Superposition and Distributed Memory in Continuous Chain-of-Thought Reasoning

Continuous chain-of-thought reasoning feeds hidden states back into a language model while retaining a persistent key–value (KV) history. In this work, we observe a distinction between latent generation and answer readout in Coconut: restricting latent-history access to recent positions during generation preserves most answers, whereas restricting it to the final position at readout changes many answers. Restoring earlier cached values also recovers much of the lost accuracy after history corruption while the final latent input remains fixed. To understand how this historical information can support reasoning, we develop a frontier–history model for graph reachability. We show that a two-block Transformer can implement exact frontier updates and answer readout by superposing the current frontier in feedback and retaining earlier frontiers in the KV cache. Further experiments on a trained two-layer Coconut model reveal depth-aligned feedback, depth-selective historical readout, and attenuation of revisited nodes. However, paired interventions show that feedback also retains update-relevant history beyond the current frontier. These results offer a distributed account of continuous reasoning: superposition need not entail cumulative storage in every feedback vector.