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REVIEW 4 major objections 5 minor 15 references

The Challenge of Teaching Reasoning to LLMs Without RL or Distillation

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Light fine-tuning on 20 long CoT examples turns a 32B base model into a competition-level reasoner.

desk verdict A genuinely interesting data-efficiency data point that is currently missing the one experiment that would make it trustworthy: a contamination check against the AIME/HMMT evaluation set. read the letter →

arxiv 2507.09850 v3 pith:5DX7ITEO submitted 2025-07-14 cs.AI

Wei Du , Branislav Kisacanin , George Armstrong , Shubham Toshniwal , Ivan Moshkov , Alexan Ayrapetyan , Sadegh Mahdavi , Dan Zhao
show 17 more authors
Shizhe Diao Dragan Masulovic Marius Stanean Advaith Avadhanam Max Wang Ashmit Dutta Shitij Govil Sri Yanamandara Mihir Tandon Sriram Ananthakrishnan Vedant Rathi David Zhang Joonseok Kang Leon Luo Titu Andreescu Boris Ginsburg Igor Gitman
This is my paper
classification cs.AI
keywords chain-of-thoughtreasoningmodesupervisedfine-tuningminimalsupervisionmathematicaldistillationQwen2.5competitionmathematics
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 asks whether long chain-of-thought reasoning can be switched on in a base language model by minimal supervision, without reinforcement learning or large-scale distillation. Its central result is that fine-tuning Qwen2.5-32B on only 20 long CoT solutions produced by QwQ-32B-Preview yields a 17.10% pass@1 and 27.73% maj@64 on the Comp-Math-24-25 benchmark, beating the much larger Qwen2.5-Math-72B-Instruct (11.72% and 16.14%). This gain is interpreted as a qualitative shift into a 'reasoning mode' rather than memorization, because 20 examples cannot convey much new factual content. The paper further shows that neither large-scale synthetic data from a non-reasoning model nor carefully drafted human solutions, even after multi-pass editing, triggers the same shift; ablations indicate that correctness, keywords, problem difficulty, and problem diversity matter less than the structural consistency of the reasoning traces themselves. A sympathetic reader would take the paper's contribution as evidence that a handful of high-quality reasoning demonstrations can unlock strong generalization, and as a challenge to identify exactly what structure does the unlocking.

What carries the argument

The central object is the 'reasoning mode' induction procedure: supervised fine-tuning of a base model on a very small set of long CoT traces, defined operationally as significant outperformance of a much larger non-reasoning model on hard math. The mechanism that carries the argument is a comparison across data sources (reasoning-model traces, non-reasoning synthetic traces, and four progressively refined human-written versions) plus ablations over solution length, correctness, difficulty, diversity, and reasoning keywords; the consistent thread is that only the reasoning-model traces, with their homogeneous exploratory structure, produce the shift.

What would settle it

Check the 50 training problems for near-duplicate statements or answer patterns in the 256-problem Comp-Math-24-25 benchmark; if any training problem reappears, or if the fine-tuned model's advantage vanishes on a freshly written, non-overlapping competition set, the claim that 20 examples activate a qualitative reasoning shift would be refuted.

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Extended reading notes

Core claim

In the paper's own terms, the discovery is that a base, non-reasoning model can be induced into a reasoning mode by supervised fine-tuning on as few as 20 long CoT traces from a reasoning model. After light fine-tuning (learning rate 1e-5, 50 steps, batch 1024), Qwen2.5-32B outperforms Qwen2.5-Math-72B-Instruct on 256 competition problems from AIME and HMMT, and the effect persists across ablations that vary solution correctness, the presence of reasoning keywords, problem difficulty, and problem diversity. The paper interprets the result as evidence of a qualitative shift in problem-solving strategy, triggered by the structure of the demonstrations rather than by memorization or scale; it also reports that the same shift does not occur with 7B/14B models, with data from non-reasoning models, or with human-written solutions, which is used to argue that the structural consistency of model-generated reasoning traces is the critical ingredient.

Load-bearing premise

The load-bearing premise is that the 50 competition problems used for training do not overlap with the 256 AIME/HMMT evaluation problems, so that the pass@1 improvement reflects a general shift in problem-solving strategy rather than retrieval of memorized answers.

Editorial extensions

If this is right

  • If 20 examples suffice, the cost of activating reasoning in a capable base model drops by orders of magnitude relative to reinforcement learning or large-scale distillation.
  • The negative results for non-reasoning and human data imply that data quality, specifically the structural consistency of exploratory traces, matters more than dataset size or curation effort.
  • The ablations imply that data filters requiring fully correct final answers, reasoning keywords, or balanced problem difficulty are not necessary for reasoning activation.
  • The failure of 7B and 14B models suggests a base-model capability threshold below which minimal CoT supervision cannot induce reasoning mode.
  • Longer traces gave slightly better results, so solution length can serve as a cheap proxy for reasoning quality in data curation.

Reading between the lines

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

  • An open question not settled by the paper is train/eval overlap: the 50 training problems could share statements or solution patterns with the 256 AIME/HMMT evaluation problems, and the paper does not report a contamination check; a near-duplicate test would settle whether the gain is transferable reasoning or memorization.
  • If the structural-consistency hypothesis is right, a natural testable extension is to generate synthetic long CoT data by paraphrasing or templating a single reasoning trace and checking whether reasoning activation survives; the paper's ablations already point in that direction.
  • The paper's operational definition of reasoning mode is benchmark-relative, so a fair reader should ask whether the effect generalizes to non-competition reasoning, code, or science, which the paper leaves as future work.
  • The model-size threshold suggests that reasoning activation via minimal SFT may depend on pretraining scale; mapping that threshold across model families would make the finding more robust.
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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

4 major / 5 minor

Summary. This paper investigates whether a base LLM (Qwen2.5-32B) can be induced into a 'reasoning mode' using only prompting or a small amount of supervised fine-tuning, without reinforcement learning or large-scale distillation. The authors use QwQ-32B-Preview to generate long CoT solutions for 50 AoPS-sourced problems, fine-tune Qwen2.5-32B on subsets of 10-50 of these examples, and evaluate on the Comp-Math-24-25 benchmark (256 AIME/HMMT 2024-2025 problems). They report that 20 examples suffice: the fine-tuned model achieves 17.10% pass@1 and 27.73% maj@64, outperforming Qwen2.5-Math-72B-Instruct by 5.38% and 11.59% respectively. The paper further explores synthetic CoT produced by non-reasoning models under various prompting and editing strategies, and human-written solutions across four refinement stages; neither alternative activates reasoning behavior. Ablation studies examine solution correctness, presence of reasoning keywords, problem difficulty, problem diversity, and solution length. The human-authored dataset is released.

Significance. If the central claim is correct, this is a striking data-efficiency result: it would imply that 20 carefully selected long-CoT traces can unlock generalization behavior in a 32B base model, a finding with practical implications for reasoning-model distillation. The paper has several genuine strengths: it compares three data sources (reasoning-model traces, non-reasoning synthetic traces, and human-written solutions), it runs a series of systematic ablations (Sections 5.1-5.5), and it releases the human-authored dataset across refinement stages. The paper is also transparent about its operational definition of 'reasoning behavior,' even though that definition is debatable. However, the headline result currently rests on a single random 20-example subset with no variance reporting, hyperparameters selected by grid search on the evaluation benchmark (Appendix D), and no decontamination check between the AoPS-sourced training pool and the AIME/HMMT evaluation set. These issues are load-bearing: any one of them, if material, could account for the reported gains without invoking a qualitative shift in reasoning.

major comments (4)
  1. [Sections 2.3, 2.4, 1] The paper provides no decontamination check between the 50 AoPS-sourced training problems (Section 2.3) and the 256 Comp-Math-24-25 evaluation problems from AIME/HMMT 2024-2025 (Section 2.2). AoPS forums are the primary public repository for AIME and HMMT problems, including the specific contests used for evaluation, so exact or near-duplicate overlaps are highly plausible. If even a few of the 20 training problems appear in the evaluation set, the reported pass@1 gain (11.72% to 17.10%) could be driven by memorized answers rather than generalizable reasoning; with only 64 generations per problem, a few memorized answers could account for the entire observed gain. The paper should report an overlap analysis (exact and near-duplicate matching, e.g., via normalized problem text or answer matching) and, ideally, re-run the headline result on the subset of evaluation problems that are verified as disjoint from the training pool.
  2. [Appendix D] The training hyperparameters (learning rate 1e-5, 50 steps) were selected by grid search on Comp-Math-24-25, the same benchmark used to report all evaluation results. The headline '20 examples suffice' result is therefore not a clean out-of-sample evaluation: it is the outcome of model selection on the test set. Table 3 shows that pass@1 varies from 6.52% to 19.29% as the learning rate changes from 1e-4 to 1e-5, so the chosen hyperparameter point is highly influential. The authors should either hold out a validation split from the benchmark, report results across a range of hyperparameters, or justify that the conclusion is stable beyond the single best grid point.
  3. [Section 2.4, Figure 1] The 20-example result is based on a single random subset of 20 examples sampled from the 50-problem pool, and no variance or confidence intervals are reported. The pass@1 values are averages over 64 generations; for a binomial proportion near 0.17 with n=64, the standard error is approximately 4.7%, so the reported 5.38% absolute gain over the 11.72% baseline is within roughly one standard error. The paper should repeat the experiment with multiple random 20-example subsets (and ideally multiple fine-tuning seeds) and report the distribution of scores, so that the reader can assess whether 'as few as 20 examples' is a robust phenomenon or a point estimate.
  4. [Section 1] The paper interprets the accuracy gain as evidence of a 'qualitative shift in problem-solving strategy' and explicitly rules out memorization or scale ('we interpret any observed performance gains not as a result of memorization or scale...'). However, the experiments only measure final-answer accuracy; they do not analyze the generated traces before and after fine-tuning. Accuracy alone cannot distinguish a strategy shift from other mechanisms, such as a change in output-length distribution, improved answer formatting, or the learning of a few problem-specific templates. To support the qualitative-shift claim, the authors should provide quantitative trace analyses (e.g., generated trace length, frequency of self-correction/backtracking phrases, number of alternative approaches explored, diversity of solution paths) for the base model and the fine-tuned model.
minor comments (5)
  1. [Throughout] No error bars or statistical significance tests are reported anywhere; at minimum, bootstrap confidence intervals for the headline pass@1 and maj@64 numbers in Table 1 (rows 14 vs 15) and Table 2 would help the reader gauge the reliability of the differences.
  2. [Table 2] Rows 1 and 8: the paper states that incorrect and correct solutions perform comparably, but the incorrect-solution dataset yields 21.21% pass@1 versus 19.29% for correct solutions; the paper should comment on this difference and whether it is within sampling noise.
  3. [Section 5.3] The difficulty levels are based on QwQ-32B-Preview's pass rate over 512 generations, but the paper does not report how the 50 problems are distributed across the three pass-rate bins; please provide this distribution.
  4. [Appendix B.2] The instruction says 'at least 35 self verification moments,' which appears to be a typo for '3-5' as in Appendix B.1; please correct.
  5. [Section 2.2] The paper should specify how final answers are extracted from the long CoT generations for evaluation (e.g., parsing of \boxed{}), since the Comp-Math-24-25 benchmark requires single numerical answers and extraction errors could affect pass@1.

Circularity Check

1 steps flagged · score 3.0 of 10

The empirical few-shot SFT result is self-contained and could have failed; the paper's only definitional circularity is labeling post-SFT outperformance as 'reasoning behavior,' while the AoPS/AIME overlap and same-benchmark hyperparameter tuning are validity risks, not derivation-circularity.

  1. self definitional [Section 1 (operational definition); Section 7 (conclusion)]
    "A base model is said to exhibit reasoning behavior, or equivalently to operate in a reasoning mode, if after minimal supervision under long CoT reasoning patterns, it significantly outperforms a much larger non-reasoning model on challenging math tasks. ... We first propose a simple and empirical definition of a reasoning model, based on the performance improvement of a base model after fine-tuning on a small number of high-quality reasoning traces, and demonstrate that as few as 20 reasoning examples can activate reasoning behavior in a base model."

    The paper defines the target construct, 'reasoning behavior,' as exactly the criterion it later reports: after minimal SFT on long CoT traces, the fine-tuned model significantly outperforms the much larger non-reasoning baseline. The concluding claim that 20 reasoning examples activate reasoning behavior is therefore the same proposition as the measured performance gain restated in the vocabulary of the definition; no independent measurement of hypothesis generation, self-verification, or reflective problem solving is supplied. The qualitative interpretation reduces by construction to the operational criterion, even though the underlying accuracy numbers themselves are empirical and could have turned out differently.

full rationale

The raw result is an honest empirical measurement: fine-tuning Qwen2.5-32B on 20 QwQ-32B-Preview traces raised pass@1 from 11.72% to 17.10% and maj@64 from 16.14% to 27.73% on Comp-Math-24-25 (Section 2.4), and these numbers are not algebraically forced by any fitted parameter. The one genuinely circular move is terminological: the paper defines 'reasoning behavior' as the very performance gain it then reports, so the conclusion that 20 examples activate reasoning is the operational criterion restated, not an independently evidenced shift to hypothesis generation or self-reflection. I do not count the AoPS seed set versus AIME/HMMT overlap risk or the Appendix D grid search on the same benchmark as circularity: those are missing-support and selection-bias concerns that weaken generalization claims but do not make the measurement equal to its inputs. The benchmark is authored by overlapping authors but is used as a dataset, not as an argument; no load-bearing self-citation chain or imported uniqueness theorem is present. Proportionate score: 3.

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

The paper introduces no new theoretical entities. Its free parameters are experimental design choices, and its assumptions are standard evaluation or interpretation assumptions.

free parameters (4)
  • learning rate and training steps = 1e-5, 50 steps
    Selected by grid search on the evaluation benchmark (Appendix D), which risks overfitting to the test set.
  • number of training examples = 20
    The paper tested 10 to 50 and reports the 20-example result as the headline; the exact number is a post hoc choice based on the observed curves.
  • solution length filter = approximately 3K tokens
    Solutions were filtered to match human data lengths, which affects what the model learns (Section 2.4).
  • correct-answer filter = 1 correct solution per problem from 512 samples
    Data selection chooses only solutions with correct final answers, a filter that strongly shapes the training set.
assumptions (4)
  • domain assumption Comp-Math-24-25 benchmark is a valid measure of mathematical reasoning.
    The paper uses this benchmark as the sole evaluation of reasoning behavior (Section 2.2).
  • domain assumption The 50 AoPS training problems do not overlap with the 256 AIME/HMMT evaluation problems.
    Overlap would allow the model to memorize answers rather than learn reasoning (Section 2.3, 2.2). The paper does not test for overlap.
  • ad hoc to paper Performance gains after 20 examples are due to reasoning mode shift, not memorization.
    Stated in Section 1 as an interpretation without direct evidence such as a memorization test or overlap check.
  • domain assumption Long CoT traces from QwQ-32B-Preview are 'high-quality' reasoning data.
    The paper selects one correct solution per problem from 512 QwQ generations and treats them as gold reasoning traces (Section 2.4).

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Cite this review

Pith. "Pith review of The Challenge of Teaching Reasoning to LLMs Without RL or Distillation." pith.science (2026). https://pith.science/paper/5DX7ITEO

@misc{pith2026250709850,
  author       = {Pith},
  title        = {Pith review of: The Challenge of Teaching Reasoning to LLMs Without RL or Distillation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5DX7ITEO}},
  note         = {Machine review of arXiv:2507.09850}
}
read the original abstract

Reasoning-capable language models achieve state-of-the-art performance in diverse complex tasks by generating long, explicit Chain-of-Thought (CoT) traces. While recent works show that base models can acquire such reasoning traces via reinforcement learning or distillation from stronger models like DeepSeek-R1, previous works demonstrate that even short CoT prompting without fine-tuning is able to improve reasoning. We ask whether long CoT can be induced in a base model using only prompting or minimal tuning. Using just 20 long CoT examples from the reasoning model \texttt{QwQ-32B-Preview}, we lightly fine-tune the base model \texttt{Qwen2.5-32B}. The resulting model outperforms the much larger \texttt{Qwen2.5-Math-72B-Instruct}, showing that a handful of high-quality examples can unlock strong reasoning capabilities. We further explore using CoT data from non-reasoning models and human annotators, enhanced with prompt engineering, multi-pass editing, and structural guidance. However, neither matches the performance of reasoning model traces, suggesting that certain latent qualities of expert CoT are difficult to replicate. We analyze key properties of reasoning data, such as problem difficulty, diversity, and answer length, that influence reasoning distillation. While challenges remain, we are optimistic that carefully curated human-written CoT, even in small quantities, can activate reasoning behaviors in base models. We release our human-authored dataset across refinement stages and invite further investigation into what makes small-scale reasoning supervision so effective.

Figures

Figures reproduced from arXiv: 2507.09850 by the authors.

Figure 1
Figure 1. SFT accuracy of Qwen2.5-32B on Comp-Math-24-25 under varying data sizes. With only 20 examples, it outperforms the baseline Qwen2.5-Math-72B-Instruct. All datasets have average token lengths between 3,400 and 3,800. solely on detailed instructional guidance, and another that augments the same instructions with the same 20 explicit reasoning examples as Section 2.4 used to conduct SFT on Qwen2.5-32B. Using the 50 pro… view at source ↗
Figure 2
Figure 2. SFT accuracy of Qwen2.5-7B and Qwen2.5-14B on Comp-Math-24-25 under varying data sizes. fixed these hyperparameters for all experiments presented in this paper. Hyperparameters pass@1 maj@64 LR = 1e-4, Steps = 50 6.52% 12.50% LR = 1e-5, Steps = 50 19.29% 33.59% LR = 1e-6, Steps = 50 8.53% 18.36% LR = 1e-5, Steps = 100 18.60% 31.64% LR = 1e-5, Steps = 200 15.05% 32.42% [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗

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