How Does Unfaithful Reasoning Emerge from Autoregressive Training? A Study of Synthetic Experiments

Chain-of-thought (CoT) reasoning generated by large language models (LLMs) is often unfaithful: intermediate steps can be logically inconsistent or fail to reflect the causal relationship leading to the final answer. Despite extensive empirical observations, a fundamental understanding of CoT is lacking--what constitutes faithful CoT reasoning, and how unfaithfulness emerges from autoregressive training. We study these questions using well-controlled synthetic experiments, training small transformers on noisy data to solve modular arithmetic expressions step by step, a task we term Arithmetic Expression Reasoning. We find that models can learn faithful reasoning that causally follows the underlying arithmetic rules, but only when the training noise is below a critical threshold, a phenomenon attributable to simplicity bias. At higher noise levels, training dynamics exhibit a transition from faithful stepwise reasoning to unfaithful skip-step reasoning via an intermediate mixed mode characterized by a transient increase in prediction entropy. Mechanistic analysis reveals that models learn to encode internal uncertainty by resolving inconsistent reasoning steps, which suggests the emergence of implicit self-verification from autoregressive training.