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arxiv: 2606.00628 · v1 · pith:V6C45T46new · submitted 2026-05-30 · 💻 cs.CL

Robust Reasoning via Dynamic Token Selection for Distribution-Aligned Self-Distillation

Ruiqi Zhang , Lingxiang Wang , Hainan Zhang Zhiming Zheng This is my paper

Pith reviewed 2026-06-28 19:10 UTC · model grok-4.3

classification 💻 cs.CL
keywords self-distillationdynamic token selectionreasoning benchmarkshigh-perplexity tokensdistribution alignmentlogical correctionsstylistic driftrobustness
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The pith

Dynamic token filtering in self-distillation preserves logical knowledge while suppressing stylistic noise to improve reasoning.

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

Self-distillation rewrites reference answers to better match the model's distribution but introduces stylistic biases that cause imitation of surface forms rather than reasoning patterns. High-perplexity tokens in the data come from two sources: beneficial logical corrections and harmful stylistic drift. DASD generates candidate tokens with an answer-aware reference model and dynamically filters them according to the base model's confidence scores. This keeps tokens that carry useful logical knowledge and discards distributionally misaligned style noise. The method yields consistent gains over baselines on math, code, and commonsense reasoning benchmarks while reducing disruptive high-PPL tokens.

Core claim

Distribution-Aligned Self-Distillation (DASD) uses an answer-aware reference model to generate candidate tokens and applies dynamic selection based on the base model's confidence, thereby preserving tokens that encode useful logical knowledge while suppressing tokens that represent distributionally misaligned style noise.

What carries the argument

Dynamic token selection in DASD that filters high-perplexity tokens by combining answer-aware reference generation with base-model confidence to align training data with the original distribution.

If this is right

  • Consistent outperformance on math, code, and commonsense reasoning benchmarks compared with competitive baselines.
  • Measurable reduction in high-perplexity tokens present in the rewritten training data.
  • Improved robustness on tasks of varying difficulty without disrupting the base model's original distribution.
  • Better preservation of useful reasoning patterns instead of surface-form imitation.

Where Pith is reading between the lines

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

  • The same separation of logical versus stylistic tokens could be tested in standard knowledge distillation beyond the self-distillation setting.
  • If the filtering reliably isolates logical content, it may reduce certain forms of output bias on tasks outside reasoning benchmarks.
  • Repeating the token-selection process on models of different sizes would test whether the two sources of high-perplexity tokens remain separable at scale.

Load-bearing premise

High-perplexity tokens arise from two cleanly separable sources—beneficial logical corrections versus harmful stylistic drift—that an answer-aware reference model and base-model confidence can reliably distinguish.

What would settle it

A controlled experiment in which DASD-trained models show no improvement over baselines on difficult reasoning tasks or fail to reduce stylistic imitation in generated outputs would falsify the claim.

Figures

Figures reproduced from arXiv: 2606.00628 by Hainan Zhang Zhiming Zheng, Lingxiang Wang, Ruiqi Zhang.

Figure 1
Figure 1. Figure 1: Correlation between average high-PPL to [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The high PPL rate distribution of different [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: A generation case on the MATH dataset. Question: original problem; Reference: standard solution; Self: base model output; Self-Distill: self-distilled result; DASD: output of our method. Yellow tokens denote mechanical imitation of reference answers that diverge from the base model style. Green tokens retain the inherent linguistic style of the base model, and blue tokens follow reasoning logic consistent … view at source ↗
Figure 5
Figure 5. Figure 5: Proportion distribution of three types of token, [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Proportions of base-selected tokens and hard [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Prompt template of the base model [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Prompt template of the reference model [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: Generation output of the base model. memory consumption compared with conventional self-distillation paradigms. However, the additional token screening and confidence verification mod￾ules introduced in DASD are extremely lightweight. Their computational overhead is negligible relative to the full model forward propagation, resulting in nearly identical inference latency and no extra time cost for the ove… view at source ↗
Figure 12
Figure 12. Figure 12: Generation output of the reference model. [PITH_FULL_IMAGE:figures/full_fig_p012_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Generation output of our DASD method. 12 [PITH_FULL_IMAGE:figures/full_fig_p012_13.png] view at source ↗
read the original abstract

Self-distillation improves learning efficiency by rewriting reference answers as training data that better matches the model's own distribution. However, reference answers also introduce strong stylistic biases, causing the generative model to imitate surface forms rather than learn useful reasoning patterns. We observe that the rewriting data contains a large number of high-perplexity (PPL) tokens, coming from two distinct sources: beneficial knowledge-enhancing logical corrections, and harmful stylistic drift induced by reference imitation. Treating all such tokens equally can disrupt the base model's original distribution and degrade performance, especially on difficult reasoning tasks. To address this, we propose Distribution-Aligned Self-Distillation (DASD), which uses an answer-aware reference model to generate candidate tokens and dynamically filters them according to the base model's confidence. DASD preserves tokens that encode useful logical knowledge while suppressing distributionally misaligned style noise. Experiments on math, code, and commonsense reasoning benchmarks show that DASD consistently outperforms competitive baselines, reduces high-PPL tokens, and improves robustness across tasks of varying difficulty.

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.

Referee Report

2 major / 1 minor

Summary. The paper introduces Distribution-Aligned Self-Distillation (DASD), which identifies high-perplexity tokens in self-distillation data as arising from either beneficial logical corrections or harmful stylistic drift. It proposes using an answer-aware reference model to generate candidates and dynamically filtering them via the base model's confidence to retain useful knowledge tokens while suppressing misaligned style noise. The central claim is that this yields consistent outperformance over baselines on math, code, and commonsense reasoning benchmarks, reduces high-PPL tokens, and improves robustness across task difficulties.

Significance. If the empirical claims hold with proper controls and ablations, the work could offer a practical refinement to self-distillation pipelines by mitigating distribution shift from stylistic imitation. The distinction between sources of high-PPL tokens is a reasonable empirical observation, and the dynamic selection approach is a targeted intervention. No machine-checked proofs or parameter-free derivations are present; credit is due for framing the problem around token-level distribution alignment rather than global loss terms.

major comments (2)
  1. [Abstract] Abstract: The assertion that DASD 'consistently outperforms competitive baselines' and 'reduces high-PPL tokens' supplies no quantitative results, error bars, dataset names, baseline identities, or effect sizes. This absence is load-bearing for the central empirical claim and prevents evaluation of whether the token-selection mechanism delivers the stated gains.
  2. [Method] Method description (inferred from abstract and introduction): The separation of high-PPL tokens into 'beneficial knowledge-enhancing logical corrections' versus 'harmful stylistic drift' is presented as an empirical design choice without an explicit algorithm, threshold formula, or ablation showing that the answer-aware reference model plus base-model confidence reliably partitions the two sources. This directly affects the validity of the dynamic filtering step.
minor comments (1)
  1. [Abstract] Abstract: Consider including one sentence with the specific benchmarks (e.g., GSM8K, HumanEval) and at least one numeric improvement to allow readers to gauge the scale of the reported gains.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below and indicate where revisions will strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The assertion that DASD 'consistently outperforms competitive baselines' and 'reduces high-PPL tokens' supplies no quantitative results, error bars, dataset names, baseline identities, or effect sizes. This absence is load-bearing for the central empirical claim and prevents evaluation of whether the token-selection mechanism delivers the stated gains.

    Authors: We agree that the abstract is too high-level. The revised version will incorporate specific quantitative highlights drawn from the experimental results, including approximate gains on named benchmarks (MATH, GSM8K, HumanEval, etc.), the primary baselines, and the observed reduction in high-PPL tokens, along with a brief note on robustness across difficulty levels. revision: yes

  2. Referee: [Method] Method description (inferred from abstract and introduction): The separation of high-PPL tokens into 'beneficial knowledge-enhancing logical corrections' versus 'harmful stylistic drift' is presented as an empirical design choice without an explicit algorithm, threshold formula, or ablation showing that the answer-aware reference model plus base-model confidence reliably partitions the two sources. This directly affects the validity of the dynamic filtering step.

    Authors: The full method section already specifies the answer-aware reference model for candidate generation and dynamic filtering via base-model token confidence. To make the partitioning criterion fully explicit, we will add a formal algorithmic description (including the exact selection rule) and an ablation isolating the effect of this confidence-based filter. This addresses the concern about clarity without altering the core approach. revision: yes

Circularity Check

0 steps flagged

No significant circularity; method is empirical design choice without derivations

full rationale

The provided abstract and description contain no equations, formal derivations, or load-bearing self-citations. The core premise—that high-PPL tokens arise from separable logical corrections versus stylistic drift, distinguishable via reference model and base confidence—is presented as an empirical observation and design choice rather than a derived necessity. DASD is described as a filtering procedure whose validity is asserted via benchmark improvements, with no reduction of any 'prediction' or uniqueness claim to fitted inputs or prior self-work by construction. Absent any mathematical chain, the paper is self-contained against external benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No technical details, equations, or experimental setup provided in abstract; free parameters, axioms, and invented entities cannot be identified.

pith-pipeline@v0.9.1-grok · 5709 in / 968 out tokens · 22360 ms · 2026-06-28T19:10:55.191283+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

19 extracted references · 10 canonical work pages · 8 internal anchors

  1. [1]

    IEEE Transactions on Audio, Speech and Language Processing , year=

    An empirical study of catastrophic forgetting in large language models during continual fine-tuning , author=. IEEE Transactions on Audio, Speech and Language Processing , year=

  2. [2]

    Findings of the association for computational linguistics: EMNLP 2024 , pages=

    Revisiting catastrophic forgetting in large language model tuning , author=. Findings of the association for computational linguistics: EMNLP 2024 , pages=

    2024

  3. [3]

    Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) , pages=

    Self-distillation bridges distribution gap in language model fine-tuning , author=. Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) , pages=

  4. [4]

    Advances in Neural Information Processing Systems , volume=

    Mitigating forgetting in llm fine-tuning via low-perplexity token learning , author=. Advances in Neural Information Processing Systems , volume=

  5. [5]

    ProFit: Leveraging High-Value Signals in SFT via Probability-Guided Token Selection

    ProFit: Leveraging High-Value Signals in SFT via Probability-Guided Token Selection , author=. arXiv preprint arXiv:2601.09195 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  6. [6]

    arXiv preprint arXiv:2602.12222 , year=

    Towards On-Policy SFT: Distribution Discriminant Theory and its Applications in LLM Training , author=. arXiv preprint arXiv:2602.12222 , year=

    work page arXiv

  7. [7]

    Proceedings of the 61st annual meeting of the association for computational linguistics (volume 1: long papers) , pages=

    Self-instruct: Aligning language models with self-generated instructions , author=. Proceedings of the 61st annual meeting of the association for computational linguistics (volume 1: long papers) , pages=

  8. [8]

    arXiv preprint arXiv:2312.06585 , year=

    Beyond human data: Scaling self-training for problem-solving with language models , author=. arXiv preprint arXiv:2312.06585 , year=

    work page arXiv

  9. [9]

    Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing , pages=

    I learn better if you speak my language: Understanding the superior performance of fine-tuning large language models with LLM-generated responses , author=. Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing , pages=

    2024

  10. [10]

    Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) , pages=

    Scar: Data selection via style consistency-aware response ranking for efficient instruction-tuning of large language models , author=. Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) , pages=

  11. [11]

    Findings of the Association for Computational Linguistics: EMNLP 2025 , pages=

    Efficiently Selecting Response Generation Strategies for Synthetic Data Construction by Self-Aligned Perplexity , author=. Findings of the Association for Computational Linguistics: EMNLP 2025 , pages=

    2025

  12. [12]

    Embarrassingly Simple Self-Distillation Improves Code Generation

    Embarrassingly simple self-distillation improves code generation , author=. arXiv preprint arXiv:2604.01193 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  13. [13]

    Star: Self-taught reasoner bootstrapping reasoning with reasoning , author=. Proc. the 36th International Conference on Neural Information Processing Systems , volume=

  14. [14]

    Measuring Mathematical Problem Solving With the MATH Dataset

    Measuring mathematical problem solving with the math dataset , author=. arXiv preprint arXiv:2103.03874 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  15. [15]

    Program Synthesis with Large Language Models

    Program synthesis with large language models , author=. arXiv preprint arXiv:2108.07732 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  16. [16]

    Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge

    Think you have solved question answering? try arc, the ai2 reasoning challenge , author=. arXiv preprint arXiv:1803.05457 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  17. [17]

    The Llama 3 Herd of Models

    The llama 3 herd of models , author=. arXiv preprint arXiv:2407.21783 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  18. [18]

    Qwen3 Technical Report

    Qwen3 technical report , author=. arXiv preprint arXiv:2505.09388 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  19. [19]

    Gemma 2: Improving Open Language Models at a Practical Size

    Gemma 2: Improving open language models at a practical size , author=. arXiv preprint arXiv:2408.00118 , year=

    work page internal anchor Pith review Pith/arXiv arXiv