How Transformers Solve Propositional Logic Problems: A Mechanistic Analysis

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" mechanisms in the network that necessitate cooperation between the attention blocks to implement the desired logic. Second, we study how pretrained LLMs, namely Mistral-7B and Gemma-2-9B, solve this problem. We characterize their reasoning circuits through causal intervention experiments, providing necessity and sufficiency evidence for the circuits. We find evidence suggesting that the two models' latent reasoning strategies are surprisingly similar, and human-like. Overall, our work systemically uncovers novel aspects of small and large transformers, and continues the study of how they plan and reason.