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Register a new userTransformer-based Machine Learning for Fast SAT Solvers and Logic Synthesis
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Added by
Feng Shi
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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CNF-based SAT and MaxSAT solvers are central to logic synthesis and verification systems. The increasing popularity of these constraint problems in electronic design automation encourages studies on different SAT problems and their properties for further computational efficiency. There has been both theoretical and practical success of modern Conflict-driven clause learning SAT solvers, which allows solving very large industrial instances in a relatively short amount of time. Recently, machine learning approaches provide a new dimension to solving this challenging problem. Neural symbolic models could serve as generic solvers that can be specialized for specific domains based on data without any changes to the structure of the model. In this work, we propose a one-shot model derived from the Transformer architecture to solve the MaxSAT problem, which is the optimization version of SAT where the goal is to satisfy the maximum number of clauses. Our model has a scale-free structure which could process varying size of instances. We use meta-path and self-attention mechanism to capture interactions among homogeneous nodes. We adopt cross-attention mechanisms on the bipartite graph to capture interactions among heterogeneous nodes. We further apply an iterative algorithm to our model to satisfy additional clauses, enabling a solution approaching that of an exact-SAT problem. The attention mechanisms leverage the parallelism for speedup. Our evaluation indicates improved speedup compared to heuristic approaches and improved completion rate compared to machine learning approaches.
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Logic synthesis is a fundamental step in hardware design whose goal is to find structural representations of Boolean functions while minimizing delay and area. If the function is completely-specified, the implementation accurately represents the function. If the function is incompletely-specified, the implementation has to be true only on the care set. While most of the algorithms in logic synthesis rely on SAT and Boolean methods to exactly implement the care set, we investigate learning in logic synthesis, attempting to trade exactness for generalization. This work is directly related to machine learning where the care set is the training set and the implementation is expected to generalize on a validation set. We present learning incompletely-specified functions based on the results of a competition conducted at IWLS 2020. The goal of the competition was to implement 100 functions given by a set of care minterms for training, while testing the implementation using a set of validation minterms sampled from the same function. We make this benchmark suite available and offer a detailed comparative analysis of the different approaches to learning
We present a novel Auxiliary Truth enhanced Genetic Algorithm (GA) that uses logical or mathematical constraints as a means of data augmentation as well as to compute loss (in conjunction with the traditional MSE), with the aim of increasing both data efficiency and accuracy of symbolic regression (SR) algorithms. Our method, logic-guided genetic algorithm (LGGA), takes as input a set of labelled data points and auxiliary truths (ATs) (mathematical facts known a priori about the unknown function the regressor aims to learn) and outputs a specially generated and curated dataset that can be used with any SR method. Three key insights underpin our method: first, SR users often know simple ATs about the function they are trying to learn. Second, whenever an SR system produces a candidate equation inconsistent with these ATs, we can compute a counterexample to prove the inconsistency, and further, this counterexample may be used to augment the dataset and fed back to the SR system in a corrective feedback loop. Third, the value addition of these ATs is that their use in both the loss function and the data augmentation process leads to better rates of convergence, accuracy, and data efficiency. We evaluate LGGA against state-of-the-art SR tools, namely, Eureqa and TuringBot on 16 physics equations from The Feynman Lectures on Physics book. We find that using these SR tools in conjunction with LGGA results in them solving up to 30.0% more equations, needing only a fraction of the amount of data compared to the same tool without LGGA, i.e., resulting in up to a 61.9% improvement in data efficiency.
At present, people usually use some methods based on convolutional neural networks (CNNs) for Electroencephalograph (EEG) decoding. However, CNNs have limitations in perceiving global dependencies, which is not adequate for common EEG paradigms with a strong overall relationship. Regarding this issue, we propose a novel EEG decoding method that mainly relies on the attention mechanism. The EEG data is firstly preprocessed and spatially filtered. And then, we apply attention transforming on the feature-channel dimension so that the model can enhance more relevant spatial features. The most crucial step is to slice the data in the time dimension for attention transforming, and finally obtain a highly distinguishable representation. At this time, global averaging pooling and a simple fully-connected layer are used to classify different categories of EEG data. Experiments on two public datasets indicate that the strategy of attention transforming effectively utilizes spatial and temporal features. And we have reached the level of the state-of-the-art in multi-classification of EEG, with fewer parameters. As far as we know, it is the first time that a detailed and complete method based on the transformer idea has been proposed in this field. It has good potential to promote the practicality of brain-computer interface (BCI). The source code can be found at: textit{https://github.com/anranknight/EEG-Transformer}.
An automated technique has recently been proposed to transfer learning in the hierarchical Bayesian optimization algorithm (hBOA) based on distance-based statistics. The technique enables practitioners to improve hBOA efficiency by collecting statistics from probabilistic models obtained in previous hBOA runs and using the obtained statistics to bias future hBOA runs on similar problems. The purpose of this paper is threefold: (1) test the technique on several classes of NP-complete problems, including MAXSAT, spin glasses and minimum vertex cover; (2) demonstrate that the technique is effective even when previous runs were done on problems of different size; (3) provide empirical evidence that combining transfer learning with other efficiency enhancement techniques can often yield nearly multiplicative speedups.
Over the last two decades, we have seen a dramatic improvement in the efficiency of conflict-driven clause-learning Boolean satisfiability (CDCL SAT) solvers on industrial problems from a variety of domains. The availability of such powerful general-purpose search tools as SAT solvers has led many researchers to propose SAT-based methods for cryptanalysis, including techniques for finding collisions in hash functions and breaking symmetric encryption schemes. Most of the previously proposed SAT-based cryptanalysis approaches are blackbox techniques, in the sense that the cryptanalysis problem is encoded as a SAT instance and then a CDCL SAT solver is invoked to solve the said instance. A weakness of this approach is that the encoding thus generated may be too large for any modern solver to solve efficiently. Perhaps a more important weakness of this approach is that the solver is in no way specialized or tuned to solve the given instance. To address these issues, we propose an approach called CDCL(Crypto) (inspired by the CDCL(T) paradigm in Satisfiability Modulo Theory solvers) to tailor the internal subroutines of the CDCL SAT solver with domain-specific knowledge about cryptographic primitives. Specifically, we extend the propagation and conflict analysis subroutines of CDCL solvers with specialized codes that have knowledge about the cryptographic primitive being analyzed by the solver. We demonstrate the power of this approach in the differential path and algebraic fault analysis of hash functions. Our initial results are very encouraging and reinforce the notion that this approach is a significant improvement over blackbox SAT-based cryptanalysis.
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