From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step
Uses a curriculum that progressively removes intermediate reasoning steps during fine-tuning, teaching a model to internalize an explicit chain of thought.
Related terms: implicit CoT, latent reasoning, latent chain-of-thought, latent CoT.
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ArXiv preprint
arXiv:2405.14838 · Initial submission: 2024-05-23
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Method comparisons
Distillation and stepwise internalization
Knowledge distillation and stepwise internalization use different training signals. Implicit CoT via Knowledge Distillation learns to predict a teacher's intermediate hidden states, which help a student produce the answer. Stepwise Internalization instead repeatedly shortens the written solution and fine-tunes the same model on what remains. Both use worked solutions during training; neither requires writing the removed steps at inference. Their reported experiments focus on multiplication and grade-school math, not a guarantee of general reasoning ability.
Sources: Deng et al. (2023), §3 · Deng et al. (2024), §3
Paper details: Implicit Chain of Thought Reasoning via Knowledge Distillation · From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step
From stepwise internalization to Coconut
Coconut explicitly credits Deng et al. (2024) as the inspiration for its multistage training curriculum. Stepwise internalization gradually removes written CoT tokens until the model answers directly. Coconut instead replaces removed steps with continuous hidden-state inputs, retaining a sequence of internal reasoning steps before the answer. It also follows the earlier work in resetting the optimizer between training stages.
Sources: Deng et al. (2024), §3 · Coconut, §3
Paper details: From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step · Training Large Language Models to Reason in a Continuous Latent Space
Changing generation order or removing written steps
Diffusion of Thought changes how a chain of thought is generated: it refines the solution through denoising rather than committing to words strictly from left to right. This changes the generation schedule, not necessarily the visibility of the reasoning. The resulting chain can still be text, unlike methods that only emit the final answer.
Sources: Diffusion of Thought · Deng et al. (2024), §3
Paper details: Diffusion of Thoughts: Chain-of-Thought Reasoning in Diffusion Language Models · From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step
Explore this approach
Internalized reasoning — Learn from worked solutions so that some or all of the reasoning can later happen without writing those steps. Training may use a separate teacher model or progressively remove written steps from the model being trained.
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