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arXiv · 2410.07432

Can Transformers Reason Logically? A Study in SAT Solving

Leyan Pan·Vijay Ganesh·Jacob Abernethy·Chris Esposo·Wenke Lee
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Abstract

We formally study the logical reasoning capabilities of decoder-only Transformers in the context of the boolean satisfiability (SAT) problem. First, we prove by construction that decoder-only Transformers can decide 3-SAT, in a non-uniform model of computation, using backtracking and deduction via Chain-of-Thought (CoT). %We prove its correctness by showing trace equivalence to the well-known DPLL SAT-solving algorithm. Second, we implement our construction as a PyTorch model with a tool (PARAT) that we designed to empirically demonstrate its correctness and investigate its properties. Third, rather than \textit{programming} a transformer to reason, we evaluate empirically whether it can be \textit{trained} to do so by learning directly from algorithmic traces (``reasoning paths'') from our theoretical construction. The trained models demonstrate strong out-of-distribution generalization on problem sizes seen during training but has limited length generalization, which is consistent with the implications of our theoretical result

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Leyan Pan, Vijay Ganesh, Jacob Abernethy, Chris Esposo, Wenke Lee. 2024-10-09. Can Transformers Reason Logically? A Study in SAT Solving. https://arxiv.org/abs/2410.07432

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