What Makes Effective Supervision in Latent Chain-of-Thought: An Information-Theoretic Analysis

Information-theoretic analysis of supervision in latent chain-of-thought reasoning

This paper analyzes Latent Chain-of-Thought (CoT) reasoning — where reasoning occurs in continuous hidden states rather than discrete text — through an information-theoretic lens, identifying a 'dual collapse' failure mode involving gradient attenuation and representational drift. The authors decompose process supervision into Trajectory Supervision and Space Supervision, and introduce the Unified Latent Probe (ULP) to quantify mutual information between latent trajectories and explicit reasoning steps. Experiments reveal an 'Information-Performance Binding' showing reasoning accuracy depends on information fidelity in the latent chain, suggesting supervision should shift from geometric imitation toward mutual information maximization.