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REVIEW 3 major objections 5 minor 34 cited by

LLMs Can Easily Learn to Reason from Demonstrations Structure, not content, is what matters!

T0 review · 3 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read A large language model can learn long reasoning from a few thousand demonstrations, and what transfers is the structure of the reasoning trace, not the correctness of its individual steps.

desk verdict A practical distillation recipe with a fresh perturbation study, but the 'structure not content' claim is overstated by the paper's own 100% digit-corruption result. read the letter →

arxiv 2502.07374 v2 pith:KHQV23NU submitted 2025-02-11 cs.AI

Dacheng Li , Shiyi Cao , Tyler Griggs , Shu Liu , Xiangxi Mo , Eric Tang , Sumanth Hegde , Kourosh Hakhamaneshi
show 4 more authors
Shishir G. Patil Matei Zaharia Joseph E. Gonzalez Ion Stoica
This is my paper · ORCID
classification cs.AI
keywords longchain-of-thoughtreasoningdistillationsupervisedfine-tuningLoRAstructurevscontentmathcodedata-efficienttraining
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 argues that the ability to produce long, self-reflective chains of thought—the kind behind the strongest reasoning models—can be distilled into an ordinary instruction-tuned LLM with very little data and very few updated parameters. It further claims that what transfers is not the content of individual reasoning steps but their global logical structure: training on traces with wrong answers or corrupted numbers barely hurts, while shuffling, deleting, or inserting steps sharply degrades downstream accuracy. If right, this means reasoning skill is largely a structural pattern that can be installed cheaply, and that data curation for reasoning models should focus on preserving coherent multi-step trajectories rather than on step-level correctness. The paper supports this with a 17k-sample fine-tune of Qwen2.5-32B-Instruct reaching 56.7% on AIME 2024 and 57.0% on LiveCodeBench, competitive with the proprietary o1-preview model.

What carries the argument

The central object is the Long CoT trace: a response with an explicit thought block containing reflection, backtracking, and self-validation steps followed by a concise solution block. The controlled study splits each trace into reasoning steps using an LLM segmenter, then applies three structural perturbations (shuffle, delete, insert) and three content perturbations (wrong answers, digit corruption, keyword removal). The argument's engine is the contrast between these perturbation families: content perturbations leave accuracy almost intact while structural perturbations degrade it monotonically with the fraction of damaged steps. This contrast is what carries the claim that structure, not content, is what the model learns.

What would settle it

Run the same 17k-trace fine-tune with traces whose steps are fully shuffled, but give the model an auxiliary training objective that lets it reconstruct the original ordering; if accuracy recovers to the correct-order level, the shuffle loss is an artifact of input format rather than evidence about learned structure.

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Extended reading notes

Core claim

The paper's central claim is that a standard instruction-tuned LLM can acquire long-form reasoning by supervised fine-tuning on a modest set of long chain-of-thought traces, and that what it acquires is a global reasoning structure rather than the local content of individual steps. On the efficiency side, 17k traces from a strong reasoning teacher push Qwen2.5-32B-Instruct to 56.7% on AIME 2024 (from 16.7%) and 57.0% on LiveCodeBench, and LoRA with a rank of 64 matches full SFT. On the structure side, training on traces whose final answers are wrong loses only 3.2% average accuracy, corrupting up to 70% of digits costs 4.3%, and removing all reasoning keywords costs 3.3%, while shuffling 67% of steps costs 13.3% on AIME 2024 and deleting all steps drops accuracy to near the untrained base model. The author's interpretation is that the logical consistency of the multi-step trajectory—reflection, backtracking, self-validation—is the carrier of the learned capability.

Load-bearing premise

The experiments assume that each perturbation changes only the intended axis—that splitting traces into steps is faithful, that inserted steps come from comparable distributions, and that single-run accuracy differences of a few points on 30-problem benchmarks are real signal rather than noise.

Editorial extensions

If this is right

  • A reasoning model can be built from a standard instruction-tuned LLM with roughly 17k demonstrations, without reinforcement learning or large proprietary pipelines.
  • Parameter-efficient LoRA, updating fewer than 5% of parameters, suffices to match full fine-tuning, implying the acquired capability is largely structural rather than knowledge-intensive.
  • Data collection for reasoning models should prioritize global coherence of traces over step-level correctness: wrong answers and noisy digits are tolerable, while step order and completeness are not.
  • Distilled models retain most non-reasoning capabilities such as MMLU, ARC-C, and IEval, avoiding the drastic forgetting seen in specialized reasoning models.
  • Long CoT fine-tuning approximates the benefit of Best-of-16 sampling at inference time, offering a cheap substitute for test-time scaling.

Reading between the lines

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

  • If structure is what transfers, synthetic data generators could deliberately produce traces with wrong turns and corrections, even fabricated errors, as long as the correction structure stays coherent, making data curation far cheaper.
  • The same perturbation logic could serve as a diagnostic: measuring how much a model's performance drops under step-shuffling estimates how 'structural' its reasoning skill is.
  • Content-insensitivity hints at a potential failure mode: models may imitate the choreography of reflection without acquiring deeper computational content, which would surface on out-of-distribution problems requiring genuine step-level novelty.
  • A testable extension is to vary the granularity of step boundaries to find the minimal structural unit that must be preserved for successful transfer.
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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 / 5 minor

Summary. The paper reports that supervised fine-tuning (SFT) of Qwen2.5-32B-Instruct on 17k Long CoT traces distilled from DeepSeek R1 produces substantial gains on math and coding benchmarks, and that LoRA fine-tuning achieves comparable results. The central scientific claim is that the global structure of Long CoT traces—the ordering and logical coherence of reasoning steps—is what matters for learning, while the local content of individual steps has minimal impact. This claim is supported by perturbation experiments on QwQ-32B-Preview traces: replacing final answers with wrong ones, corrupting 20-70% of digits, and removing reasoning keywords cause small accuracy drops, whereas shuffling, deleting, or inserting whole reasoning steps causes larger drops. Additional ablations cover data scale, student model architectures, non-reasoning benchmarks, and comparison to Best-of-N sampling.

Significance. If the structure-versus-content claim is valid, it has practical implications: data collection for reasoning distillation could focus on logical coherence rather than correctness of every intermediate step, and parameter-efficient fine-tuning could be more widely used. The paper contributes an open, reproducible study with released code and a clear experimental design. However, the central claim is currently overstated and internally contradicted by the 100% digit-corruption condition, and the absence of uncertainty quantification makes the quantitative comparisons hard to evaluate. With a careful re-scoping of the claim and additional statistical support, this would be a useful empirical contribution to the understanding of reasoning distillation.

major comments (3)
  1. [4.1, Table 2] The 100% corrupted-digits condition is a content-only perturbation that reduces average accuracy from 66.3 (Correct) to 2.7, a 63.6-point drop that is the largest in the entire table. Yet the abstract and Section 4.1 conclude that 'the content of individual reasoning steps has minimal impact.' This is an internal inconsistency in the manuscript's central claim. The claim should be re-scoped to apply to locally coherent content (e.g., 20-70% digit corruption, wrong final answers, keyword removal) and the exceptional 100% case should be explicitly reconciled with the stated conclusion.
  2. [4, Table 2] All perturbation results come from single training runs with no confidence intervals, repeated seeds, or significance tests. Because AIME 2024 contains only 30 problems, the key differences around 3-10 percentage points (e.g., Correct 40.0 vs Wrong Answers 30.0, or Correct 40.0 vs 70% corrupted digits 30.0) are within the sampling error of roughly ±9 percentage points at 95% confidence. The 'little impact' and 'significantly degrade' conclusions need uncertainty estimates, multiple seeds, or a larger evaluation set to be convincing.
  3. [4.2] The structural perturbation pipeline relies on Llama-3.3-70B-Instruct to segment reasoning traces into distinct steps, but the paper provides no validation of segmentation quality. If step boundaries are inaccurate, the delete/insert/shuffle operations may also alter local content or introduce distributional shifts (e.g., cross-domain topic changes in the insertion condition) rather than purely global ordering. The shuffle condition is the cleanest test, but its 100% drop (to 56.1) is still much smaller than the 100% digit-corruption drop (to 2.7), so the paper needs to either validate the segmentation or address the confound before concluding that global structure, not content, is the dominant factor.
minor comments (5)
  1. [3.1] The phrase 'difficulty higher than Leval 3' contains a typo; it should read 'Level 3'.
  2. [5.2, Figure 4] Model names are inconsistent: 'Qwen2.5-7-Base' vs 'Qwen2.5-7B-Base' and 'Llama-8b-Base' vs 'Llama-3.1-8B' appear in different places; please standardize them.
  3. [Table 1 vs Figure 1b] The o1-preview AMC 2023 score is reported as 87.5 in Table 1 but as 85.0 in Figure 1b; these values should be reconciled.
  4. [Table 4 caption] 'Table 4 summaries the statistics' should read 'summarizes the statistics'.
  5. [1, paragraph 2] 'the modelcan achieve' contains a missing space between 'model' and 'can'.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the central claims are supported by external benchmarks and controlled perturbations, and the authors' self-reference to their Sky-T1 release is not load-bearing.

full rationale

This paper is an empirical study rather than a derivation, so the circularity burden is low. The main results (data- and parameter-efficient Long CoT distillation) are evaluated on external benchmarks (Math-500, AIME 2024, AMC 2023, OlympiadBench, LiveCodeBench) that are distinct from the training traces, and the reported gains are compared against the base Qwen2.5-32B-Instruct model and against o1-preview; no fitted parameter is renamed as a prediction. The structure-versus-content conclusion is operationalized through two separate perturbation families (content: wrong answers, digit corruption, keyword removal; structure: deletion, insertion, shuffling of segmented steps), and the comparison is made against a 'Correct' baseline and the original model. The paper's statement that it is 'the academic paper of our previous released Sky-T1-32B-Preview model' is a self-reference but is not used as evidence; the fine-tuning and evaluation are reported in this paper. The system prompt is adopted from Still-2 (Min et al., 2024), an external citation, and the reasoning-keyword bank is described as created by manual inspection, not imported as an authoritative theorem. The acknowledged confounds are correctness concerns rather than circularity: Section 4.2 notes that deleting steps also shortens responses ('as more steps are deleted, the response lengths also decrease significantly, which could contribute to reduced accuracy'), and Section 4.1 concedes that 100% digit corruption is 'a severe corruption' whose average accuracy plunges to 2.7%, which tensions with the unqualified 'content has minimal impact' claim. These are internal-validity or overgeneralization issues, not definitional equivalences or self-citation chains, so they do not raise the circularity score.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The paper introduces no new physical or mathematical entities. The load-bearing assumptions are about the validity of the perturbation methodology and the stability of small benchmark differences; the central claim rests on those assumptions rather than on fitted parameters or new constructs.

free parameters (2)
  • LoRA rank = 64 or 256
    LoRA rank is chosen by hand in Section 3.1; the claim that parameter-efficient fine-tuning works is demonstrated for these ranks, not for all ranks.
  • Data difficulty thresholds = math > Level 3, Olympiad > Level 8, all AIME/AMC
    Section 3.1 uses GPT-4o-mini difficulty classification to select training traces; results could shift with different thresholds.
assumptions (6)
  • domain assumption Next-token-prediction supervised fine-tuning on demonstration traces can transfer reasoning behavior.
    Section 3.1 states the training objective is next token prediction; this is standard in LLM post-training but not proven by the paper.
  • domain assumption Exact-match and code-execution verification correctly identifies 'correct' reasoning traces.
    Section 3.1 uses exact matching for math and code execution for coding; this may miss partially correct reasoning or subtle label errors.
  • domain assumption Llama-3.3-70B can segment long CoTs into meaningful reasoning steps.
    Section 4.2 relies on this segmentation for all structural perturbations; the paper provides examples but no quantitative validation of segmentation quality.
  • ad hoc to paper Digit, keyword, and final-answer perturbations change local content without changing global reasoning structure.
    Section 4.1 assumes content perturbations leave structure intact, but the paper does not verify that step boundaries, difficulty, or cross-step references remain unchanged.
  • ad hoc to paper Shuffle, delete, and insert operations change only global structure while preserving local content.
    Section 4.2 assumes these operations isolate structure, but inserted steps come from other problems and can also shift topic distribution and introduce cross-domain contamination.
  • domain assumption Single-run benchmark scores without confidence intervals are stable enough to support 3 to 20 point conclusions.
    Table 2 reports one run per condition; AIME 2024 has 30 problems, so a 3.2% average gap is about one question and may be within noise.

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Cite this review

Pith. "Pith review of LLMs Can Easily Learn to Reason from Demonstrations Structure, not content, is what matters!." pith.science (2026). https://pith.science/paper/KHQV23NU

@misc{pith2026250207374,
  author       = {Pith},
  title        = {Pith review of: LLMs Can Easily Learn to Reason from Demonstrations Structure, not content, is what matters!},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KHQV23NU}},
  note         = {Machine review of arXiv:2502.07374}
}
read the original abstract

Large reasoning models (LRMs) tackle complex reasoning problems by following long chain-of-thoughts (Long CoT) that incorporate reflection, backtracking, and self-validation. However, the training techniques and data requirements to elicit Long CoT remain poorly understood. In this work, we find that a Large Language model (LLM) can effectively learn Long CoT reasoning through data-efficient supervised fine-tuning (SFT) and parameter-efficient low-rank adaptation (LoRA). With just 17k long CoT training samples, the Qwen2.5-32B-Instruct model achieves significant improvements on a wide range of math and coding benchmarks, including 56.7% (+40.0%) on AIME 2024 and 57.0% (+8.1%) on LiveCodeBench, competitive to the proprietary o1-preview model's score of 44.6% and 59.1%. More importantly, we find that the structure of Long CoT is critical to the learning process, whereas the content of individual reasoning steps has minimal impact. Perturbations affecting content, such as training on incorrect samples or removing reasoning keywords, have little impact on performance. In contrast, structural modifications that disrupt logical consistency in the Long CoT, such as shuffling or deleting reasoning steps, significantly degrade accuracy. For example, a model trained on Long CoT samples with incorrect answers still achieves only 3.2% lower accuracy compared to training with fully correct samples. These insights deepen our understanding of how to elicit reasoning capabilities in LLMs and highlight key considerations for efficiently training the next generation of reasoning models. This is the academic paper of our previous released Sky-T1-32B-Preview model. Codes are available at https://github.com/NovaSky-AI/SkyThought.

Figures

Figures reproduced from arXiv: 2502.07374 by the authors.

Figure 1
Figure 1. Learning to reason is data- and parameter-efficient. When fine-tuned on a small amount (17k) of Long CoT samples distilled and reject-sampled from DeepSeek-R1 with either LoRA or full-parameter tuning, the model easily learns to perform reflection and backtracking by using keywords such as “However” and “Alternatively” (Top). Consequently, the fine-tuned models improve significantly across five popular math and codi… view at source ↗
Figure 2
Figure 2. Model accuracy with different data sizes, and comparison to DeepSeek R1. The teacher model is DeepSeek R1, and the student model is Qwen-32B-Instruct trained with full parameter fine-tuning. While the stu￾dent model continues to benefits from more SFT data from DeepSeek R1, a small amount of data, e.g., 16k is sufficient to significantly boost the average performance by 15.2%. data size, ranging from 4k to 64k sampl… view at source ↗
Figure 3
Figure 3. Reasoning step modifications. To evaluate perturbations to global structure across reasoning steps, we perform three modifications: deletion, insertion, and shuffling. These modifications break logical consistency across steps and degrade model accuracy far more than changes to local content within reasoning steps. we report the resulting performance in Tab. 2 and response lengths and reasoning keyword counts in App… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Generalization to other models. Accuracy for models of different sizes and architectures without SFT (green) and with SFT (blue). Most models show significant improvements when fine-tuned with 17k samples from R1- Preview, showing that the Long CoT fine-tuning is benef…
Figure 5
Figure 5. Figure 5: SFT with Long CoT vs Best-of-N. Accuracy of Qwen2.5-32B-Instruct before SFT (Zero-Shot), after SFT on 17k R1 samples (Fine-tuned), and Best-of-N samples on OlympiadBench. We find that fine-tuning on Long CoT achieves performance similar to Best of 2 to 16 samples. Spec…

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Reference graph

Works this paper leans on

13 extracted references · 13 canonical work pages · cited by 34 Pith papers

  1. [1]

    For the fraction to be nonnegative, we need log n − 3 > 0

    Condition for the Denominator The denominator of the fraction is log n − 3. For the fraction to be nonnegative, we need log n − 3 > 0. This implies that log n >3, which translates to n >103 = 1000. Therefore, n must be greater than 1000

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    Using logarithmic properties, we can rewrite log(n2) as 2 logn

    Simplifying the Numerator The numerator of the fraction is log(n2) − (log n)2. Using logarithmic properties, we can rewrite log(n2) as 2 logn. Thus, the numerator becomes 2 logn − (log n)2

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    This leads to the inequality: 2 logn − (log n)2 ≥ 0

    Analyzing the Fraction Substituting the simplified numerator into the fraction, we get: 2 logn − (log n)2 log n − 3 For this fraction to be nonnegative, given that the denominator is positive (from step 1), the numerator 2 logn − (log n)2 must also be nonnegative. This leads to the inequality: 2 logn − (log n)2 ≥ 0

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    Factoring, log n(log n − 2) ≤ 0

    Solving the Inequality The inequality 2 logn − (log n)2 ≥ 0 can be rewritten as (log n)2 − 2 logn ≤ 0. Factoring, log n(log n − 2) ≤ 0. Solving this inequality, we find that 0 ≤ log n ≤ 2. Converting back to n, this implies: 1 ≤ n ≤ 100

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    However, these two conditions are contradictory

    Combining Conditions From step 1, we have n > 1000, and from step 4, we have 1 ≤ n ≤ 100. However, these two conditions are contradictory. The correct interpretation should be that n must satisfy both the condition of being greater than 1000 (from the denominator analysis) and the condition derived from the inequality, which was misinterpreted in the comb...

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    Counting these integers, we find there are 100 such integers

    Conclusion The integers n that satisfy the given conditions are those for which 1 ≤ n ≤ 100. Counting these integers, we find there are 100 such integers. 13 Submission and Formatting Instructions for ICML 2025 Long CoT answer (1/4) <|begin of thought|> So I’ve got this problem here: s log(n2) − (log n)2 log n − 3 And I need to find out for how many integ...

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    log n = 0⇒ n = 100 = 1

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Show all 13 references
  1. [9]

    log n − 3 = 0⇒ log n = 3⇒ n = 103 = 1000 These points divide the number line into intervals where the expression doesn’t change sign. So, the intervals to consider are: - 1 < n <100 - 100 < n <1000 - n >1000 14 Submission and Formatting Instructions for ICML 2025 Long CoT answ...

    2025

  2. [10]

    Then, the expression simplifies to: x(2 − x) x − 3 16 Submission and Formatting Instructions for ICML 2025 Long CoT answer (4/4)

    Simplifying the expression Using the logarithm power rule, we have: log(n2) = 2 logn Thus, the expression becomes: 2 logn − (log n)2 log n − 3 Let x = logn. Then, the expression simplifies to: x(2 − x) x − 3 16 Submission and Formatting Instructions for ICML 2025 Long CoT answer (4/4)

    2025

  3. [11]

    Finding critical points The critical points are where the numerator or denominator equals zero: - x = 0⇒ n = 1- 2 − x = 0⇒ x = 2⇒ n = 100- x − 3 = 0⇒ x = 3⇒ n = 1000

  4. [12]

    - For 1 < n <100: The expression is negative, not acceptable

    Analyzing intervals The intervals to consider are: - 1 < n <100 - n = 100- 100 < n <1000 - n = 1000- n >1000 Testing the sign of the expression in each interval: - For n = 1: The expression equals 0, which is acceptable. - For 1 < n <100: The expression is negative, not accept...

  5. [13]

    Alternatively

    Counting acceptable integers The acceptable ranges are: - n = 1- 100 ≤ n <1000 The number of integers in 100 ≤ n <1000 is 900 (from 100 to 999 inclusive). Adding n = 1gives a total of: 1 + 900 = 901 Thus, the number of integer values of n that satisfy the condition is: 901 <|e...

    2024

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Reviewed August 8, 2026 · model on record in the stance chip above.