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.
For example: A teacher model solves a problem in several written steps. A student model learns to produce the answer directly, using information from the teacher's intermediate reasoning during training.
These research demos may take a moment to start. Check the model details for training and usage information.
Compare GPT-2 models using implicit CoT, explicit CoT, or no CoT on two numbers of up to 20 digits each.
The models can make mistakes, including on valid inputs. The implicit model writes answer digits, not intermediate steps.
Try a Mistral-7B model trained with stepwise internalization on grade-school math word problems.
Answers can be wrong. This model is trained for grade-school math word problems, not general conversation. It still generates the answer token by token.
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
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
Dates usually refer to the first arXiv submission. Search or filter these papers →
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.
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.
Uses outputs from a slower deliberative process as training data for a faster model, studying when System-2-like behavior can be compressed into direct prediction.
Randomizes which reasoning steps remain visible during training so one model can interpolate between direct and explicit reasoning.
Compresses visible reasoning into hidden thinking states to reduce generated reasoning length while preserving task performance.
Compresses segments of a generated reasoning chain into dense states while retaining a stepwise inference process.
Uses self-distillation to align continuous internal reasoning states with explicit chain-of-thought behavior while reducing visible reasoning tokens.
Dynamically compresses portions of a reasoning chain into latent states according to the problem and intermediate context.
Uses reinforcement learning to choose and train a mixture of latent and written reasoning steps.
Learns dynamic shortcuts between language and latent states to skip portions of an otherwise explicit reasoning trajectory.
Distills an autoregressive textual reasoner into a model that carries the intermediate process through silent internal states.
Trains continuous intermediate states with explicit supervision so reasoning can proceed without emitting a full textual trace.
Compresses textual reasoning into semantically aligned implicit tokens intended to preserve useful intermediate computation with fewer generated steps.
Analyzes how skipping intermediate steps weakens learning signals in a simplified parity-task model. Introduces NatBool-DAG to test logical dependencies and ALiCoT, which supervises learned token states with intermediate logical labels or explicit-CoT representations.
Trains on synthetic traces that rank document pages and extract relevant evidence, then uses low-strength model merging to internalize the trained reasoning behavior. Compares answering with and without written reasoning on long visual documents.
Post-trains a single model to internalize the computation of a multi-agent debate rather than emitting the debate as text.
Provides theoretical and empirical results on when transformers trained with a curriculum learn to internalize explicit reasoning steps.
Distills a teacher's interleaved visual and textual reasoning into a student that no longer generates intermediate visual representations. The student still writes a textual chain of thought; what is internalized is the visual portion of the reasoning.
Trains a language model to score labels supplied at inference in one forward pass, without generating a reasoning trace. Distills label distributions from repeated teacher reasoning and studies routing uncertain decisions back to explicit reasoning.