Do Latent-CoT Models Think Step-by-Step? A Mechanistic Study on Sequential Reasoning Tasks

Latent Chain-of-Thought aims to enable step-by-step computation without emitting long rationales, yet its internal mechanisms remain unclear. We study CODI, a continuous-thought teacher-student distillation model, on strictly sequential polynomial-iteration tasks with known intermediate states. Using logit-lens decoding, linear probes, attention analysis, and activation patching, we localize intermediate-state representations and trace how they are routed to the final readout. In short-horizon, low-hop tasks, CODI forms faithful bridge states across latent-thought positions, while the final input follows a separate near-direct route; predictions arise through late fusion at the answer readout. As task depth and difficulty increase, however, CODI does not reliably sustain a full latent rollout: it either compresses computation into a partial late-intermediate pathway or, in harder regimes, loses the latent reasoning signature altogether. To explain this transition, we show theoretically that the task's algebraic structure controls its effective memory: compressible regimes support late-bottleneck reasoning, while incompressible regimes preserve full-history dependence and destabilize latent rollouts. Overall, our results characterize when CODI-style latent-CoT yields faithful iterative computation versus compressed or shortcut strategies.