How Transformers Solve Propositional Logic Problems: A Mechanistic Analysis
Keywords: Mechanistic Interpretability, Language Models, Transformers, Logical Reasoning, Learned Representations
TL;DR: We mechanistically analyze how small and large language models solve synthetic propositional logic problems.
Abstract: Large language models (LLMs) have shown amazing performance on tasks that require planning and reasoning. Motivated by this, we investigate the internal mechanisms that underpin a network's ability to perform complex logical reasoning. We first construct a synthetic propositional logic problem that serves as a concrete test-bed for network training and evaluation. Crucially, this problem demands nontrivial planning to solve. We perform our study on two fronts. First, we pursue an understanding of precisely how a three-layer transformer, trained from scratch and attains perfect test accuracy, solves this problem. We are able to identify certain "planning" and "reasoning" circuits in the network that necessitate cooperation between the attention blocks to implement the desired logic. Second, we study how a pretrained LLM, Mistral 7B, solves this problem. Using activation patching, we characterize internal components that are critical in solving our logic problem. Overall, our work systemically uncovers novel aspects of small and large transformers, and continues the study of how they plan and reason.
Primary Area: interpretability and explainable AI
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Submission Number: 13137
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