Learning To Solve Circuit-SAT: An Unsupervised Differentiable Approach
Recent efforts to combine Representation Learning with Formal Methods, commonly known as the Neuro-Symbolic Methods, have given rise to a new trend of applying rich neural architectures to solve classical combinatorial optimization problems. In this paper, we propose a neural framework that can learn to solve the Circuit Satisfiability problem. Our framework is built upon two fundamental contributions: a rich embedding architecture that encodes the problem structure and an end-to-end differentiable training procedure that mimics Reinforcement Learning and trains the model directly toward solving the SAT problem. The experimental results show the superior out-of-sample generalization performance of our framework compared to the recently developed NeuroSAT method.
 The Authors of this paper investigate Neuro-Symbolic methods in the context of learning a SAT solver generalized to the Circuit-SAT problem. Using a reinforcement learning – inspired approach to demonstrate a framework that is capable of (unsupervised) learning, by means of an end-to-end differentiable training procedure. Their formulation incorporates the solving of a given SAT problem into the architecture, meaning the algorithm is trained to produce a solution if a given problem is satisfiable. This is in contrast to previous similar work by (Selsam et al. 2018), where the framework was trained as a SAT classifier. Their results outline the performance increase over the previous work (Selsam et al. 2018) on finding a given solution for a SAT problem, on in-sample and out-sample results. Neg: Figure descriptions are not very clear When it comes to comparing the results, they do use a prepossessing step for their algorithm which they do not incorporate into the results Pros: Clear outline of the data sets used for benchmarks. Good Literature review, expressing in-depth knowledge of the current state of the art formulation for same/similar tasks Extensive background section, that explains the theoretical concepts and their architecture used well. Clear outline of the Solver, where the individual parts/networks are explained and justified in detail Very well outlined argumentation for approaching this particular problem by the proposed method/ The experimental results as well are easy to follow and show promising results for the proposed framework The proposed method as well is novel and outperforms similar algorithms in the experimental evaluation. The paper is very well written, proposes a novel Neuro-Symbolic approach to the classical SAT problem, and demonstrates promising results.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Learning To Solve Circuit-SAT: An Unsupervised Differentiable Approach
Recent efforts to combine Representation Learning with Formal Methods, commonly known as the Neuro-Symbolic Methods, have given rise to a new trend of applying rich neural architectures to solve classical combinatorial optimization problems. In this paper, we propose a neural framework that can learn to solve the Circuit Satisfiability problem. Our framework is built upon two fundamental contributions: a rich embedding architecture that encodes the problem structure and an end-to-end differentiable training procedure that mimics Reinforcement Learning and trains the model directly toward solving the SAT problem. The experimental results show the superior out-of-sample generalization performance of our framework compared to the recently developed NeuroSAT method.
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<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



 The Authors of this paper investigate Neuro-Symbolic methods in the context of learning a SAT solver generalized to the Circuit-SAT problem. Using a reinforcement learning – inspired approach to demonstrate a framework that is capable of (unsupervised) learning, by means of an end-to-end differentiable training procedure. Their formulation incorporates the solving of a given SAT problem into the architecture, meaning the algorithm is trained to produce a solution if a given problem is satisfiable. This is in contrast to previous similar work by (Selsam et al. 2018), where the framework was trained as a SAT classifier. Their results outline the performance increase over the previous work (Selsam et al. 2018) on finding a given solution for a SAT problem, on in-sample and out-sample results. Neg: Figure descriptions are not very clear When it comes to comparing the results, they do use a prepossessing step for their algorithm which they do not incorporate into the results Pros: Clear outline of the data sets used for benchmarks. Good Literature review, expressing in-depth knowledge of the current state of the art formulation for same/similar tasks Extensive background section, that explains the theoretical concepts and their architecture used well. Clear outline of the Solver, where the individual parts/networks are explained and justified in detail Very well outlined argumentation for approaching this particular problem by the proposed method/ The experimental results as well are easy to follow and show promising results for the proposed framework The proposed method as well is novel and outperforms similar algorithms in the experimental evaluation. The paper is very well written, proposes a novel Neuro-Symbolic approach to the classical SAT problem, and demonstrates promising results.
assistant
 The Authors of this paper investigate Neuro-Symbolic methods in the context of learning a SAT solver generalized to the Circuit-SAT problem. Using a reinforcement learning – inspired approach to demonstrate a framework that is capable of (unsupervised) learning, by means of an end-to-end differentiable training procedure. Their formulation incorporates the solving of a given SAT problem into the architecture, meaning the algorithm is trained to produce a solution if a given problem is satisfiable. This is in contrast to previous similar work by (Selsam et al. 2018), where the framework was trained as a SAT classifier. Their results outline the performance increase over the previous work (Selsam et al. 2018) on finding a given solution for a SAT problem, on in-sample and out-sample results. Neg: Figure descriptions are not very clear When it comes to comparing the results, they do use a prepossessing step for their algorithm which they do not incorporate into the results Pros: Clear outline of the data sets used for benchmarks. Good Literature review, expressing in-depth knowledge of the current state of the art formulation for same/similar tasks Extensive background section, that explains the theoretical concepts and their architecture used well. Clear outline of the Solver, where the individual parts/networks are explained and justified in detail Very well outlined argumentation for approaching this particular problem by the proposed method/ The experimental results as well are easy to follow and show promising results for the proposed framework The proposed method as well is novel and outperforms similar algorithms in the experimental evaluation. The paper is very well written, proposes a novel Neuro-Symbolic approach to the classical SAT problem, and demonstrates promising results.