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, but we can train a small transformer to achieve perfect accuracy. Building on our set-up, we then pursue an understanding of precisely how a three-layer transformer, trained from scratch, 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. To expand our findings, we then study a larger model, Mistral 7B. 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.

本研究探讨了大型语言模型在复杂逻辑推理中的内部机制，旨在填补对其推理能力理解的空白。论文构建了一个合成的命题逻辑问题，并发现小型变压器能够完美解决这一问题，揭示了注意力模块之间的合作如何实现所需逻辑。该研究的重要发现为理解小型和大型变压器的推理过程提供了新见解，具有潜在的广泛影响。

变压器如何解决命题逻辑问题：机制分析