Implicit Chain of Thought Reasoning via Knowledge Distillation
First proposes implicit chain-of-thought reasoning: learning to reason through continuous hidden states instead of generating explicit intermediate steps. Implements this framework by distilling an explicit-CoT teacher's intermediate representations into an emulator and a student that produces the answer.
Related terms: implicit CoT, latent reasoning, latent chain-of-thought, latent CoT.
First public:
Related-method demo: Multiplication without written steps · Model details
Related-method demo: Math word problems without written steps · Model details
Related-method demos are not implementations of this paper; see the model details for the method used.
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ArXiv preprint
arXiv:2311.01460 · Initial submission: 2023-11-02
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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
Hidden-state distillation: the 2023 method and CODI
The 2023 implicit CoT paper proposes reasoning through hidden states and implements it with a teacher, a thought emulator and an answer-generating student. CODI also transfers explicit reasoning through hidden-state supervision, but uses one model for both teacher and student tasks. It aligns their states just before the answer, while the student takes successive continuous reasoning steps.
Sources: Deng et al. (2023), §2.3 · Deng et al. (2023), §3 · CODI, §3
Paper details: Implicit Chain of Thought Reasoning via Knowledge Distillation · CODI: Compressing Chain-of-Thought into Continuous Space via Self-Distillation
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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