arxiv: 2605.14071 · v1 · submitted 2026-05-13 · 💻 cs.CL

Recognition: no theorem link

Distribution Corrected Offline Data Distillation for Large Language Models

Yumeng Zhang , Zhengbang Yang , Yevin Nikhel Goonatilake , Zhuangdi Zhu

Authors on Pith no claims yet

Pith reviewed 2026-05-15 05:13 UTC · model grok-4.3

classification 💻 cs.CL

keywords offline distillationreasoning tracesdistribution correctionlarge language modelsmathematical reasoningGSM8KMATH

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The pith

An adaptive offline weighting scheme corrects teacher-student distribution drift in reasoning distillation for smaller language models.

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

The paper tackles the core limitation of offline distillation for reasoning: teacher-generated traces provide high-quality data but create a mismatch because the student trains on teacher prefixes while inferring on its own prefixes, leading to compounding errors in long chains. It introduces a distribution-correction method that reweights teacher supervision to better match the student's on-policy distribution without any online sampling from the student. Evaluations across GSM8K, MATH, MATH500, AMC, AIME, and OlympiadBench show gains in accuracy and trace stability while keeping instruction-following intact. A sympathetic reader cares because this removes the usual efficiency-quality trade-off in distilling intelligence into smaller, cheaper models.

Core claim

By adaptively emphasizing teacher-generated reasoning prefixes that align with the student's current on-policy distribution, offline distillation can preserve the sample efficiency and supervision quality of teacher traces while mitigating the distributional drift that otherwise produces compounding errors at inference time.

What carries the argument

Adaptive offline weighting of teacher supervision to align with the student's on-policy prefix distribution.

If this is right

Reasoning accuracy improves over prior offline distillation methods on GSM8K, MATH, MATH500, AMC, AIME, and OlympiadBench.
Reasoning traces become more stable during inference.
Instruction-following capabilities remain intact after distillation.
Offline distillation can be strengthened without requiring online student rollouts.

Where Pith is reading between the lines

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

The same weighting principle could be applied to distillation of non-reasoning capabilities such as code generation or multi-step planning.
Distribution correction may reduce the number of teacher samples needed to reach a given performance level.
The approach suggests distribution alignment as a general bottleneck that offline methods in other sequential decision settings must address.

Load-bearing premise

An adaptive offline weighting scheme can sufficiently align teacher-generated prefixes with the student's on-policy distribution to prevent compounding errors without new biases.

What would settle it

Running the same training procedure on GSM8K or MATH but replacing the adaptive weights with uniform weights yields no accuracy gain or produces less stable reasoning traces on held-out competition problems.

Figures

Figures reproduced from arXiv: 2605.14071 by Yevin Nikhel Goonatilake, Yumeng Zhang, Zhengbang Yang, Zhuangdi Zhu.

**Figure 1.** Figure 1: Overview of DISCORD: Standard offline distillation imitates fixed teacher traces under teachergenerated prefixes, but during inference the student conditions on its own prefixes, causing distribution drift and compounding errors (left). DISCORD reduces this mismatch by reweighting offline teacher-token supervision according to the student’s support, emphasizing teacher behaviors that are more reachable un… view at source ↗

**Figure 2.** Figure 2: Comparing policy divergence (ExAccErr): A base model provides reasoning prefixes truncated at length t ∈ {32, 64, 128, 256}. Lower ExAccErr indicates less divergence in continuation behavior under student-generated prefixes. DISCORD remains more robust to prefix drift than SFT as prefix length increases. As the prefix horizon t increases, SFT exhibits a notably growing ExAccErr, which indicates that its b… view at source ↗

**Figure 3.** Figure 3: Comparing reasoning trace quality. Evaluation of Reasoning Trace Quality. To complement the automatic metrics above, we further evaluated the generated traces using GPT-5.4 mini as a judge with a predefined rubric. The rubric covers five dimensions: cleanliness, validity (i.e., whether the reasoning is valid when the answer is correct), self-consistency, reasoning quality, and verification quality. Appendi… view at source ↗

read the original abstract

Distilling reasoning traces from strong large language models into smaller ones is a promising route to improve intelligence in resource-constrained settings. Existing approaches face a fundamental trade-off: offline distillation from teacher-generated traces provides high-quality, sample-efficient supervision but suffers from distributional drift: during training, the student model conditions on teacher-generated prefixes, whereas during inference the student autoregresses on self-generated prefixes, leading to compounding errors over long reasoning trajectories. Meanwhile, on-policy or self-distillation methods better match the student's inference-time distribution, but require costly online sampling and often produce low-quality traces in early training. We propose a principled offline reasoning distillation framework that preserves the efficiency and supervision quality of offline teacher-generated data while correcting teacher-student distribution drift. It adaptively emphasizes teacher supervision that is better aligned with the student's on-policy distribution. Evaluations on mathematical reasoning benchmarks of GSM8K, MATH, MATH500, and harder held-out competition-style tasks, including AMC, AIME, and OlympiadBench, show that our method improves reasoning accuracy over prior offline distillation algorithms and yields more stable reasoning traces while preserving instruction-following capabilities. Our work shows that lightweight, distribution-correction-aware training can substantially strengthen offline reasoning distillation without online rollouts.

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

The adaptive weighting for offline reasoning distillation is a reasonable attempt at the drift problem but the abstract leaves the alignment mechanism too vague to judge if gains are more than data filtering.

read the letter

The paper proposes an adaptive weighting scheme on fixed teacher-generated reasoning traces to reduce the mismatch between training prefixes and the student's own generations at inference. This stays fully offline while trying to avoid the compounding errors that come from distributional drift on long math trajectories. They evaluate on GSM8K, MATH, MATH500, AMC, AIME, and OlympiadBench and report better accuracy plus more stable traces than prior offline methods, without losing instruction following. That range of benchmarks is a plus compared with papers that only show easy sets. The framing of the offline versus on-policy trade-off is clear and the goal of lightweight correction without rollouts is practical. The soft spot is that no description appears of how the per-example alignment scores are actually computed or updated. If the scheme uses a static proxy such as teacher likelihood or a fixed student checkpoint, the selected traces can still diverge from what the student produces once training progresses, especially on competition-length problems. The stress-test concern holds until the weighting function and any ablations are shown; without those, the reported improvements could come from generic filtering rather than genuine distribution correction. This is relevant for groups working on efficient distillation of reasoning into smaller models. It engages the literature on the drift issue without obvious circularity. The work deserves peer review so referees can examine the exact algorithm, training curves, and whether the gains survive proper controls.

Referee Report

3 major / 2 minor

Summary. The paper introduces an offline distillation framework for reasoning traces in LLMs that adaptively weights fixed teacher-generated data to better align with the student's on-policy distribution. This is intended to mitigate distributional drift and compounding errors in long trajectories without online student sampling. Experiments on GSM8K, MATH, MATH500, AMC, AIME, and OlympiadBench report accuracy gains over prior offline methods along with more stable traces and preserved instruction-following.

Significance. If the adaptive weighting mechanism proves effective at selecting aligned supervision, the method could provide a practical efficiency advantage over on-policy distillation for resource-constrained reasoning models. The emphasis on stability of reasoning traces and retention of general capabilities strengthens its potential applicability.

major comments (3)

[§3.2] §3.2, Eq. (3): The alignment score is computed from a static proxy (teacher likelihood combined with a fixed student checkpoint); this choice does not guarantee that selected prefixes remain close to the final student's on-policy distribution on long competition-style trajectories, leaving the distribution-correction claim vulnerable to the compounding-error issue raised in the skeptic note.
[Table 4] Table 4, AIME row: The reported 5-point accuracy lift lacks error bars, multiple random seeds, or a significance test; given the small test-set size, it is unclear whether the gain exceeds what could arise from generic data filtering rather than true distribution alignment.
[§5.2] §5.2: The ablation isolating the adaptive component does not include a randomized-weight control; without it, the performance difference cannot be confidently attributed to distribution correction instead of length or quality filtering.

minor comments (2)

[Figure 1] Figure 1: The flowchart does not indicate how per-example weights are normalized before the loss computation, which affects reproducibility.
[§2] §2: The related-work discussion omits recent self-distillation baselines that also avoid full online rollouts; adding them would better situate the contribution.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the strengths and limitations of our distribution-correction framework. We address each major point below with honest responses and indicate planned revisions.

read point-by-point responses

Referee: [§3.2] §3.2, Eq. (3): The alignment score is computed from a static proxy (teacher likelihood combined with a fixed student checkpoint); this choice does not guarantee that selected prefixes remain close to the final student's on-policy distribution on long competition-style trajectories, leaving the distribution-correction claim vulnerable to the compounding-error issue raised in the skeptic note.

Authors: We agree that the fixed student checkpoint provides only an approximation to the evolving on-policy distribution, and this is a practical compromise to retain the offline nature of the method. The checkpoint is selected at a mid-training point where the student has begun to internalize reasoning patterns but has not yet converged, which our preliminary analysis shows correlates with final inference behavior on shorter trajectories. On long competition tasks, the empirical gains in trace stability and accuracy (Table 4) suggest the proxy remains useful, though we acknowledge it does not fully eliminate compounding risk. In revision we will expand §3.2 with a clearer statement of this approximation and its scope, plus a short analysis of how alignment scores evolve across training checkpoints. revision: partial
Referee: [Table 4] Table 4, AIME row: The reported 5-point accuracy lift lacks error bars, multiple random seeds, or a significance test; given the small test-set size, it is unclear whether the gain exceeds what could arise from generic data filtering rather than true distribution alignment.

Authors: We concur that the AIME evaluation would be more convincing with statistical controls. In the revised manuscript we will rerun the AIME experiments with at least three random seeds, report mean accuracy with standard deviation, and include a paired significance test against the strongest baseline. This will help separate the contribution of distribution alignment from generic filtering effects. revision: yes
Referee: [§5.2] §5.2: The ablation isolating the adaptive component does not include a randomized-weight control; without it, the performance difference cannot be confidently attributed to distribution correction instead of length or quality filtering.

Authors: This is a fair criticism. To isolate the adaptive weighting mechanism, we will add a randomized-weight control ablation in §5.2: weights drawn from the same marginal distribution but randomly permuted across examples. Comparing this control against both uniform weighting and our adaptive scores will clarify whether gains stem from distribution correction rather than incidental length or quality biases. We will include the new results in the revision. revision: yes

Circularity Check

0 steps flagged

No circularity: adaptive weighting scheme remains independent of claimed gains

full rationale

The paper introduces an adaptive offline weighting mechanism to correct distributional drift between teacher prefixes and student on-policy behavior, but the provided text contains no equations, fitted parameters, or self-citations that reduce the reported accuracy improvements on GSM8K/MATH/AMC/AIME to a redefinition or tautological renaming of the inputs. The central claim is supported by external benchmark evaluations rather than internal consistency checks, and the weighting scheme is presented as a design choice whose effectiveness is tested empirically rather than assumed by construction. This is the most common honest outcome for a method paper whose core contribution is algorithmic rather than a closed-form derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; the method is described only at the conceptual level of adaptive emphasis.

pith-pipeline@v0.9.0 · 5522 in / 1049 out tokens · 60327 ms · 2026-05-15T05:13:02.763136+00:00 · methodology

discussion (0)

Reference graph

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Ning Yang, Hai Lin, Yibo Liu, Baoliang Tian, Guoqing Liu, and Haijun Zhang. Token- importance guided direct preference optimization. In The Fourteenth International Conference on Learning Representations, 2026. URL https://openreview.net/forum?id=cMEnMV vMw9

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TLCR: Token-level continuous reward for fine-grained reinforcement learning from human feedback

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Longhui Yu, Weisen Jiang, Han Shi, Jincheng Yu, Zhengying Liu, Yu Zhang, James T. Kwok, Zhenguo Li, Adrian Weller, and Weiyang Liu. MetaMath: Bootstrap your own mathematical questions for large language models. In International Conference on Learning Representations,

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DAPO: An Open-Source LLM Reinforcement Learning System at Scale

Qiying Yu, Zheng Zhang, Ruofei Zhu, Yufeng Yuan, Xiaochen Zuo, Yu Yue, Weinan Dai, Tiantian Fan, Gaohong Liu, Lingjun Liu, et al. Dapo: An open-source llm reinforcement learning system at scale. arXiv preprint arXiv:2503.14476, 2025. doi: 10.48550/arXiv.2503.14476. URLhttps://arxiv.org/abs/2503.14476

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Token- level direct preference optimization

Yongcheng Zeng, Guoqing Liu, Weiyu Ma, Ning Yang, Haifeng Zhang, and Jun Wang. Token- level direct preference optimization. In Ruslan Salakhutdinov, Zico Kolter, Katherine Heller, Adrian Weller, Nuria Oliver, Jonathan Scarlett, and Felix Berkenkamp, editors, Proceedings of the 41st International Conference on Machine Learning, volume 235 of Proceedings of...

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[52]

<understanding>...</understanding>

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[53]

<strategy>...</strategy>

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[54]

<solution>...</solution>

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<verification>...</verification>

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final”, “answer

Answer: \boxed{FINAL_ANSWER} ## 1. UNDERSTAND <understanding> - Identify what is given and what needs to be found - Note any constraints or special conditions </understanding> ## 2. PLAN <strategy> - Outline your solution approach step-by-step - Identify which mathematical techniques/theorems you will use - Consider if there are multiple viable approaches...

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[57]

Do not compare models in this prompt

Evaluate one trace at a time. Do not compare models in this prompt

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[58]

Distinguish final-answer correctness from reasoning quality

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[59]

Pay special attention to whether the trace is internally self-consistent, whether it contains a substantive mathematical error before the first final answer, whether it verifies its result in a meaningful way, and whether the final answer may be correct despite unreliable reasoning

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[60]

What you must check A

If the trace becomes repetitive, contradictory, or continues after the final answer, treat that as a reasoning-trace quality issue even if the final answer is correct. What you must check A. Final-answer correctness

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[61]

Determine whether the final answer given by the model is correct relative to GOLD_ANSWER

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[62]

If the model gives multiple candidate final answers, treat that as a serious reliability issue

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[63]

If the final answer is missing, malformed, or impossible to identify, mark it as ambiguous. B. Self-consistency

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[64]

Check whether the trace is logically consistent with itself

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[65]

Look for contradictions between earlier derivation and later verification

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[66]

Look for answer changes, inconsistent variable use, incompatible intermediate claims, or incompatible restatements of the result. C. Substantive error before the first final answer

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[67]

Check whether there is a real mathematical or logical error before the first final answer appears

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[68]

Count only substantive errors: wrong algebra, wrong arithmetic, wrong counting argument, wrong unit conversion, invalid inference, use of a false statement, or an unsupported claim that materially affects the derivation

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[69]

Do not count mere verbosity, repetition, or formatting noise as a substantive error by itself

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[70]

If the trace has only a small gap or a minor imprecision that does not clearly break the reasoning, use the minor_or_repairable label. 18 D. Overall reasoning quality

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[71]

Judge whether the trace is high, medium, or low quality as reasoning

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[72]

High quality means mathematically sound, coherent, relevant, and easy to trust

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[73]

Medium quality means mostly usable but somewhat noisy, incomplete, repetitive, or weakly justified

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[74]

Low quality means hard to trust because of substantial errors, severe inconsistency, degeneration, or obvious unreliability. E. Verification quality

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[75]

Judge whether the trace includes a meaningful verification or checking step

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[76]

High verification quality means the trace checks the final result against the problem conditions, validates key assumptions, catches and repairs any detected issue, or otherwise gives a substantive reason to trust the answer

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[77]

Medium verification quality means there is some checking, but it is shallow, incomplete, or mostly restates the answer

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Low verification quality means verification is absent, perfunctory, plainly wrong, or contradicted by the trace

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verification

Do not reward a trace for merely having a section named "verification" if the content does not actually verify the reasoning or answer. F. Post-final-answer degeneracy

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[80]

Check whether the trace continues in a degenerate way after the first final answer

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[81]

Examples include repeated final answers, looped restarts, repeated markdown blocks, contradictory re-verification, or self-dialogue after already answering

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[82]

If there is no meaningful post-answer degeneration, mark none. G. Reasoning-invalid-but-finally-correct

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Showing first 80 references.