $s_{j}\in\mathbb{R}^{N}$ is a random
assignment, non-overlapping with $s_{i},\ \forall i\neq j$

Calculate any-way loss
$L_{a}=\sum_{j=1}^{J}L(S_{j}(g_{a}(f(x_{\text{support}}))),y)$ and update the
model parameters $\theta$ using $L_{a}$

Calculate logit for the query set: logit
$=\sum_{j=1}^{J}S_{j}(g_{a}(f(x_{\text{query}})))$

Calculate accuracy, and update meta-parameters based on logit and the actual
labels of the query set

end for

return trained model with parameters $\theta$

### Any-way Meta-Learning

As mentioned earlier, there exists an equivalence among numeric labels. We can
leverage these characteristics to enhance the meta-ability of the model.

Firstly, our model’s output dimension, $O$, is set to be greater than the
maximum cardinality of the tasks’ label sets, implying that each time we
sample a task $\tau_{i}$ with $N_{i}$ classes, we must assign $N_{i}$ labels
among $O$ output nodes.

With our proposed configuration , we maintain output-to-class assignments
during each episode. This not only determines a unique and unchanging pathway
for selecting numeric labels but also restricts gradient updates to occur
exclusively along this fixed way, thereby accommodating the execution of
standard meta-learning tasks. Unlike traditional methods that fix the
cardinality of the task when conducting task sampling, our approach also
involves sampling the cardinality. This enables our model to handle tasks with
any cardinality, hence fostering a cardinality-independent learning
environment, i.e., any-way meta-learning. However, a potential problem arises
when the output dimensionality $O$ significantly exceeds the expected task
cardinality. In this case, the chance of each classifier node being selected
in each episode approaches zero. Consequently, classifier nodes might undergo
less training than the encoder throughout the training procedure, resulting in
an underfit. To remedy this, we assign a set of output nodes to a numeric
label. We assign a numeric label to (almost) all nodes for classification,
rather than assigning a numeric label to just one output node and ignoring the
unassigned nodes.

Let $f(x)$ be a feature map for the input $x$ and $g_{a}(\cdot)$ be an any-way
classifier consisting of $O$ output nodes. For a task with $N$ classes, we can
constitute $J=\lfloor O/N\rfloor$ assignments $s_{j}\in\mathbb{R}^{N}$,
$j\in[J]$ whose $i$-th element corresponds to the output node for the $i$-th
numeric class label333For example, consider a scenario with eight classifier
output nodes and three classes in a task, thus, three numeric labels. In this
case, it can be $s_{1}=[3,5,2]^{T}$, $s_{2}=[7,4,8]^{T}$ and nodes 1 and 6 are
unassigned. . Here, $\lfloor\cdot\rfloor$ is the floor operation, and $[n]$
denotes a set of natural numbers from $1$ to $n$. We then aggregate the loss
for each assignment to constitute our any-way loss $L_{a}$ as

$L_{a}=\sum_{j=1}^{J}L(S_{j}(g_{a}(f(x))),y).$ (1)

Here, $S_{j}:\mathbb{R}^{O}\rightarrow\mathbb{R}^{N}$ uses the vector $s_{j}$
as an index function to extract $N$ elements, e.g. $S_{1}(v)$ with
$s_{1}=[3,5,2]^{T}$ outputs $[v_{3},v_{5},v_{2}]^{T}$. As different
assignments do not overlap, i.e., $\text{set}(s_{i})\ \cap\
\text{set}(s_{j})=\phi$ where $\text{set}(v)$ is the set consisting of
elements of the vector $v$, this additional assignment procedure requires no
additional computation. i.e., no additional backpropagation nor inference.

### Injecting Semantic Class Information to Model

While it’s possible to implement any-way meta-learning through label
equivalence, relying solely on numeric labels leaves out important semantic
information. To overcome this, we introduce an auxiliary classifier to fill
this gap. The overall structure is illustrated at the bottom of Fig. 2
($g_{s}$).

During the inner training loop, the auxiliary classifier employs features
produced by the encoder. These features originate from an initial set point
defined by meta-parameters. Our main objective is to ensure that these
features encapsulate the semantic information of the class. To verify this, we
use the auxiliary classifier to discern different semantic classes. To
maintain consistency and simplicity, the encoder remains unchanged throughout
this process, allowing for a single pass through the network. The majority of
computations are streamlined through a compact linear layer, ensuring minimal
computational overhead.

In our implementation, the semantic loss, $L_{s}$, which is a typical cross-
entropy loss with $C(\gg N)$ classes, is added to the original loss (either a
fixed-way loss or an any-way loss in (1)) using a balancing weight $\lambda$,
i.e., $L_{total}=L_{original}+L_{s}$.

The inclusion of the auxiliary classifier provides a gateway to information
that was previously inaccessible in conventional episode-based meta-learning.
This unique structure, where supervised learning is inherent in the auxiliary
classifier in every episode, paves the way for incorporating conventional
supervised learning techniques into our approach. As an exemplar, we employ
the Mixup technique, one of the most commonly used data-augmentation
techniques in supervised learning. Using the known semantic classes, we apply
this technique as it is used in supervised learning. While the numeric labels
stay unchanged, we blend the semantic class across tasks, generating new
input-output pairings. This practical implementation of the Mixup technique in
our methodology emphasizes our central assertion: conventional supervised
learning strategies can be seamlessly and effectively integrated within the
meta-learning landscape.

Table 2: f denotes ‘fixed-way’ while a is used for ‘any-way’. For implementing
10-way-1-shot f-MAML, we encountered many corruption in this case. i.e., the
model does not trained. We discarded all these failed experiments and sampled
three ’successed’ models with different seeds for performance report. For
a-MAML, we did not encountered any corruption.

Dataset miniImageNet TieredImageNet Cars CUB Num-Way 3 5 10 3 5 10 3 5 10 3 5
10 f-MAML (1) 59.56(1.48) 46.86(0.95) 31.91(0.50) 46.86(0.95) 46.76(0.58)
46.86(0.95) 64.02(0.95) 49.19(0.56) 32.84(1.91) 46.86(0.95) 57.35 (0.58)
46.86(0.95) a-MAML (1) 63.15 (0.52) 48.33(0.26) 31.34(0.28) 61.92 (0.26)
47.43(0.28) 31.62(0.18) 64.72 (0.24) 50.24(0.23) 33.79(0.26) 72.21 (0.19)
58.85(0.33) 41.66(0.42) \+ semantic (1) 64.25 (1.42) 49.16(0.83) 32.28(0.87)
62.80 (0.92) 48.33(1.02) 32.41(0.80) 65.08(0.94) 50.93(0.89) 34.04(0.33)
72.63(0.22) 59.27(0.45) 41.82(0.96) f-MAML (5) 76.64(0.41) 65.41 (1.04)
51.18(0.27) - 67.69 (0.23) - 79.54(0.85) 66.59 (1.22) 50.05(1.38) - 74.71
(0.40) - a-MAML (5) 79.06(0.38) 66.73(0.42) 50.28(0.49) 79.30(0.47)
68.10(0.63) 52.19(0.78) 81.55(0.49) 70.42(0.88) 52.67(2.23) 84.77 75.62 60.8
\+ semantic (5) 78.89(0.42) 66.91(0.10) 50.16(0.0.06) 79.08(1.26) 67.40(1.29)
51.12(1.73) 81.65(0.19) 70.56(0.12) 52.125(0.78) 84.77 (0.15) 75.36(0.12)
59.76 (0.26)

## Experiment

### Implementation Details

Datasets We evaluated our methodology on a diverse range of datasets. The
general datasets, denoted as ‘G’, such as miniImageNet dataset:miniImageNet
and TieredImageNet dataset:tieredimagenet (subsets of the more extensive
ImageNet dataset:imagenet with 100 and 400 classes respectively) serve as
versatile bases for broader tasks. In contrast, the Cars dataset:cars and CUB
dataset:cub datasets, representing specific datasets or ‘S’, are widely used
for fine-grained image classification evaluations due to their focus on
closely related objects with subtle variations. By utilizing these datasets,
we are able to comprehensively evaluate the performance of our methodology
across different task spectrums.

Task sampling For each episode’s initiation, the task cardinality was sampled
from {3, 5, 7, 9}. While tests were conducted on 3-way, 5-way, and 10-way, the
10-way cardinality was excluded from our sampling pool.

Hyperparameters In line with episodic:GBML:BOIL, our experiments involved
sampling 60,000 episodes. We adopted the 4-conv architecture as detailed in
dataset:miniImageNet. The learning rates were set at 0.5 for the inner loop
and 0.001 for the outer loop. Depending on the shot type, the $\lambda$ values
were adjusted: 0.1 for 1-shot and 0.5 for 5-shot for MAML. And 0.1 for 5-shot
and 0.01 for 1-shot in ProtoNet. For the mixup showcase, we followed the
convention of sampling mixup rate from beta distribution with
$\alpha=\beta=0.5$. Four images were mixed to generate a mixup image. Also,
when constructing prototye vectors, the EMA rate was set to 0.05 for 5-shot
and 0.01 for 1-shot.

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enalblingdiscenrrn delicate delvedthe utilizatio non of the mix up technique
yrPㅇ이 ㅏㅍ파팥파트튿트도 ㅈ자잘 ㅇ이잏이해 ㅇ아안 ㄱ가감 ㅎ하한 ㅂ버번 ㄷ ㄷ더 ㄷ다ㄷ더ㄷ다닷다시 ㅈ저정ㄹ리맇리해햅해보봐봤ㅇ으음으며면
ㅈ조좋ㄱ게겠ㅇㅁㅇ으음/. ㅈ주중ㅂ보복ㄷ도되된되느는 ㅇ으의읨의미?ㄱ가 ㄴ너ㅜ ㅁ무 ㄴ내냉내요용ㅇ이 ㅈ조좀 ㅁ마만많ㅇ으은 ㄱ거것 ㄱ가같ㄱ고,
ㅅ서설섦설며명ㅇ이 ㅈ자장ㅎ호화황ㅎ하함..TCCCUbBㅛㅛㄱㄱ:yr: yr”: dㅇ으음음 and assigned the model with
the highest score as the best model and assigned the model with the highest
score as the best model and assigned the model with the highest score as the
best model.(metric-basedㄴ느는는 ㄱ그극그게게 ㅇ어업없없ㅇ어엇어서서 ㅇ어어ㄸ떠떻떻ㄱ게게 ㅎ하할할ㄲ까까) Initially,
our study centered around models eq capable of we since metric-based models
lack usuch classifiers, we recognized the need for refining our algorithm
apporroach. anmd explored seminal research in the field of continual learning
essentialpisodic:MBML:Protonet, a well-acknowledged method within MBML.
Demonstrating efficacy in both GBML and MAML reinforced our propositions. To
select the best-performing validation model, in the case of any-way MAML, we
simply summed accuracy scores across task pools and assigned the model with
the highest score as the best model. 문장이 무얼 말하고 싶은지 잘 이해가 안 감. 그림 2의 inference
phase에서의 sum하는 부분을 말하는 건지?  Scenarios As articulated in
nonepisodic:transferminitocars, the merit of meta-learning extends beyond
achieving high performance within the trained distribution. It’s equally
pivotal to maintain competent performance when the test distribution deviates
from the training paradigm. Therefore, our experimental designs spanned four
distinct cross-adaptation scenarios: transfer within general datasets
(G$\rightarrow$G), transfer from general to specific datasets
(G$\rightarrow$S), transfer from specific to general datasets
(S$\rightarrow$G), and transfer within specific datasets (S$\rightarrow$S).
Expansion to Metric-Based Learning Initially, our study centered around models
equipped with classifiers capable of discerning semantic classes. However,
since metric-based models lack such classifiers, we recognized the need for
refining our algorithm approach and explored seminal research in the field of
continual learning. Noteworthy contributions, as highlighted by
continual:catastrophic; catastrophygunbon; continual:memoryrehearsal,
elucidate essential techniques to mitigate the ’catastrophic forgetting’
dilemma — a phenomenon where models unintentionally discard previously
acquired knowledge during subsequent learning. Informed by these insights, we
architected a scheme centered around crafting a list of prototype vectors,
with each vector symbolizing a distinct semantic class. In every episode’s
lifecycle, we not only generate a prototype vector but also ensure its
progressive refinement via the Exponential Moving Average (EMA) technique.
This step is succeeded by optimizing the model, targeting the reduction of the
disparity between the newly minted prototype vector and its semantically
aligned counterpart. This cyclical mechanism bolsters our model’s capability
to preserve and leverage information inherent to each semantic class
seamlessly. The metric delineating the divergence between the semantic and
prototype vectors in each episode has been incorporated as a pivotal balancing
term, akin to the role it plays in $L_{\text{semantic}}$.

Table 3: We tested the performance of our model‘s generalibility within
various scenarioes. G: General, S: Specific, Mini: miniImageNet, Tiered:
TieredImagenet

Scenario G$\rightarrow{}$G S$\rightarrow{}$S G$\rightarrow{}$S
S$\rightarrow{}$G Train $\rightarrow{}$ Test Mini $\rightarrow{}$Tiered
Cars$\rightarrow{}$CUB Mini$\rightarrow{}$Cars Cars$\rightarrow{}$Mini Num-Way
3 5 10 3 5 10 3 5 10 3 5 10 f-MAML (1) 61.86(1.29) 50.78(0.77) 36.62(0.12)
45.24(1.18) 31.38(0.28) 18.13(1.26) 49.29(0.73) 35.09(0.66) 22.06(0.11)
43.42(0.91) 28.76(0.91) 15.95(1.04) f-MAML + semantic (1) a-MAML(1)
66.27(0.36) 52.27(0.25) 35.62(0.2) 46.92(0.17) 32.01(0.14) 17.72(0.62)
49.51(0.04) 35.22(0.28) 21.36(0.07) 43.66(0.20) 28.64(0.08) 15.58(0.3) a-MAML
+ semantic (1) 66.26(0.70) 52.22(0.57) 35.94(0.47) 47.28(2.06) 31.62(2.08)
17.02(1.98) 49.06(0.26) 34.80(0.32) 22.01(0.18) 45.18(1.54) 29.60(0.81)
15.96(0.41) f-MAML (5) 78.70(0.37) 68.54(1.17) 54.64(0.34) 56.57(0.30)
43.60(1.40) 27.35(0.59) 61.58(1.53) 48.07(1.83) 34.67(0.67) 51.91(0.86)
39.41(0.62) 24.76(0.81) f-MAML + semantic (5) a-MAML (5) 80.46(0.17)
69.73(0.17) 53.68(0.19) 62.04(0.97) 45.63(1.58) 27.02(2.47) 63.58(0.72)
49.80(0.83) 34.82(0.96) 57.29(0.55) 41.13(0.79) 24.15(1.13) a-MAML + semantic
(5) 80.66(0.58) 69.31(0.81) 53.31(0.94) 62.80(1.03) 46.25(1.68) 26.98 (1.87)
62.77(0.77) 49.06(0.71) 34.07 (0.78) 57.85(0.97) 40.88(1.44) 23.45(1.47)

Table 4: Accuracy of the any-way MAML model across various datasets, shots,
and ensembling techniques we measured performance on 5-way setting. Ensembling
methods include: (i) Original \- direct summation of output logits, (ii)
Softmax \- prior softmax operation on logits, and (iii) Max \- selection of
the maximum output logit per assignment set.

train dataset | miniimagenet
---|---
test dataset | miniimagenet | cars
method | original | softmax | torch max | original | softmax | torch max
1 | 65 (0.46) | 65 (0.46) | 65 (0.46) | 47.66 (0.82) | 47.66 (0.82) | 47.66 (0.82)
2 | 66.2 (0.34) | 66.18 (0.36) | 65.11 (0.4) | 49.02 (0.66) | 49.01 (0.67) | 47.81 (0.73)
3 | 66.58 (0.5) | 66.57 (0.49) | 66.22 (0.46) | 49.31 (1.12) | 49.3 (1.09) | 48.86 (1.11)
6 | 66.82 (0.25) | 66.81 (0.25) | 66.54 (0.28) | 49.83 (0.99) | 49.81 (0.97) | 49.48 (0.9)
12 | 66.99 (0.34) | 66.97 (0.33) | 66.69 (0.37) | 49.81 (1.06) | 49.82 (1.07) | 49.48 (1.08)
18 | 66.82 (0.54) | 66.81 (0.55) | 66.59 (0.61) | 49.98 (1.04) | 49.95 (1.06) | 49.59 (0.99)

Table 5: semantic fixed

Scenario | Same | Same |  G $\rightarrow$ S |  S$\rightarrow$G
---|---|---|---|---
Train Test |  M $\rightarrow$ M |  C $\rightarrow$ C |  M $\rightarrow$ C |  C $\rightarrow$ M
f-MAML (1) | 46.86 (0.95) | 49.19 (0.56) | 35.09 (0.66) | 28.76 (0.91)
+semantic | 48.32 (0.89) | 51.21(0.36) | 34.65 (0.20) | 29.48 (0.36)
f-MAML (5) | 65.41 (1.04) | 70.42 (0.88) | 48.07 (1.83) | 39.41 (0.62)
+semantic | 66.89 (0.35) | 71.45 (1.10) | 46.19 (2.76) | 40.46 (0.61)

Table 6: semantic.. Scenario | Same | Same |  G $\rightarrow$ S |  S $\rightarrow$ G
---|---|---|---|---
Train $\rightarrow$ Test |  mini $\rightarrow$ mini |  cars $\rightarrow$ cars |  mini $\rightarrow$ cars |  cars $\rightarrow$ mini
Num-Way | 5 | 10 | 5 | 10 | 5 | 10 | 5 | 10
ProtoNet (1) | 55.55(.55) | 55.55(.55) | 55.55(.55) | 55.55(.55) | 55.55(.55) | 55.55(.55) | 55.55(.55) | 55.55(.55)
+semantic |  |  |  |  |  |  |  |
\+ mixup |  |  |  |  |  |  |  |
a-MAML (1) |  |  |  |  |  |  |  |
+semantic |  |  |  |  |  |  |  |
\+ mixup |  |  |  |  |  |  |  |
ProtoNet (5) |  |  |  |  |  |  |  |
+semantic |  |  |  |  |  |  |  |
\+ mixup |  |  |  |  |  |  |  |
a-MAML (5) |  |  |  |  |  |  |  |
+semantic |  |  |  |  |  |  |  |
\+ mixup |  |  |  |  |  |  |  |

### Any-way meta learning surpasses fixed-way methods

As indicated by Table 2 and Table 7, our a-MAML (any-way MAML) outperforms
most benchmarks. One might conventionally assume that f-MAML, trained in a
fixed-way, would be specialized for a specific episode distribution. However,
the superiority of our approach, which remains agnostic to task-cardinality,
challenges this conventional assumption. One might argue that the improved
performance is due to the exposure to a larger support set, as seen in 9-way
episodes, even though the number of episodes remains constant. However, this
perspective is refuted by the elevated performance observed in 10-way tasks,
which was not part of our training scenarios. Considering that the average
task cardinality is 6, one would expect superior performance when trained
exclusively on a 10-way. Nevertheless, a-MAML remains comparable to the
baseline This performance pattern highlights that our model, which is trained
on a mixture of multiple datasets, demonstrates its robust generalization
capability, contrary to models trained strictly on individual datasets.
Generally, models become susceptible to biases from specific training
datasets, potentially compromising performance on unfamiliar datasets. Yet,
our results defy this expectation. The robustness of our model highlights the
hightened adaptability which is provided by our training paradigm across
diverse data distributions. This observation contrasts with conventional
wisdom, where models trained on various biased specific datasets often
experience a sharp decrease in performance theory:specificdataset. Thus, our
results not only challenge conventional assumptions but also emphasize the
innovative nature of our approach.

### a-MAML Through the Lens of Ensemble

Ensenble on Assigned sets Our ensemble-based perspective provides insights
into the improved performance of our algorithm. As highlighted previously, the
flexibility in assigning numeric labels offers a way to generate diverse
models without any additional costs. By harnessing the multiple logits derived
from the same task set, we can ensemble and utilize? take advantage of? these
‘independent’ pieces of information. Table 7 corroborates this idea. As the
number of assignment sets increases, the performance improves due to the model
ensembling with logits generated by each distinct set. Furthermore, the
versatility of our approach allows us to generate an ‘almost’ infinite number
of such assignment sets, each acting as a representation of an independent
model. This suggests that we can, at least theoretically, increase the number
of independent logits. We conducted various basic ensemble methods and all of
those methods have shown promising performance improvements as the number of
models increases. In essence, our methodology harnesses the power of ensemble
by utilizing varying numeric label assignments. This diversification, when
combined, forms a robust model that is more adaptable and delivers superior
performance.

Figure 3: A graph which compares validation accuracy upon training epochs. The
number in paraenthethis indicates number of shots. The validation accuracy is
measured in 5-way case.

Ensemble on Different Cardinality Episodes. From Fig. 3, it is evident that
our algorithm, a-MAML, converges more swiftly than f-MAML. Beyond its faster
convergence, a-MAML also demonstrates superior performance in comparison to
f-MAML. This distinction provides insights into the challenges faced during
the training of fixed-10-way-1-shot TieredImageNet. Specifically, as the
complexity of the task increases, the duration of the “Start-up Stall” phase —
where performance remains stagnant after initialization — becomes more
pronounced. Given that TieredimageNet is one of the most challenging datasets,
primarily due to its expansive semantic class pool (361) and the intricate
nature of the task (classifying unseen numeric labels within a single shot),
the advantages of a-MAML become even more apparent. By ensembling across
different cardinalities, a-MAML swiftly moves past the Start-up Stall phase
during simpler tasks like 3-way episodes. This proficiency with easier tasks
subsequently empowers the algorithm to tackle harder tasks, such as 9-way
episodes, more effectively.

### Injecting Semantic information into model

In our experiments, as detailed in Tables 6 and 5, we found that the
integration of semantic class information significantly enhanced the
performance of models, especially when tailored for fine-grained datasets.
However, the effects of this integration varied depending on the
characteristics of the datasets. For models trained on coarse-grained
datasets, there was a potential decrease in generalizability, as evidenced by
diminished performance on intricate datasets like “Cars”. In contrast, models
trained on detailed datasets, such as “Cars” or “CUB”, not only maintained but
even demonstrated enhanced versatility across varied test scenarios. This
suggests that the subtle intricacies of fine-grained datasets are further
emphasized with semantic nuances, enabling models to discern delicate class
differences with greater precision. Crafting a Euclidean-Like Landscape: Mixup
$\&$ Feature Space Refinement Building on the foundation of semantic class
insights, we delved into the utilization of the mixup technique, a staple in
supervised learning, to enhance our model’s generalizability. Our auxiliary
classifier’s unique architecture, designed to interpret semantic class
information, positioned us advantageously to tap into mixup’s potential. 이 파트도
잘 이해 안 감 한 번 다시 정리해봤으면 좋겠음. 중복되는 내용이 좀 많은 것 같음.. In our implementation, the
auxiliary classifier’s role was pivotal. It assessed the extent of feature
fusion, ensuring the mix mirrored the intermingling of the actual images.
Through such deliberate feature blending, we shaped a dataset’s convex hull
reminiscent of Euclidean structures, thereby optimizing operations like
distance measurements. This not only fostered intuitive feature clustering but
also elevated overall model efficiency. Our approach to mixup stands distinct
in the Gradient-Based Meta-Learning (GBML) landscape. While many resort to
mixup to mitigate data scarcity, expanding shot counts in episodes, we chose a
different path. We kept the shot count consistent during mixup, emphasizing
the transformation of the feature space over increasing data quantities. This
focus, coupled with our model’s adeptness at semantic information extraction,
set our methodology apart. As showcased in Table 6, the integration of mixup
not only amplified performance across the board but also excelled in
challenges like 10-way classification, even when confronted with previously
uncharted training distributions.

###

## Conclusion and Future Work

## Future work

1\. Doing ensemble is really straightforward in our section, more methods can
be studied for future work. 2\. Also, we just showcased the possibility of
integration between supervison and meta learning. Someone can think this
feature prevents overfitting and helps generalization. However, any model
cannot learn The outer space of convex hall. The more we provide the data, the
more the model can learn. Sum up, the task sampling method in GBML has double-
edged feature. It makes GBML possible, but it lacks the information. In this
paper, we propose two techniques which exploits the double-edged feature of
task sampling method in GBML. First, we propse a model which can classify any
number of classes without changing the task sampling method itself. which
means we can classify any number of classes with fixed-way training. As we
remained the task sampling method, this technique can be applied to any GBML
model. This technique was possible as the label itself does not contain any
information. Second, we propolse an algorithm which injects the information of
label to the model by adding lightweight classifier. This method requare
little computational burden. Also, as this classifier is similar to normal
supervised learning setting, We can apply the technique of supervised
learning. In this paper, we use the technique of mixup, which is known to be
effective and common technique in supervised learning. We can apply this
technique if we have labeled data, also, we can expect additional performance
gain by adopting techniques in supervised learning which is not introduced in
this paper.

Table 7: Accuracy of the any-way MAML model across various datasets, shots,
and ensembling techniques we measured performance on 5-way setting. Ensembling
methods include: (i) Original \- direct summation of output logits, (ii)
Softmax \- prior softmax operation on logits, and (iii) Max \- selection of
the maximum output logit per assignment set.

shot 1 shot 5 shot train dataset miniImageNet Cars test dataset miniImageNet
Cars miniImageNet Cars method original softmax max original softmax max
original softmax max original softmax max 1 47.64 (0.53) 47.64 (0.53) 47.64
(0.53) 34.45 (0.21) 34.45 (0.21) 34.45 (0.21) 38.66 (1.05) 38.66 (1.05) 38.66
(1.05) 67.18 (1.21) 67.18 (1.21) 67.18 (1.21) 2 48.11 (0.3) 48.11 (0.28) 47.56
(0.28) 35.05 (0.12) 35.03 (0.12) 34.59 (0.07) 39.9 (0.83) 39.91 (0.85) 38.84
(0.96) 68.65 (0.9) 68.7 (1.06) 66.89 (1.19) 3 48.02 (0.8) 48.03 (0.78) 47.84
(0.82) 35.05 (0.2) 35.03 (0.2) 34.84 (0.24) 40.13 (0.83) 40.19 (0.87) 39.66
(0.86) 69.52 (0.8) 69.58 (0.99) 68.99 (1.09) 6 48.24 (0.34) 48.23 (0.35) 48.13
(0.35) 35.11 (0.06) 35.1 (0.05) 34.98 (0.08) 40.8 (0.9) 40.8 (0.98) 40.44
(1.12) 70.24 (0.84) 70.32 (1.01) 69.92 (1.09) 12 48.41 (0.29) 48.4 (0.3) 48.26
(0.38) 35.18 (0.1) 35.16 (0.12) 35.06 (0.13) 40.9 (0.78) 40.93 (0.85) 40.57
(0.96) 70.12 (1.07) 70.19 (1.2) 69.77 (1.34) 18 48.55 (0.34) 48.56 (0.34)
48.45 (0.34) 35.27 (0.17) 35.25 (0.16) 35.16 (0.19) 40.63 (0.6) 40.66 (0.66)
40.33 (0.72) 70.27 (0.88) 70.37 (1.05) 69.95 (1.22)

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>     Ω\documentclass[letterpaper]{article}Ω\usepackage[submission]{aaai24}
> \usepackage{times} \usepackage{helvet} \usepackage{courier}
> \usepackage[hyphens]{url} \usepackage{graphicx} \urlstyle{rm}
> \def\UrlFont{\rm} \usepackage{graphicx} \usepackage{natbib}
> \usepackage{caption} \frenchspacing\setlength{\pdfpagewidth}{8.5in}
> \setlength{\pdfpageheight}{11in} \pdfinfo{Ω/TemplateVersion
> (2024.1)Ω}Ω\end{verbatim}\end{scriptsize}Ω\end{quote}Ω\par\subsection{Preparing
> Your Paper}Ω\parAfter the preamble above, you should prepare your paper as
> follows:Ω\begin{quote}Ω\begin{scriptsize}\begin{verbatim}Ω\begin{document}Ω\maketitle\begin{abstract}Ω\end{abstract}\end{verbatim}\end{scriptsize}Ω\end{quote}Ω\par\noindentYou
> should then continue with the body of your paper. Your paper must conclude
> with the references, which should be inserted as
> follows:Ω\begin{quote}Ω\begin{scriptsize}\begin{verbatim}Ω\bibliography{Bibliography-
> File}Ω\end{document}Ω\end{verbatim}\end{scriptsize}Ω\end{quote}Ω\par\begin{quote}Ω\begin{scriptsize}\begin{verbatim}Ω\begin{document}\\Ω\maketitle\\Ω...\\Ω\bibliography{Bibliography-
> File}\\Ω\end{document}\\Ω\end{verbatim}\end{scriptsize}Ω\end{quote}Ω\par\subsection{Commands
> and Packages That May Not Be
> Used}Ω\begin{table*}[t]Ω\centering\par\begin{tabular}{l|l|l|l}Ω\textbackslashabovecaption
> &Ω\textbackslashabovedisplay &Ω\textbackslashaddevensidemargin
> &Ω\textbackslashaddsidemargin \\Ω\textbackslashaddtolength
> &Ω\textbackslashbaselinestretch &Ω\textbackslashbelowcaption
> &Ω\textbackslashbelowdisplay \\Ω\textbackslashbreak
> &Ω\textbackslashclearpage &Ω\textbackslashclip &Ω\textbackslashcolumnsep
> \\Ω\textbackslashfloat &Ω\textbackslashinput &Ω\textbackslashinput
> &Ω\textbackslashlinespread \\Ω\textbackslashnewpage
> &Ω\textbackslashpagebreak &Ω\textbackslashrenewcommand
> &Ω\textbackslashsetlength \\Ω\textbackslashtext height &Ω\textbackslashtiny
> &Ω\textbackslashtop margin &Ω\textbackslashtrim \\Ω\textbackslashvskip\{-
> &Ω\textbackslashvspace\{- \\Ω\end{tabular}Ω\caption{Commands that must not
> be
> used}Ω\label{table1}Ω\end{table*}Ω\par\begin{table}[t]Ω\centering\begin{tabular}{l|l|l|l}Ωauthblk
> & babel & cjk & dvips \\Ωepsf & epsfig & euler & float \\Ωfullpage &
> geometry & graphics & hyperref \\Ωlayout & linespread & lmodern & maltepaper
> \\Ωnavigator & pdfcomment & pgfplots & psfig \\Ωpstricks & t1enc & titlesec
> & tocbind \\ΩulemΩ\end{tabular}Ω\caption{LaTeX style packages that must not
> be used.}Ω\label{table2}Ω\end{table}Ω\parThere are a number of packages,
> commands, scripts, and macros that are incompatable with aaai24.sty. The
> common ones are listed in tables \ref{table1} and \ref{table2}. Generally,
> if a command, package, script, or macro alters floats, margins, fonts,
> sizing, linespacing, or the presentation of the references and citations, it
> is unacceptable. Note that negative vskip and vspace may not be used except
> in certain rare occurances, and may never be used around tables, figures,
> captions, sections, subsections, subsubsections, or
> references.Ω\par\par\subsection{Page Breaks}ΩFor your final camera ready
> copy, you must not use any page break commands. References must flow
> directly after the text without breaks. Note that some conferences require
> references to be on a separate page during the review process. AAAI Press,
> however, does not require this condition for the final
> paper.Ω\par\par\subsection{Paper Size, Margins, and Column Width}ΩPapers
> must be formatted to print in two-column format on 8.5 x 11 inch US letter-
> sized paper. The margins must be exactly as
> follows:Ω\begin{itemize}Ω\itemTop margin: 1.25 inches (first page), .75
> inches (others)Ω\itemLeft margin: .75 inchesΩ\itemRight margin: .75
> inchesΩ\itemBottom margin: 1.25 inchesΩ\end{itemize}Ω\par\parThe default
> paper size in most installations of \LaTeX{} is A4. However, because we
> require that your electronic paper be formatted in US letter size, the
> preamble we have provided includes commands that alter the default to US
> letter size. Please note that using any other package to alter page size
> (such as, but not limited to the Geometry package) will result in your final
> paper being returned to you for correction.Ω\par\par\subsubsection{Column
> Width and Margins.}ΩTo ensure maximum readability, your paper must include
> two columns. Each column should be 3.3 inches wide (slightly more than 3.25
> inches), with a .375 inch (.952 cm) gutter of white space between the two
> columns. The aaai24.sty file will automatically create these columns for
> you.Ω\par\subsection{Overlength Papers}ΩIf your paper is too long and you
> resort to formatting tricks to make it fit, it is quite likely that it will
> be returned to you. The best way to retain readability if the paper is
> overlength is to cut text, figures, or tables. There are a few acceptable
> ways to reduce paper size that don’t affect readability. First, turn on
> \textbackslashfrenchspacing, which will reduce the space after periods.
> Next, move all your figures and tables to the top of the page. Consider
> removing less important portions of a figure. If you use
> \textbackslashcentering instead of \textbackslashbegin\{center\} in your
> figure environment, you can also buy some space. For mathematical
> environments, you may reduce fontsize {\bfbut not below 6.5
> point}.Ω\par\parCommands that alter page layout are forbidden. These include
> \textbackslashcolumnsep, \textbackslashfloat, \textbackslashtopmargin,
> \textbackslashtopskip, \textbackslashtextheight, \textbackslashtextwidth,
> \textbackslashoddsidemargin, and \textbackslashevensizemargin (this list is
> not exhaustive). If you alter page layout, you will be required to pay the
> page fee. Other commands that are questionable and may cause your paper to
> be rejected include \textbackslashparindent, and \textbackslashparskip.
> Commands that alter the space between sections are forbidden. The title sec
> package is not allowed. Regardless of the above, if your paper is obviously
> ‘‘squeezed" it is not going to to be accepted. Options for reducing the
> length of a paper include reducing the size of your graphics, cutting text,
> or paying the extra page charge (if it is offered).Ω\par\par\subsection{Type
> Font and Size}ΩYour paper must be formatted in Times Roman or Nimbus. We
> will not accept papers formatted using Computer Modern or Palatino or some
> other font as the text or heading typeface. Sans serif, when used, should be
> Courier. Use Symbol or Lucida or Computer Modern for \textit{mathematics
> only. }Ω\parDo not use type 3 fonts for any portion of your paper, including
> graphics. Type 3 bitmapped fonts are designed for fixed resolution printers.
> Most print at 300 dpi even if the printer resolution is 1200 dpi or higher.
> They also often cause high resolution imagesetter devices to crash.
> Consequently, AAAI will not accept electronic files containing obsolete type
> 3 fonts. Files containing those fonts (even in graphics) will be rejected.
> (Authors using blackboard symbols must avoid packages that use type 3
> fonts.)Ω\parFortunately, there are effective workarounds that will prevent
> your file from embedding type 3 bitmapped fonts. The easiest workaround is
> to use the required times, helvet, and courier packages with \LaTeX{}2e.
> (Note that papers formatted in this way will still use Computer Modern for
> the mathematics. To make the math look good, you’ll either have to use
> Symbol or Lucida, or you will need to install type 1 Computer Modern fonts
> --- for more on these fonts, see the section ‘‘Obtaining Type 1 Computer
> Modern.")Ω\parIf you are unsure if your paper contains type 3 fonts, view
> the PDF in Acrobat Reader. The Properties/Fonts window will display the font
> name, font type, and encoding properties of all the fonts in the document.
> If you are unsure if your graphics contain type 3 fonts (and they are
> PostScript or encapsulated PostScript documents), create PDF versions of
> them, and consult the properties window in Acrobat Reader.Ω\parThe default
> size for your type must be ten-point with twelve-point leading (line
> spacing). Start all pages (except the first) directly under the top margin.
> (See the next section for instructions on formatting the title page.) Indent
> ten points when beginning a new paragraph, unless the paragraph begins
> directly below a heading or subheading.Ω\par\par\subsubsection{Obtaining
> Type 1 Computer Modern for \LaTeX{}.}Ω\parIf you use Computer Modern for the
> mathematics in your paper (you cannot use it for the text) you may need to
> download type 1 Computer fonts. They are available without charge from the
> American Mathematical
> Society:Ωhttp://www.ams.org/tex/type1-fonts.html.Ω\par\subsubsection{Nonroman
> Fonts.}ΩIf your paper includes symbols in other languages (such as, but not
> limited to, Arabic, Chinese, Hebrew, Japanese, Thai, Russian and other
> Cyrillic languages), you must restrict their use to bit-mapped
> figures.Ω\par\subsection{Title and Authors}ΩYour title must appear centered
> over both text columns in sixteen-point bold type (twenty-four point
> leading). The title must be written in Title Case according to the Chicago
> Manual of Style rules. The rules are a bit involved, but in general verbs
> (including short verbs like be, is, using, and go), nouns, adverbs,
> adjectives, and pronouns should be capitalized, (including both words in
> hyphenated terms), while articles, conjunctions, and prepositions are lower
> case unless they directly follow a colon or long dash. You can use the
> online tool \url{https://titlecaseconverter.com/} to double-check the proper
> capitalization (select the "Chicago" style and mark the "Show explanations"
> checkbox).Ω\parAuthor’s names should appear below the title of the paper,
> centered in twelve-point type (with fifteen point leading), along with
> affiliation(s) and complete address(es) (including electronic mail address
> if available) in nine-point roman type (the twelve point leading). You
> should begin the two-column format when you come to the
> abstract.Ω\par\subsubsection{Formatting Author Information.}ΩAuthor
> information has to be set according to the following specification depending
> if you have one or more than one affiliation. You may not use a table nor
> may you employ the \textbackslashauthorblk.sty package. For one or several
> authors from the same institution, please separate them with commas and
> write all affiliation directly below (one affiliation per line) using the
> macros \textbackslashauthor and
> \textbackslashaffiliations:Ω\par\begin{quote}\begin{scriptsize}\begin{verbatim}Ω\author{ΩAuthor
> 1, ..., Author n\\Ω}Ω\affiliations{ΩAddress line\\Ω... \\ΩAddress
> line\\Ω}Ω\end{verbatim}\end{scriptsize}\end{quote}Ω\par\par\noindentFor
> authors from different institutions, use \textbackslashtextsuperscript
> \{\textbackslashrm x \} to match authors and affiliations. Notice that there
> should not be any spaces between the author name (or comma following it) and
> the
> superscript.Ω\par\begin{quote}\begin{scriptsize}\begin{verbatim}Ω\author{ΩAuthorOne,\equalcontrib\textsuperscript{\rm1,\rm2}ΩAuthorTwo,\equalcontrib\textsuperscript{\rm2}ΩAuthorThree,\textsuperscript{\rm3}\\ΩAuthorFour,\textsuperscript{\rm4}ΩAuthorFive
> \textsuperscript{\rm5}}Ω}
>     \affiliations {
>         \textsuperscript{\rm 1}AffiliationOne,\\
>         \textsuperscript{\rm 2}AffiliationTwo,\\
>         \textsuperscript{\rm 3}AffiliationThree,\\
>         \textsuperscript{\rm 4}AffiliationFour,\\
>         \textsuperscript{\rm 5}AffiliationFive\\
>         \{email<EMAIL_ADDRESS>><EMAIL_ADDRESS>><EMAIL_ADDRESS>><EMAIL_ADDRESS>>     }
>

You can indicate that some authors contributed equally using the \equalcontrib
command. This will add a marker after the author names and a footnote on the
first page. Note that you may want to break the author list for better
visualization. You can achieve this using a simple line break (\\\\).

###  LaTeX Copyright Notice

The copyright notice automatically appears if you use aaai24.sty. It has been
hardcoded and may not be disabled.

### Credits

Any credits to a sponsoring agency should appear in the acknowledgments
section, unless the agency requires different placement. If it is necessary to
include this information on the front page, use \thanks in either the \author
or \title commands. For example:

> \title{Very Important Results in AI\thanks{This work is supported by
> everybody.}}

Multiple \thanks commands can be given. Each will result in a separate
footnote indication in the author or title with the corresponding text at the
botton of the first column of the document. Note that the \thanks command is
fragile. You will need to use \protect. Please do not include \pubnote
commands in your document.

### Abstract

Follow the example commands in this document for creation of your abstract.
The command \begin{abstract} will automatically indent the text block. Please
do not indent it further. Do not include references in your abstract!

### Page Numbers

Do not print any page numbers on your paper. The use of \pagestyle is
forbidden.

### Text

The main body of the paper must be formatted in black, ten-point Times Roman
with twelve-point leading (line spacing). You may not reduce font size or the
linespacing. Commands that alter font size or line spacing (including, but not
limited to baselinestretch, baselineshift, linespread, and others) are
expressly forbidden. In addition, you may not use color in the text.

### Citations

Citations within the text should include the author’s last name and year, for
example (Newell 1980). Append lower-case letters to the year in cases of
ambiguity. Multiple authors should be treated as follows: (Feigenbaum and
Engelmore 1988) or (Ford, Hayes, and Glymour 1992). In the case of four or
more authors, list only the first author, followed by et al. (Ford et al.
1997).

### Extracts

Long quotations and extracts should be indented ten points from the left and
right margins.

> This is an example of an extract or quotation. Note the indent on both
> sides. Quotation marks are not necessary if you offset the text in a block
> like this, and properly identify and cite the quotation in the text.

### Footnotes

Use footnotes judiciously, taking into account that they interrupt the reading
of the text. When required, they should be consecutively numbered throughout
with superscript Arabic numbers. Footnotes should appear at the bottom of the
page, separated from the text by a blank line space and a thin, half-point
rule.

### Headings and Sections

When necessary, headings should be used to separate major sections of your
paper. Remember, you are writing a short paper, not a lengthy book! An
overabundance of headings will tend to make your paper look more like an
outline than a paper. The aaai24.sty package will create headings for you. Do
not alter their size nor their spacing above or below.

#### Section Numbers.

The use of section numbers in AAAI Press papers is optional. To use section
numbers in LaTeX, uncomment the setcounter line in your document preamble and
change the 0 to a 1. Section numbers should not be used in short poster papers
and/or extended abstracts.

#### Section Headings.

Sections should be arranged and headed as follows:

  1. 1.

Main content sections

  2. 2.

Appendices (optional)

  3. 3.

Ethical Statement (optional, unnumbered)

  4. 4.

Acknowledgements (optional, unnumbered)

  5. 5.

References (unnumbered)

#### Appendices.

Any appendices must appear after the main content. If your main sections are
numbered, appendix sections must use letters instead of arabic numerals. In
LaTeX you can use the \appendix command to achieve this effect and then use
\section{Heading} normally for your appendix sections.

#### Ethical Statement.

You can write a statement about the potential ethical impact of your work,
including its broad societal implications, both positive and negative. If
included, such statement must be written in an unnumbered section titled
_Ethical Statement_.

#### Acknowledgments.

The acknowledgments section, if included, appears right before the references
and is headed “Acknowledgments”. It must not be numbered even if other
sections are (use \section*{Acknowledgements} in LaTeX). This section includes
acknowledgments of help from associates and colleagues, credits to sponsoring
agencies, financial support, and permission to publish. Please acknowledge
other contributors, grant support, and so forth, in this section. Do not put
acknowledgments in a footnote on the first page. If your grant agency requires
acknowledgment of the grant on page 1, limit the footnote to the required
statement, and put the remaining acknowledgments at the back. Please try to
limit acknowledgments to no more than three sentences.

#### References.

The references section should be labeled “References” and must appear at the
very end of the paper (don’t end the paper with references, and then put a
figure by itself on the last page). A sample list of references is given later
on in these instructions. Please use a consistent format for references.
Poorly prepared or sloppy references reflect badly on the quality of your
paper and your research. Please prepare complete and accurate citations.

### Illustrations and Figures

Your paper must compile in PDFLaTeX. Consequently, all your figures must be
.jpg, .png, or .pdf. You may not use the .gif (the resolution is too low),
.ps, or .eps file format for your figures. Figures, drawings, tables, and
photographs should be placed throughout the paper on the page (or the
subsequent page) where they are first discussed. Do not group them together at
the end of the paper. If placed at the top of the paper, illustrations may run
across both columns. Figures must not invade the top, bottom, or side margin
areas. Figures must be inserted using the \usepackage{graphicx}. Number
figures sequentially, for example, figure 1, and so on. Do not use minipage to
group figures. If you normally create your figures using pgfplots, please
create the figures first, and then import them as pdfs with proper bounding
boxes, as the bounding and trim boxes created by pfgplots are fragile and not
valid. When you include your figures, you must crop them outside of LaTeX. The
command \includegraphics*[clip=true, viewport 0 0 10 10]… might result in a
PDF that looks great, but the image is not really cropped. The full image can
reappear (and obscure whatever it is overlapping) when page numbers are
applied or color space is standardized. Figures LABEL:fig1, and LABEL:fig2
display some unwanted results that often occur. If your paper includes
illustrations that are not compatible with PDFTeX (such as .eps or .ps
documents), you will need to convert them. The epstopdf package will usually
work for eps files. You will need to convert your ps files to PDF in either
case.

#### Figure Captions.

The illustration number and caption must appear under the illustration. Labels
and other text with the actual illustration must be at least nine-point type.
However, the font and size of figure captions must be 10 point roman. Do not
make them smaller, bold, or italic. (Individual words may be italicized if the
context requires differentiation.)

### Tables

Tables should be presented in 10 point roman type. If necessary, they may be
altered to 9 point type. You may not use any commands that further reduce
point size below nine points. Tables that do not fit in a single column must
be placed across double columns. If your table won’t fit within the margins
even when spanning both columns, you must split it. Do not use minipage to
group tables.

#### Table Captions.

The number and caption for your table must appear under (not above) the table.
Additionally, the font and size of table captions must be 10 point roman and
must be placed beneath the figure. Do not make them smaller, bold, or italic.
(Individual words may be italicized if the context requires differentiation.)

#### Low-Resolution Bitmaps.

You may not use low-resolution (such as 72 dpi) screen-dumps and GIF
files—these files contain so few pixels that they are always blurry, and
illegible when printed. If they are color, they will become an indecipherable
mess when converted to black and white. This is always the case with gif
files, which should never be used. The resolution of screen dumps can be
increased by reducing the print size of the original file while retaining the
same number of pixels. You can also enlarge files by manipulating them in
software such as PhotoShop. Your figures should be 300 dpi when incorporated
into your document.

####  LaTeX Overflow.

LaTeX users please beware: LaTeX will sometimes put portions of the figure or
table or an equation in the margin. If this happens, you need to make the
figure or table span both columns. If absolutely necessary, you may reduce the
figure, or reformat the equation, or reconfigure the table. Check your log
file! You must fix any overflow into the margin (that means no overfull boxes
in LaTeX). Nothing is permitted to intrude into the margin or gutter.

#### Using Color.

Use of color is restricted to figures only. It must be WACG 2.0 compliant.
(That is, the contrast ratio must be greater than 4.5:1 no matter the font
size.) It must be CMYK, NOT RGB. It may never be used for any portion of the
text of your paper. The archival version of your paper will be printed in
black and white and grayscale. The web version must be readable by persons
with disabilities. Consequently, because conversion to grayscale can cause
undesirable effects (red changes to black, yellow can disappear, and so
forth), we strongly suggest you avoid placing color figures in your document.
If you do include color figures, you must (1) use the CMYK (not RGB)
colorspace and (2) be mindful of readers who may happen to have trouble
distinguishing colors. Your paper must be decipherable without using color for
distinction.

#### Drawings.

We suggest you use computer drawing software (such as Adobe Illustrator or,
(if unavoidable), the drawing tools in Microsoft Word) to create your
illustrations. Do not use Microsoft Publisher. These illustrations will look
best if all line widths are uniform (half- to two-point in size), and you do
not create labels over shaded areas. Shading should be 133 lines per inch if
possible. Use Times Roman or Helvetica for all figure call-outs. Do not use
hairline width lines — be sure that the stroke width of all lines is at least
.5 pt. Zero point lines will print on a laser printer, but will completely
disappear on the high-resolution devices used by our printers.

#### Photographs and Images.

Photographs and other images should be in grayscale (color photographs will
not reproduce well; for example, red tones will reproduce as black, yellow may
turn to white, and so forth) and set to a minimum of 300 dpi. Do not prescreen
images.

#### Resizing Graphics.

Resize your graphics before you include them with LaTeX. You may not use trim
or clip options as part of your \includegraphics command. Resize the media box
of your PDF using a graphics program instead.

#### Fonts in Your Illustrations.

You must embed all fonts in your graphics before including them in your LaTeX
document.

#### Algorithms.

Algorithms and/or programs are a special kind of figures. Like all
illustrations, they should appear floated to the top (preferably) or bottom of
the page. However, their caption should appear in the header, left-justified
and enclosed between horizontal lines, as shown in Algorithm 2. The algorithm
body should be terminated with another horizontal line. It is up to the
authors to decide whether to show line numbers or not, how to format comments,
etc. In LaTeX algorithms may be typeset using the algorithm and algorithmic
packages, but you can also use one of the many other packages for the task.

Algorithm 2 Example algorithm

Input: Your algorithm’s input
Parameter: Optional list of parameters
Output: Your algorithm’s output

Let $t=0$. condition Do some action. conditional Perform task A. Perform task
B. returnsolution

#### Listings.

Listings are much like algorithms and programs. They should also appear
floated to the top (preferably) or bottom of the page. Listing captions should
appear in the header, left-justified and enclosed between horizontal lines as
shown in Listing 1. Terminate the body with another horizontal line and avoid
any background color. Line numbers, if included, must appear within the text
column.

Listing 1 Example listing quicksort.hs

⬇

1quicksort :: Ord a => [a] $\rightarrow$ [a]

2quicksort [] = []

3quicksort (p:xs) = (quicksort lesser) ++ [p] ++ (quicksort greater)

4 where

5 lesser = filter (< p) xs

6 greater = filter (>= p) xs

### References

The AAAI style includes a set of definitions for use in formatting references
with BibTeX. These definitions make the bibliography style fairly close to the
ones specified in the Reference Examples appendix below. To use these
definitions, you also need the BibTeX style file “aaai24.bst,” available in
the AAAI Author Kit on the AAAI web site. Then, at the end of your paper but
before \enddocument, you need to put the following lines:

> \bibliography{bibfile1,bibfile2,…}

Please note that the aaai24.sty class already sets the bibliographystyle for
you, so you do not have to place any \bibliographystyle command in the
document yourselves. The aaai24.sty file is incompatible with the hyperref and
navigator packages. If you use either, your references will be garbled and
your paper will be returned to you. References may be the same size as
surrounding text. However, in this section (only), you may reduce the size to
\small if your paper exceeds the allowable number of pages. Making it any
smaller than 9 point with 10 point linespacing, however, is not allowed. A
more precise and exact method of reducing the size of your references
minimally is by means of the following command:

> \fontsize{9.8pt}{10.8pt} \selectfont

You must reduce the size equally for both font size and line spacing, and may
not reduce the size beyond {9.0pt}{10.0pt}. The list of files in the
\bibliography command should be the names of your BibTeX source files (that
is, the .bib files referenced in your paper). The following commands are
available for your use in citing references:

> \cite: Cites the given reference(s) with a full citation. This appears as
> “(Author Year)” for one reference, or “(Author Year; Author Year)” for
> multiple references.
> \shortcite: Cites the given reference(s) with just the year. This appears as
> “(Year)” for one reference, or “(Year; Year)” for multiple references.
> \citeauthor: Cites the given reference(s) with just the author name(s) and
> no parentheses.
> \citeyear: Cites the given reference(s) with just the date(s) and no
> parentheses.

You may also use any of the _natbib_ citation commands.

## Proofreading Your PDF

Please check all the pages of your PDF file. The most commonly forgotten
element is the acknowledgements — especially the correct grant number. Authors
also commonly forget to add the metadata to the source, use the wrong
reference style file, or don’t follow the capitalization rules or comma
placement for their author-title information properly. A final common problem
is text (expecially equations) that runs into the margin. You will need to fix
these common errors before submitting your file.

## Improperly Formatted Files

In the past, AAAI has corrected improperly formatted files submitted by the
authors. Unfortunately, this has become an increasingly burdensome expense
that we can no longer absorb). Consequently, if your file is improperly
formatted, it will be returned to you for correction.

## Naming Your Electronic File

We require that you name your LaTeX source file with the last name (family
name) of the first author so that it can easily be differentiated from other
submissions. Complete file-naming instructions will be provided to you in the
submission instructions.

## Submitting Your Electronic Files to AAAI

Instructions on paper submittal will be provided to you in your acceptance
letter.

## Inquiries

If you have any questions about the preparation or submission of your paper as
instructed in this document, please contact AAAI Press at the address given
below. If you have technical questions about implementation of the aaai style
file, please contact an expert at your site. We do not provide technical
support for LaTeX or any other software package. To avoid problems, please
keep your paper simple, and do not incorporate complicated macros and style
files.

> AAAI Press
> 1900 Embarcadero Road, Suite 101
> Palo Alto, California 94303-3310 USA
> Telephone: (650) 328-3123
> E-mail: See the submission instructions for your particular conference or
> event.

## Additional Resources

LaTeX is a difficult program to master. If you’ve used that software, and this
document didn’t help or some items were not explained clearly, we recommend
you read Michael Shell’s excellent document (testflow doc.txt V1.0a
2002/08/13) about obtaining correct PS/PDF output on LaTeX systems. (It was
written for another purpose, but it has general application as well). It is
available at www.ctan.org in the tex-archive.

##  Appendix A Reference Examples

* Formatted bibliographies should look like the following examples. You should use BibTeX to generate the references. Missing fields are unacceptable when compiling references, and usually indicate that you are using the wrong type of entry (BibTeX class).

##### Book with multiple authors

Use the @book class.
em:86.

##### Journal and magazine articles

Use the @article class.
r:80.
hcr:83.

##### Proceedings paper published by a society, press or publisher

Use the @inproceedings class. You may abbreviate the _booktitle_ field, but
make sure that the conference edition is clear.
c:84.
c:83.

##### University technical report

Use the @techreport class.
r:86.

##### Dissertation or thesis

Use the @phdthesis class.
c:79.

##### Forthcoming publication

Use the @misc class with a note="Forthcoming" annotation.

>
>     @misc(key,
>       [...]
>       note="Forthcoming",
>     )
>

c:21.

##### ArXiv paper

Fetch the BibTeX entry from the ”Export Bibtex Citation” link in the arXiv
website. Notice it uses the @misc class instead of the @article one, and that
it includes the eprint and archivePrefix keys.

>
>     @misc(key,
>       [...]
>       eprint="xxxx.yyyy",
>       archivePrefix="arXiv",
>     )
>

c:22.

##### Website or online resource

Use the @misc class. Add the url in the howpublished field and the date of
access in the note field:

>
>     @misc(key,
>       [...]
>       howpublished="\url{http://...}",
>       note="Accessed: YYYY-mm-dd",
>     )
>

c:23. For the most up to date version of the AAAI reference style, please
consult the AI Magazine Author Guidelines at
https://aaai.org/ojs/index.php/aimagazine/about/submissions#authorGuidelines

##  Appendix B Acknowledgments

AAAI is especially grateful to Peter Patel Schneider for his work in
implementing the original aaai.sty file, liberally using the ideas of other
style hackers, including Barbara Beeton. We also acknowledge with thanks the
work of George Ferguson for his guide to using the style and BibTeX files —
which has been incorporated into this document — and Hans Guesgen, who
provided several timely modifications, as well as the many others who have,
from time to time, sent in suggestions on improvements to the AAAI style. We
are especially grateful to Francisco Cruz, Marc Pujol-Gonzalez, and Mico
Loretan for the improvements to the BibTeX and LaTeX files made in 2020. The
preparation of the LaTeX and BibTeX files that implement these instructions
was supported by Schlumberger Palo Alto Research, AT&T Bell Laboratories,
Morgan Kaufmann Publishers, The Live Oak Press, LLC, and AAAI Press.
Bibliography style changes were added by Sunil Issar. `\`pubnote was added by
J. Scott Penberthy. George Ferguson added support for printing the AAAI
copyright slug. Additional changes to aaai24.sty and aaai24.bst have been made
by Francisco Cruz and Marc Pujol-Gonzalez.

Thank you for reading these instructions carefully. We look forward to
receiving your electronic files!