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REVIEW 3 major objections 6 minor 41 references

Efficient Long CoT Reasoning in Small Language Models

T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper claims that distilling long chain-of-thought reasoning into small models works better when each teacher trace is first cut, by binary search with the small model as its own judge, to the shortest prefix that still yields the…

desk verdict Useful, practical recipe for pruning long CoT into 7B models, but the minimal-prefix guarantee in Algorithm 1 is overstated and the on-policy validation filter needs a bias check. read the letter →

arxiv 2505.18440 v2 pith:5PURD63E submitted 2025-05-24 cs.CL cs.AI

Zhaoyang Wang , Jinqi Jiang , Tian Qiu , Hui Liu , Xianfeng Tang , Huaxiu Yao This is my paper · ORCID
classification cs.CLcs.AI
keywords longchain-of-thoughtdistillationsmalllanguagemodelsbinarycuttingon-policyvalidationmathematicalreasoningefficiencypreferenceoptimization
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper claims that distilling long chain-of-thought (step-by-step reasoning) into small language models fails in part because teacher traces are padded with redundant verification steps, and that removing those steps before training is what unlocks efficient long CoT. It proposes cutting each trace, using binary search with backtracking, to the shortest contiguous prefix of thinking steps that still lets the target small model produce the correct final answer, with the small model itself acting as judge. After supervised fine-tuning and preference optimization on these trimmed prefixes, the small models keep most of the accuracy of full-trace distillation while generating 30-70% fewer thinking tokens on GSM8K, MATH, and AIME. A careful reader should care because the long-token overhead of reasoning models is one of the main barriers to deploying them at small scale, and the paper shows that a data-curation step can remove much of that overhead without redesigning the training pipeline.

What carries the argument

The load-bearing mechanism is binary cutting with backtracking, driven by an on-policy validation function $\phi(Q,T_{1:k},A;M)=\mathbf{1}\{M_t(Q,T_{1:k},P_{\mathrm{policy}})=A\}$, where $M_t$ is the target small model asked to answer from the prefix alone. Each iteration tests the midpoint prefix, keeps the shortest prefix that passes validation, and, if a cut prefix fails, resets the lower bound and searches upward so essential late steps are recovered. This reduces the search from $O(n)$ prefix checks to $O(\log_2 n)$ while the retained steps stay contiguous, and it ties the distilled data to the inductive biases of the exact model that will be trained.

What would settle it

Run the curation twice on a fixed set of problems: once with the untrained base model as validator and once with the same model after SFT on the distilled data. If the retained examples stay the same and gains concentrate on easy problems, then the on-policy filter is selecting questions the model already solves rather than teaching new reasoning; alternatively, stress-test on problems whose decisive step appears only near the end of the trace and check whether backtracking restores it.

Watch

Extended reading notes

Core claim

In the paper's own terms, the right unit of distillation is not the full long CoT trace but the shortest contiguous prefix of its thinking steps that the target SLM itself can still answer from. The method implements this by splitting the thinking part into steps, running a binary-cutting search on prefixes, and accepting a prefix only when the on-policy validation function returns true, i.e. when the target model, prompted to answer from the question and that prefix alone, gives the ground-truth answer. A backtracking stage restores steps that were over-pruned so the final selected segment remains a valid prefix. The paper reports that training on these streamlined segments via SFT and DPO preserves accuracy to within a few points of full-trace SFT while reducing generated thinking tokens by roughly 30-70%, and that random deletion or validation by another model clearly degrades the result.

Load-bearing premise

The method assumes that a small model's ability to produce the correct final answer from a truncated thinking prefix before any training reliably predicts that training on that same prefix as a full response will teach or preserve the desired reasoning, so the curated data may be biased toward questions the model can already answer.

Editorial extensions

If this is right

  • Training on pruned prefixes cuts average thinking tokens by roughly 30-70% on GSM8K, MATH, and AIME while keeping accuracy within a few points of full-trace SFT.
  • DPO with the pruned response preferred and the original long response dispreferred further compresses output, but on hard tasks it lowers accuracy unless the SFT objective is kept in the loss.
  • The target SLM's own validation matters: curated prefixes from another, similar-sized model train less well, and random deletion of steps substantially hurts reasoning, so the content and provenance of the retained steps carry the effect.
  • The search finds a valid answer-yielding prefix in $O(\log_2 n)$ validation calls instead of checking each prefix linearly, which makes the streamlining step cheap enough to apply to large teacher datasets.
  • Most teacher traces do not survive validation: about 25k useful samples remain from 93.7k train traces, meaning the filtering step itself is a strong data selection mechanism.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the validator is the untrained model, the distilled dataset may be enriched for questions the small model can already answer from a short prefix; a difficulty-stratified accuracy comparison would show whether the method teaches new reasoning or mostly selects easy cases.
  • The same binary-cutting recipe should transfer to any task with an automatically checkable answer, such as code execution or factual lookup, where a final answer can be verified without an external judge model.
  • The $O(\log_2 n)$ guarantee assumes that prefix validity is reasonably monotone; traces with a decisive late step will trigger deep backtracking, and measuring the backtracking depth on such traces would reveal the practical limit.
  • Restricting the search to contiguous prefixes preserves coherence but excludes reordering or skipping steps; a variant that searches over chunks or allows small gaps could find shorter training prefixes when the key reasoning is spread across the trace.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper proposes a data-curation pipeline for distilling long chain-of-thought (CoT) reasoning from large reasoning models into small language models. Given a teacher trace, the method splits the thinking part into steps, uses a binary-cutting search with a backtracking mechanism to find a short prefix that still lets the target SLM produce the correct final answer, and validates each prefix with the target model itself (on-policy validation). The resulting pruned traces are used for SFT and then DPO training. Experiments on GSM8K, MATH, and AIME with Llama-3.1-8B-Instruct and Qwen2.5-7B-Instruct report substantial token-count reductions (roughly 30--70%) while keeping accuracy within a few points of full long-CoT SFT, alongside ablations, LLM-as-a-judge, and human-preference evaluations.

Significance. If the central claims were delivered, this would be a practically useful contribution: it targets the real cost of long-CoT reasoning in small models, avoids expensive RL reward redesign, and proposes a model-adaptive way to select training prefixes. The empirical trend is clear and consistent across two model families and three benchmarks, and the paper includes useful ablations (random deletion, cross-model data) and both machine and human evaluations. However, the advertised algorithmic guarantee about finding the minimal valid prefix is not delivered by the implemented algorithm, and the on-policy filtering introduces a selection effect that makes it difficult to attribute the observed gains specifically to learning concise reasoning. The contribution is therefore promising but needs a substantial revision before the claims can be accepted.

major comments (3)
  1. [§3.2.2, Algorithm 1] Section 3.2.2 states that the binary-cutting strategy "guarantees the discovery of the minimal valid prefix" in O(log2 n), and Algorithm 1's Ensure clause promises the "shortest valid contiguous long CoT segment." This is false even under monotone validity. For example, let n=100 and suppose the minimal valid prefix is T1:40. The first loop tests mid=50, which is valid, so best=T1:50 and high=50. It then tests mid=25, which is invalid, and breaks. The backtracking loop resets low=25 and high=n=100, computes mid=63, and returns T1:63 if that prefix is valid, despite the fact that T1:50 was already known to be valid and T1:40 is shorter. If the test at 63 is invalid, the search moves upward and may eventually return T1:100; the known valid bound best is never used to tighten the search. Thus the returned prefix can be much longer than the minimal valid prefix. The argument also silently assumes that the validity predicate is monotone in prefix length, which is not established for a stochastic SLM validator. Please either implement a correct binary search that continues tightening the upper bound after a valid prefix is found, or restate the contribution as finding a valid prefix without a minimality guarantee and reinterpret Tables 1 and 2 accordingly.
  2. [§3.2.3, Eq. (1); Table 3] The on-policy validation uses the untrained target model M to decide which prefixes are kept, so the distilled dataset is restricted to examples for which the base model already produces the correct answer from some prefix. This makes it difficult to attribute post-SFT gains to learning concise reasoning: the filter may simply select questions that are easy for the base model, and the same filter changes the difficulty distribution of the training set. The paper does not report how M's validation decisions change after SFT, nor does it compare against a fixed external-oracle validator while controlling for the data filter. The ablation labeled "Qwen data" in Table 3 varies the validator but not the filtering mechanism, so it does not isolate the selection effect. Please add a control that applies the same filtering procedure with a fixed external validator (or with the model after SFT) and reports accuracy separately on the filtered and unfiltered evaluation sets.
  3. [Table 2 and §4.2] The comparison to FCS in Table 2 is not a controlled comparison of pruning algorithms. The table note says "only data deemed valid by the on-policy method is reused by FCS," so the two methods are evaluated on different effective data filters: FCS is restricted to examples that pass the target SLM's on-policy validity, while Ours is optimized for that same filter. Moreover, if FCS is the linear minimal-prefix search described in §4.1, its remaining ratio is the minimal prefix under the external judge; Ours can report a smaller ratio simply because the target SLM accepts a shorter prefix than the external judge on this filtered subset. This does not demonstrate that binary cutting finds shorter prefixes than linear search. Please compare both methods under the same validity function, for example by reporting the prefix lengths produced by the linear minimal search and by Algorithm 1 when both use the same validator, and separately describe how the data filter is applied to FCS.
minor comments (6)
  1. [§3.2.2] The sentence beginning "as 61.83% of the samples contain the answer in the last 10 steps, cutting from the beginning is not effective for SLM training" is unclear and appears to conflate the remaining-token ratio in Table 2 with the location of the answer in the trace; please clarify the intended statistic and its connection to the design.
  2. [Algorithm 1] The Ensure clause promises the "shortest valid contiguous long CoT segment," but the algorithm only searches over prefixes; please use consistent terminology and say "prefix" rather than "contiguous segment" if that is what is intended.
  3. [§3.3.2] The text says an SFT loss with weight 0.3 is added to Eq. (3), but the combined objective is not written out; please provide the actual loss used in the experiments.
  4. [Table 1] The table note states that all methods except Base and Short CoT count only tokens inside <think>...</think>; please clarify whether the full-output token counts also include the final answer part, since the reported reductions may otherwise overstate the end-to-end savings.
  5. [Figure 3 caption] The caption contains an apparent encoding artifact, a run of "/uni000000..." tokens, which should be removed before publication.
  6. [§5.3 and Table 4] There are several small language issues, for example "We are surprising to find" in §5.3 and "natureal drawback" near Table 4; please proofread the manuscript.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the measured benchmark accuracies and token counts are independent of the on-policy validation criterion, so no prediction reduces to its input by construction.

full rationale

The paper's central pipeline curates long-CoT data via binary cutting plus on-policy validation (Eq. 1), then reports post-SFT/DPO accuracy and token counts on held-out benchmarks. No fitted parameter is renamed as a prediction, and no measured quantity is defined in terms of the validation function itself. The on-policy validation is self-referential in the sense that the untrained target model selects prefixes it can already interpret, but the final evaluation is an independent generalization measurement, not an identity with the curation filter. The binary-cutting algorithm's stated guarantee of finding the minimal valid prefix is algorithmically questionable under the paper's own backtracking pseudocode, but that is a correctness concern, not circularity. The only potentially load-bearing self-citation is absent: prior work by the authors (e.g., Wang et al. 2023b) appears only in related-work context and is not used to justify the method's premises. The comparison against FCS is a fair external baseline, and the token-reduction results are empirical outputs rather than consequences of how the method was defined. Therefore the paper's derivation chain is self-contained with respect to the circularity patterns considered.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The method rests on assumptions about prefix-validity monotonicity, the reliability of the student-as-validator, and the quality of paragraph-level segmentation. These are domain assumptions, not invented entities or fitted physical parameters.

free parameters (2)
  • DPO SFT loss weight = 0.3 for Llama, 0.1 for Qwen
    Selected in Appendix B across values 0.1-0.3 and data sizes 5K-20K to balance accuracy and token reduction; main Table 1 results match different settings per model.
  • DPO temperature beta = 0.1
    Fixed hyperparameter in Eq. 3; not swept, but the central empirical comparison depends on it.
assumptions (4)
  • domain assumption Validity of a prefix is sufficiently monotone that binary search over prefix lengths identifies a useful minimal valid prefix.
    Section 3.2.2 uses binary cutting and backtracking over prefix indices; if adding steps sometimes makes the target model's answer worse, the search may return a non-minimal or misleading prefix.
  • domain assumption The target SLM's direct-answer behavior under the on-policy prompt is a reliable proxy for how the model will learn from that prefix during SFT/DPO.
    Section 3.2.3, Eq. (1): validation uses the pre-training model; fine-tuning changes the model, so the assumption is not verified.
  • domain assumption Paragraph-level segmentation of the thinking trace into atomic reasoning steps preserves the logical units needed for pruning.
    Section 4.1 says a Qwen2.5-14B model segments the thinking part; no segmentation prompt or quality check is provided.
  • domain assumption The final-answer exact-match extraction via regex is a correct measure of reasoning success.
    Section 4.1 uses regex and format rules; formatting differences could affect measured accuracy.

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Cite this review

Pith. "Pith review of Efficient Long CoT Reasoning in Small Language Models." pith.science (2026). https://pith.science/paper/5PURD63E

@misc{pith2026250518440,
  author       = {Pith},
  title        = {Pith review of: Efficient Long CoT Reasoning in Small Language Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5PURD63E}},
  note         = {Machine review of arXiv:2505.18440}
}
read the original abstract

Recent large reasoning models such as DeepSeek-R1 exhibit strong complex problems solving abilities by generating long chain-of-thought (CoT) reasoning steps. It is challenging to directly train small language models (SLMs) to emerge long CoT. Thus, distillation becomes a practical method to enable SLMs for such reasoning ability. However, the long CoT often contains a lot of redundant contents (e.g., overthinking steps) which may make SLMs hard to learn considering their relatively poor capacity and generalization. To address this issue, we propose a simple-yet-effective method to prune unnecessary steps in long CoT, and then employ an on-policy method for the SLM itself to curate valid and useful long CoT training data. In this way, SLMs can effectively learn efficient long CoT reasoning and preserve competitive performance at the same time. Experimental results across a series of mathematical reasoning benchmarks demonstrate the effectiveness of the proposed method in distilling long CoT reasoning ability into SLMs which maintains the competitive performance but significantly reduces generating redundant reasoning steps.

Figures

Figures reproduced from arXiv: 2505.18440 by the authors.

Figure 1
Figure 1. Illustration of redundant reasoning to a simple [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Overview of the proposed streamlining long CoT method which includes 3 key stages for data curation. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Distribution of the remaining tokens ratio [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: A case study of streamlining process of long CoT using our method. Underlined parts are the segments [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: On-policy answering prompt format. LLM-as-a-Judge Prompt [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: LLM-as-a-judge prompt format. 12 [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: It can be observed that with proper CoT prefix, the SLM can infer [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: It can be observed that the model has completed the inference before the original step "Let me check that [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]

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    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.