Exploring Layer Activation Dynamic of CoT via Knowledge Probe

Chain-of-thought (CoT) reasoning has emerged as a crucial paradigm for enhancing large language model (LLM) performance on multi-step reasoning tasks. However, the internal mechanisms by which LLMs invoke knowledge and propagate information across different steps of the CoT are poorly understood. To fill this gap, we propose a multi-stage probing framework that enforces structured reasoning with three explicit stages: keyword extraction, theorem generation, and computation execution. The framework integrates attention knockout to trace cross-layer information flow and theorem probing to examine how specific contents are encoded within representations. To enable controlled and stage-aligned analysis, we construct a structured CoT dataset that covers the mathematics and physics domains. Experiments on four instruction-tuned LLMs reveal distinct stage-specific patterns. First, keyword information is progressively aggregated into the final token in later layers. Second, theorem semantics are encoded in the mid-to-late layers and undergo two stages of propagation. Finally, parameter substitution is achieved through joint extraction by the final token and other tokens. The first parameter predominantly relies on the final token, whereas later parameters increasingly depend on information extracted by other tokens. Overall, our findings shed light on the neural implementation of CoT reasoning and provide actionable insights for developing more interpretable and reasoning-capable LLMs. We further evaluate a free-form prompting setting without labeled fields and observe consistent qualitative trends.