arxiv: 2405.14838 · v1 · submitted 2024-05-23 · 💻 cs.CL · cs.AI· cs.LG

Recognition: 2 theorem links

· Lean Theorem

From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step

Yuntian Deng , Yejin Choi , Stuart Shieber

Authors on Pith no claims yet

Pith reviewed 2026-05-16 11:40 UTC · model grok-4.3

classification 💻 cs.CL cs.AIcs.LG

keywords chain-of-thoughtreasoning internalizationfine-tuningmultiplicationlanguage modelsGSM8Kimplicit reasoning

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The pith

A progressive fine-tuning method lets language models internalize chain-of-thought steps so they can solve harder reasoning tasks without producing explicit intermediate outputs.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that models can be taught to internalize chain-of-thought reasoning by beginning with explicit step-by-step training and then gradually removing those intermediate steps while fine-tuning on the final answers alone. This schedule enables a GPT-2 Small model to reach up to 99 percent accuracy on nine-by-nine digit multiplication, a scale far beyond what standard training achieves. The same process works on larger models such as Mistral 7B, producing over 50 percent accuracy on GSM8K while generating no reasoning steps at all. A reader would care because the method suggests a route to more compact and efficient reasoning inside the model rather than in its visible output.

Core claim

Starting from a model trained to produce explicit chain-of-thought sequences, successively shorter versions of those sequences are created by dropping intermediate steps; continued fine-tuning on the shortened sequences causes the model to compress the missing reasoning into its internal activations, so that it can reach the correct final answer directly.

What carries the argument

The progressive removal schedule that shortens the chain-of-thought target at each fine-tuning stage, forcing the model to internalize the deleted steps.

If this is right

GPT-2 Small reaches 99 percent accuracy on nine-by-nine multiplication without any explicit steps.
Mistral 7B exceeds 50 percent on GSM8K while producing no intermediate reasoning.
Models can solve tasks that exceed the scale solvable by standard direct-answer training.
Reasoning can be performed implicitly, shortening generated sequences at inference time.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Inference cost may drop because the model no longer needs to emit long reasoning traces.
The method could be tried on non-arithmetic reasoning domains to test whether internalization generalizes.
Internal activations might be probed to recover what the compressed steps look like.
Limits of the approach could be tested by scaling to still larger multiplication problems.

Load-bearing premise

Performance gains come specifically from the model internalizing the removed reasoning steps rather than from extra training exposure or other side effects of the fine-tuning schedule.

What would settle it

A control run that applies the same total number of fine-tuning steps but removes CoT steps randomly or all at once instead of progressively, and then checks whether nine-by-nine multiplication accuracy still reaches 99 percent.

read the original abstract

When leveraging language models for reasoning tasks, generating explicit chain-of-thought (CoT) steps often proves essential for achieving high accuracy in final outputs. In this paper, we investigate if models can be taught to internalize these CoT steps. To this end, we propose a simple yet effective method for internalizing CoT steps: starting with a model trained for explicit CoT reasoning, we gradually remove the intermediate steps and finetune the model. This process allows the model to internalize the intermediate reasoning steps, thus simplifying the reasoning process while maintaining high performance. Our approach enables a GPT-2 Small model to solve 9-by-9 multiplication with up to 99% accuracy, whereas standard training cannot solve beyond 4-by-4 multiplication. Furthermore, our method proves effective on larger language models, such as Mistral 7B, achieving over 50% accuracy on GSM8K without producing any intermediate steps.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Gradual removal of explicit CoT steps during fine-tuning produces large gains on narrow arithmetic for small models, but the gains may trace to the training schedule rather than genuine internalization.

read the letter

The main result is that starting from explicit CoT and then progressively shortening the target sequences during fine-tuning lets GPT-2 small reach 99% accuracy on 9-by-9 multiplication, while ordinary training fails past 4-by-4. The same schedule lifts Mistral 7B above 50% on GSM8K with no steps shown at inference. The new piece is the incremental removal curriculum itself; earlier CoT and distillation papers do not describe this exact staged shortening of targets. The multiplication numbers are the clearest contribution. The task is tightly defined, the accuracy jump is large, and the procedure is simple to reproduce, so the empirical claim is easy to test. The soft spot is the missing isolation of the mechanism. The progressive schedule could improve optimization through curriculum or regularization effects even if the model never learns to run the removed steps internally. The abstract gives no ablation that holds total training steps fixed while varying the removal pattern, so it remains possible the benefit is schedule-driven rather than internalization-driven. The GSM8K lift is also smaller, which suggests the effect may be narrower than the headline implies. This is useful reading for anyone trying to compress reasoning into smaller models or cut inference cost by shortening outputs. The experimental claims are concrete enough that a referee can ask for the necessary controls and check whether the numbers replicate. I would send it to review.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes a method to internalize chain-of-thought (CoT) reasoning in language models: begin with explicit CoT training and then progressively remove intermediate steps while fine-tuning. The central empirical claim is that this procedure enables a GPT-2 Small model to reach up to 99% accuracy on 9-by-9 multiplication (where standard training fails beyond 4-by-4) and allows Mistral 7B to exceed 50% accuracy on GSM8K without emitting any intermediate steps.

Significance. If the reported gains are shown to arise specifically from internalization rather than from the progressive training schedule itself, the work would offer a practical route to shorter, faster inference on arithmetic and mathematical reasoning tasks while preserving accuracy. The results on both small and 7B-scale models provide a concrete demonstration that explicit CoT can be compressed into implicit computation.

major comments (3)

[§4] §4 (Experiments): No control condition is reported that applies the identical progressive fine-tuning schedule while retaining explicit CoT targets or using a non-removal curriculum (e.g., gradually increasing operand size without step deletion). Without this ablation, the 99% accuracy on 9-by-9 multiplication cannot be attributed specifically to internalization rather than to curriculum or optimization artifacts of the staged schedule.
[§3] §3 (Method): The precise mechanics of step removal—selection of which tokens or steps are deleted at each stage, the functional form of the removal schedule, and whether the model continues to see the full original dataset—are not specified. This omission prevents replication and leaves open the possibility that the target sequences are being altered in ways that change the learning problem independently of internalization.
[Table 1] Table 1 / §4.1: The multiplication results lack reported standard deviations across random seeds, details on the exact train/test split sizes, and confirmation that test operands were never seen during any training stage. These omissions weaken the claim that the model has internalized general multiplication rather than memorizing patterns under the progressive regime.

minor comments (2)

[Abstract] Abstract: The phrase 'up to 99% accuracy' should be replaced by the exact accuracy and the precise operand range (e.g., '99% on 9-by-9') to avoid ambiguity.
[§5] §5 (Discussion): The comparison to 'standard training' should explicitly state whether the baseline used the same total number of gradient steps and data volume as the proposed schedule.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading and valuable feedback on our manuscript. We believe the suggested revisions will improve the clarity and rigor of our work. We address each major comment in detail below.

read point-by-point responses

Referee: [§4] §4 (Experiments): No control condition is reported that applies the identical progressive fine-tuning schedule while retaining explicit CoT targets or using a non-removal curriculum (e.g., gradually increasing operand size without step deletion). Without this ablation, the 99% accuracy on 9-by-9 multiplication cannot be attributed specifically to internalization rather than to curriculum or optimization artifacts of the staged schedule.

Authors: We concur that an ablation study isolating the effect of step removal from the progressive training schedule is necessary to attribute the performance gains specifically to internalization. Accordingly, we will conduct and report in the revised manuscript a control experiment that applies the identical progressive fine-tuning schedule but retains the full explicit CoT targets throughout. We will also include a curriculum that gradually increases operand size without any step deletion for comparison. These additions will clarify whether the observed 99% accuracy on 9x9 multiplication stems from the internalization process or from the staged optimization itself. revision: yes
Referee: [§3] §3 (Method): The precise mechanics of step removal—selection of which tokens or steps are deleted at each stage, the functional form of the removal schedule, and whether the model continues to see the full original dataset—are not specified. This omission prevents replication and leaves open the possibility that the target sequences are being altered in ways that change the learning problem independently of internalization.

Authors: We apologize for the lack of specificity in §3 regarding the step removal procedure. In the revised manuscript, we will provide a detailed account of how steps are selected and removed at each stage, the exact functional form of the removal schedule, and confirmation that the model sees the full original dataset during fine-tuning. We will include an algorithm description and all necessary hyperparameters to allow for exact replication of our experiments. revision: yes
Referee: [Table 1] Table 1 / §4.1: The multiplication results lack reported standard deviations across random seeds, details on the exact train/test split sizes, and confirmation that test operands were never seen during any training stage. These omissions weaken the claim that the model has internalized general multiplication rather than memorizing patterns under the progressive regime.

Authors: We will update Table 1 to include standard deviations across multiple random seeds. Additionally, we will clarify in §4.1 the train/test split sizes and explicitly confirm that the test operands were generated independently and never appeared in the training data at any stage. These changes will address concerns about potential memorization versus true internalization. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical training procedure evaluated on held-out tests

full rationale

The paper presents an empirical method of progressive fine-tuning that removes explicit CoT steps from targets. Performance claims (99% on 9x9 multiplication for GPT-2 Small, >50% on GSM8K for Mistral) are measured on held-out test sets rather than derived from any equation or parameter fit. No self-definitional loops, fitted inputs renamed as predictions, or load-bearing self-citations appear in the derivation. The central result is an experimental outcome, not a reduction to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach rests on the standard assumption that fine-tuning on progressively abbreviated targets causes the model to compress reasoning into its parameters; no new free parameters, axioms, or invented entities are introduced.

axioms (1)

domain assumption Fine-tuning on shortened CoT sequences causes the model to internalize the omitted reasoning steps rather than adopt shortcuts
Central premise of the training procedure described in the abstract.

pith-pipeline@v0.9.0 · 5470 in / 1158 out tokens · 36552 ms · 2026-05-16T11:40:00.849486+00:00 · methodology

discussion (0)

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