Abstract: Chain-of-Thought (CoT) reasoning could in principle enable a deeper understanding of a language model's (LM) internal reasoning. However, prior work suggests that LMs can answer questions similarly despite changes in their CoT, suggesting that those models are not truly using the CoT. We propose an reinforcement learning technique to produce CoTs that are sufficient alone for predicting future text, independent of other context. This methodology ensures that if the LM can predict future tokens, then it must have used the CoT to understand its context. We formalize the informativeness of a sender to a receiver LM as the degree to which the sender helps the receiver predict their future observations, and we define a "Markovian" LM as one which predicts future text given only a CoT as context. We derive a "Markovian training" procedure by applying our definition of informativeness to a Markovian LM and optimizing via policy gradient and Proximal Policy Optimization (PPO). We demonstrate our training algorithm's effectiveness on fifteen-term arithmetic problems, show the model utilizes the CoT, and externally validate that the generated CoT is meaningful and usable by another model.

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