Daily Papers

The notion of variation is introduced for the Boolean set and based on which Boolean logic backpropagation principle is developed. Using this concept, deep models can be built with weights and activations being Boolean numbers and operated with Boolean logic instead of real arithmetic. In particular, Boolean deep models can be trained directly in the Boolean domain without latent weights. No gradient but logic is synthesized and backpropagated through layers.

Deep learning is computationally intensive, with significant efforts focused on reducing arithmetic complexity, particularly regarding energy consumption dominated by data movement. While existing literature emphasizes inference, training is considerably more resource-intensive. This paper proposes a novel mathematical principle by introducing the notion of Boolean variation such that neurons made of Boolean weights and inputs can be trained -- for the first time -- efficiently in Boolean domain using Boolean logic instead of gradient descent and real arithmetic. We explore its convergence, conduct extensively experimental benchmarking, and provide consistent complexity evaluation by considering chip architecture, memory hierarchy, dataflow, and arithmetic precision. Our approach achieves baseline full-precision accuracy in ImageNet classification and surpasses state-of-the-art results in semantic segmentation, with notable performance in image super-resolution, and natural language understanding with transformer-based models. Moreover, it significantly reduces energy consumption during both training and inference.

Existing datasets that contain boolean questions, such as BoolQ and TYDI QA , provide the user with a YES/NO response to the question. However, a one word response is not sufficient for an explainable system. We promote explainability by releasing a new set of annotations marking the evidence in existing TyDi QA and BoolQ datasets. We show that our annotations can be used to train a model that extracts improved evidence spans compared to models that rely on existing resources. We confirm our findings with a user study which shows that our extracted evidence spans enhance the user experience. We also provide further insight into the challenges of answering boolean questions, such as passages containing conflicting YES and NO answers, and varying degrees of relevance of the predicted evidence.

We introduce Reverse Derivative Ascent: a categorical analogue of gradient based methods for machine learning. Our algorithm is defined at the level of so-called reverse differential categories. It can be used to learn the parameters of models which are expressed as morphisms of such categories. Our motivating example is boolean circuits: we show how our algorithm can be applied to such circuits by using the theory of reverse differential categories. Note our methodology allows us to learn the parameters of boolean circuits directly, in contrast to existing binarised neural network approaches. Moreover, we demonstrate its empirical value by giving experimental results on benchmark machine learning datasets.

Many approaches such as Quine-McCluskey algorithm, Karnaugh map solving, Petrick's method and McBoole's method have been devised to simplify Boolean expressions in order to optimize hardware implementation of digital circuits. However, the algorithmic implementations of these methods are hard-coded and also their computation time is proportional to the number of minterms involved in the expression. In this paper, we propose KarNet, where the ability of Convolutional Neural Networks to model relationships between various cell locations and values by capturing spatial dependencies is exploited to solve Karnaugh maps. In order to do so, a Karnaugh map is represented as an image signal, where each cell is considered as a pixel. Experimental results show that the computation time of KarNet is independent of the number of minterms and is of the order of one-hundredth to one-tenth that of the rule-based methods. KarNet being a learned system is found to achieve nearly a hundred percent accuracy, precision, and recall. We train KarNet to solve four variable Karnaugh maps and also show that a similar method can be applied on Karnaugh maps with more variables. Finally, we show a way to build a fully accurate and computationally fast system using KarNet.

Logic synthesis, a pivotal stage in chip design, entails optimizing chip specifications encoded in hardware description languages like Verilog into highly efficient implementations using Boolean logic gates. The process involves a sequential application of logic minimization heuristics (``synthesis recipe"), with their arrangement significantly impacting crucial metrics such as area and delay. Addressing the challenge posed by the broad spectrum of design complexities - from variations of past designs (e.g., adders and multipliers) to entirely novel configurations (e.g., innovative processor instructions) - requires a nuanced `synthesis recipe` guided by human expertise and intuition. This study conducts a thorough examination of learning and search techniques for logic synthesis, unearthing a surprising revelation: pre-trained agents, when confronted with entirely novel designs, may veer off course, detrimentally affecting the search trajectory. We present ABC-RL, a meticulously tuned alpha parameter that adeptly adjusts recommendations from pre-trained agents during the search process. Computed based on similarity scores through nearest neighbor retrieval from the training dataset, ABC-RL yields superior synthesis recipes tailored for a wide array of hardware designs. Our findings showcase substantial enhancements in the Quality-of-result (QoR) of synthesized circuits, boasting improvements of up to 24.8% compared to state-of-the-art techniques. Furthermore, ABC-RL achieves an impressive up to 9x reduction in runtime (iso-QoR) when compared to current state-of-the-art methodologies.

Recent machine reading comprehension datasets include extractive and boolean questions but current approaches do not offer integrated support for answering both question types. We present a multilingual machine reading comprehension system and front-end demo that handles boolean questions by providing both a YES/NO answer and highlighting supporting evidence, and handles extractive questions by highlighting the answer in the passage. Our system, GAAMA 2.0, is ranked first on the Tydi QA leaderboard at the time of this writing. We contrast two different implementations of our approach. The first includes several independent stacks of transformers allowing easy deployment of each component. The second is a single stack of transformers utilizing adapters to reduce GPU memory footprint in a resource-constrained environment.

This paper considers the Pointer Value Retrieval (PVR) benchmark introduced in [ZRKB21], where a 'reasoning' function acts on a string of digits to produce the label. More generally, the paper considers the learning of logical functions with gradient descent (GD) on neural networks. It is first shown that in order to learn logical functions with gradient descent on symmetric neural networks, the generalization error can be lower-bounded in terms of the noise-stability of the target function, supporting a conjecture made in [ZRKB21]. It is then shown that in the distribution shift setting, when the data withholding corresponds to freezing a single feature (referred to as canonical holdout), the generalization error of gradient descent admits a tight characterization in terms of the Boolean influence for several relevant architectures. This is shown on linear models and supported experimentally on other models such as MLPs and Transformers. In particular, this puts forward the hypothesis that for such architectures and for learning logical functions such as PVR functions, GD tends to have an implicit bias towards low-degree representations, which in turn gives the Boolean influence for the generalization error under quadratic loss.

Implementing Boolean functions with circuits consisting of logic gates is fundamental in digital computer design. However, the implemented circuit must be exactly equivalent, which hinders generative neural approaches on this task due to their occasionally wrong predictions. In this study, we introduce a generative neural model, the "Circuit Transformer", which eliminates such wrong predictions and produces logic circuits strictly equivalent to given Boolean functions. The main idea is a carefully designed decoding mechanism that builds a circuit step-by-step by generating tokens, which has beneficial "cutoff properties" that block a candidate token once it invalidate equivalence. In such a way, the proposed model works similar to typical LLMs while logical equivalence is strictly preserved. A Markov decision process formulation is also proposed for optimizing certain objectives of circuits. Experimentally, we trained an 88-million-parameter Circuit Transformer to generate equivalent yet more compact forms of input circuits, outperforming existing neural approaches on both synthetic and real world benchmarks, without any violation of equivalence constraints.