Pith. sign in

REVIEW 3 major objections 5 minor 55 references

Which Reasoning Trajectories Teach Students to Reason Better? A Simple Metric of Informative Alignment

T0 review · 3 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A single forward pass through the student model can predict which reasoning trajectories will teach it best, because the ratio of token rank to surprisal measures how informative and how aligned a trajectory is.

desk verdict RSR is a plausible, cheap heuristic for trajectory selection, but the 0.86 correlation is partly in-sample selection and the paper needs held-out validation. read the letter →

arxiv 2601.14249 v5 pith:R4XXJIEG submitted 2026-01-20 cs.CL

Yuming Yang , Mingyoung Lai , Wanxu Zhao , Xiaoran Fan , Zhiheng Xi , Mingqi Wu , Chiyue Huang , Jun Zhao
show 8 more authors
Haijun Lv Jian Tong Yunhua Zhou Yicheng Zou Qipeng Guo Tao Gui Qi Zhang Xuanjing Huang
This is my paper
classification cs.CL
keywords Rank-SurprisalRatioreasoningdistillationchain-of-thoughtdataselectionstudent-teachersuitabilitysurprisaltokenrankSFT
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

This paper tries to settle a practical question in reasoning distillation: given a student model and a pile of teacher-generated chain-of-thought traces, which traces will actually improve the student after fine-tuning? The answer it proposes is a single number, the Rank-Surprisal Ratio (RSR): the trajectory's average token rank divided by its average surprisal under the student model. The paper argues that good teaching traces are both informative and aligned: they deviate from what the student would write (low absolute probability) while staying within the student's behavioral repertoire (relatively high rank among alternatives). Across five student models and eleven teachers, dataset-level RSR correlates with post-training math performance with average Spearman 0.86, beating probability-only, rank-only, gradient-based, and quality-based metrics. If right, RSR gives a cheap, one-forward-pass way to select training data and teachers before spending compute on fine-tuning.

What carries the argument

The central object is the Rank-Surprisal Ratio (RSR), defined for a trajectory as the sum of clipped token ranks divided by the sum of token surprisals under the student model, typically with rank clipped at a threshold of 100. Rank here is the position of a token in the student's vocabulary distribution (1 = most probable), and surprisal is its negative log probability. A surprisal-weighted averaging scheme, equivalent to the trajectory-level ratio, prevents a few highly predictable tokens from dominating the score, while rank clipping prevents highly unfamiliar tokens from inflating it. The metric requires only one forward pass through the student model, needs no verifier, correctness labe

What would settle it

A direct test would hold dataset-level RSR constant while varying training conditions—for example, training on the same RSR-scored trajectories for one epoch versus several, or in different orders—and checking whether post-training performance diverges; if two datasets with identical RSR systematically produce different students, RSR is not capturing the learning-relevant property. A sharper version: fine-tune the student for a few steps, recompute RSR on the partially trained model, and see whether the teacher ranking flips; if it does, the base-model single-pass assumption fails.

Watch

Extended reading notes

Core claim

The paper's central discovery is that the suitability of a reasoning trajectory for a given student can be read off from two token-level statistics under the student's own model, combined as a ratio. RSR(x) is defined as the sum of clipped token ranks divided by the sum of token surprisals, i.e., negative log-likelihoods, under the student model. The numerator measures relative familiarity—whether the student would already place the token near the top of its prediction distribution—and the denominator measures absolute unfamiliarity—how surprised the student is by the token. Departing from likelihood-based selection, which favors familiar but uninformative traces, the paper claims the best t

Load-bearing premise

The load-bearing premise is that a single forward pass of the untrained base student model fully measures a trajectory's downstream training value; the paper's own limitations section concedes the metric has no deeper theoretical derivation and has been tested mainly on math, so if SFT gains depend on optimization dynamics or cross-sample interaction after the initial pass, RSR's predictive power fails.

Editorial extensions

If this is right

  • Dataset-level RSR predicts post-training math performance with an average Spearman correlation of 0.86 across five student models and eleven teachers, outperforming surprisal-only, rank-only, gradient-based, influence-based, and LLM-judged quality metrics.
  • RSR-based trajectory selection from a 33-to-1 candidate pool yields better post-training students than random, length-based, quality-based, surprisal-based, and gradient-based selection, and is comparable to or better than the best single teacher for four of five students.
  • Teacher selection using RSR computed on only 200 trajectories per teacher approaches oracle-level results, making it practical when generating full training data for every candidate teacher is expensive.
  • The 5,000 trajectories selected by RSR match or exceed a 55,000-trajectory unfiltered baseline on most student models, showing that suitability-based selection can improve both data efficiency and quality.
  • RSR remains effective when each teacher contributes only one trajectory per problem, indicating it captures cross-teacher suitability differences, not just generation noise.

Reading between the lines

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

  • Because RSR requires only a single forward pass and no labels, it could serve as an online filter during data generation, pruning low-suitability trajectories before they are stored or trained on.
  • The ratio of rank to surprisal suggests a more general curriculum principle: pick examples the student finds unfamiliar but within reach; this could apply beyond chain-of-thought to instruction tuning or general pretraining data selection.
  • The paper leaves the theoretical foundation open, so a testable extension would be connecting RSR to learning-theoretic quantities such as gradient alignment or generalization bounds, which might explain why the ratio works.
  • One could also test RSR as a dynamic signal, recomputed after a few fine-tuning steps, to see whether the best trajectories change as the student improves; if they do, RSR could drive adaptive curricula.
Share X Bluesky LinkedIn Reddit HN

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 proposes Rank-Surprisal Ratio (RSR), defined in Eq. (7) as the sum of clipped token ranks divided by the sum of token surprisals under the base student model, as a suitability metric for reasoning-trajectory distillation. The authors argue that effective trajectories balance informativeness (low absolute probability) with alignment (relatively high token rank). Across five base student models and eleven teacher models, they report that dataset-level RSR correlates with post-SFT math benchmark performance at average Spearman 0.86 (Table 4), outperforming probability-, rank-, gradient-, and quality-based baselines, and that RSR-based trajectory and teacher selection improves over existing methods (Tables 6–7). The paper includes a large distillation study, ablations, and practical selection experiments, and releases code and data.

Significance. If the reported correlation is reliable, RSR is a practically valuable and extremely cheap metric: a single forward pass of the base student suffices, with no verifier or additional test data. The empirical coverage is broad for this line of work: 5 students × 11 teachers, three trajectory generations per teacher, multiple benchmarks, ablations, and two application scenarios. The release of code and data is a strength. However, the central claim is supported almost entirely by the correlation analysis, since the paper explicitly disclaims a theoretical derivation in its Limitations section. The main risk is that the metric form, rank clipping threshold, and aggregation scheme are selected on the same 55 teacher–student pairs used to measure the headline correlation, and no confidence intervals, leave-one-out analysis, or held-out validation are reported. The practical selection results provide some independent evidence, but they share the same hyperparameters and underlying data.

major comments (3)
  1. [§3.4, §4.1, Tables 5 and 11] The headline average Spearman of 0.86 is computed on the same teacher–student grid used to choose the metric's functional form and hyperparameters. Section 3.4 states that using the top 30% highest-surprisal tokens was chosen because it 'yields stronger correlation with post-training performance (Table 2)'; §4.1 sets r_max=100 and adopts surprisal-weighted aggregation because they 'yield slightly higher correlation'. Table 5 compares r_max=50, r_max=500, no clipping, filtered averaging, and no weighted averaging; Table 11 compares roughly a dozen further variants. Each per-student Spearman is based on only 11 teacher-level points (standard error roughly 0.3), so selecting the best among ~15 variants can materially inflate the observed correlation. The paper reports no confidence intervals, no leave-one-teacher-out or leave-one-student-out analysis, and no independent validation set. Sinc
  2. [§5.1, §5.2] The trajectory-selection and teacher-selection experiments are encouraging and provide a form of external validation, but they use the same r_max=100 and surprisal-weighted aggregation tuned in §4.1, and the same pool of teachers and students. The metric could be overfit to the aggregate correlation without transferring to per-problem selection; the fact that it does transfer is evidence, but not a substitute for an out-of-sample correlation analysis. Please report whether any selection-method hyperparameters were tuned on the selection results, and consider evaluating with a small held-out set of teachers not used in the correlation analysis.
  3. [§3.3 and §A.6] The simulation study contains additional fitted choices that support the metric's design but are not validated out-of-sample: the Zipf exponent alpha=2.3 and mixture masses M_A=1,000,000, M_B=250,000 are described as based on a 'preliminary fit to reasoning data' (§A.6), and the conclusion that high-surprisal tokens should be emphasized is drawn from the same correlation grid (Table 2). These choices are part of the in-sample selection problem identified above. Please disclose the fitting procedure and, if possible, test the sensitivity of the simulation conclusions to alpha and mixture parameters, or evaluate the top-30% choice on held-out data.
minor comments (5)
  1. [Table 4] The 'Average' column for Teacher Params (0.01) and Influence Score (0.11) is not consistent with the individual absolute values shown in the same table (e.g., Teacher Params entries 0.04, 0.34, 0.20, 0.02, 0.26 average to 0.172 as absolute values). The caption or §A.7 should clarify exactly how signed correlations are averaged before taking the absolute value, and the table should not mix absolute per-student values with an average over signed values without explanation.
  2. [Eq. (6)] The 'simple derivation' in Eq. (6) is an algebraic identity, not a derivation of why surprisal weighting is the right aggregation. The modeling choice is the weighting, not the algebra; please phrase this more carefully to avoid implying that the weighting is theoretically forced.
  3. [§4.2, Table 5] The 'Reduced sample size (200)' row reports a correlation of 0.864, slightly higher than the full-sample 0.856. This is a useful robustness result, but it is still on the same in-sample grid; please avoid describing it as out-of-sample evidence.
  4. [§C.4.1, Table 12] The 'No Selection (55k combined)' baseline trains on 55k trajectories while the RSR-selected rows train on 5k. This is not an apples-to-apples comparison of selection methods; please state this limitation in the text or add a same-size baseline.
  5. [Throughout] Minor typos: 'datset' in §A.7; abbreviations such as 'L3.1-8B' and 'Q2.5-3B' should be defined in table captions; Table 17's color coding ('darker red') is described in the caption but not visible in a monochrome print version.

Circularity Check

2 steps flagged · score 5.0 of 10

Partial circularity: the headline 0.86 correlation is partly a fitted in-sample statistic because r_max, the top-30% surprisal filter, and surprisal-weighted aggregation were selected on the same 55 teacher–student pairs; the §3.3 simulation also labels the winning trajectory type 'effective' by construction.

  1. fitted input called prediction [§3.4, §4.1, §4.2 (Eq. 5–7, Table 5, Table 4)]
    "Empirically, we find that using the top 30% highest-surprisal tokens yields stronger correlation with post-training performance (Table 2). ... We use a clipping threshold of r_max = 100 for RSR in all subsequent experiments. ... As shown in Table 5, removing either rank clipping or the surprisal-weighted averaging substantially degrades the correlation, validating the necessity of both components in our metric."

    The operational form of Eq. 7 (top-30% surprisal filter, r_max=100, surprisal-weighted aggregation at both trajectory and dataset level) was chosen by comparing correlations with post-training performance on the same 55 teacher–student pairs that then yield the headline average Spearman 0.86 in Table 4. No held-out split, leave-one-teacher-out analysis, or confidence intervals are reported. Table 5 shows the chosen configuration beats r_max=50 (0.696), no clipping (0.700), and no weighted averaging (0.391) on the same data; the reported 0.86 is therefore an in-sample maximum over tested variants rather than an out-of-sample prediction.

  2. self definitional [§3.3 (Table 3)]
    "effective reasoning trajectories are expected to align with the distribution of Z_B, and thus resemble X_B. ... Table 3 shows that trajectories of the preferred type X_B achieve the lowest average RSRtoken (1.30), whereas the misaligned X_C achieve the highest, suggesting that this ratio may be a reliable indicator for identifying effective reasoning trajectories that balance informativeness and alignment."

    In the simulation, X_B is defined as the 'effective'/'preferred' trajectory type by construction—it is sampled from the minor mode Z_B that the paper stipulates represents strong reasoning patterns—and RSR is then shown to rank X_B first. This is a consistency check of the metric against its own labeling rather than independent evidence. The paper's actual support for low-RSR improving performance is the correlation analysis, which is itself in-sample with respect to the hyperparameter choices (see above).

full rationale

The derivation of Eq. 7 is not definitionally equivalent to post-training performance: RSR is computed from a single forward pass of the base student model, and the observed correlations could plausibly have been weak. There is also no load-bearing self-citation chain; the author self-citations ([43], [44]) are background related-work only. However, two steps create partial circularity. First, the metric's functional form and hyperparameters are fitted to the outcome it is then said to predict: §3.4 selects a top-30% surprisal filter because it yields higher correlation with post-training performance; §4.1 fixes r_max=100 for 'all subsequent experiments'; and §4.2/Table 5 (plus Table 11) choose surprisal-weighted aggregation over simple averaging on the same 55 teacher–student pairs that produce the headline 0.86. No held-out split, teacher-level cross-validation, or confidence intervals are reported, so 0.86 is the maximum over roughly 15 correlated variants on the same data, i.e., partly a fitted statistic. Robustness to r_max=500 (0.822) and 200-trajectory measurement (0.864) lessens but does not remove the selection effect. Second, the §3.3 simulation is self-confirming: X_B is labeled 'effective'/'preferred' by construction, and RSR is then shown to rank it first, which adds no independent support. The Limitations passage ('it remains unclear whether it arises from deeper mathematical principles') concedes there is no theoretical derivation, making the in-sample correlation more load-bearing. That said, the GPQA-Diamond evaluation and the trajectory/teacher selection experiments provide partially external evidence that RSR has practical value beyond the single fitted correlation; hence the score is moderate rather than high.

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

The central claim rests primarily on empirical evaluation, not on derivation. The main assembled inputs are: the choice of r_max and aggregation (tuned on the same evaluation), the Zipf simulation (constructed to illustrate the intuition), and the domain premise that static token probabilities under the base student predict SFT utility.

free parameters (4)
  • Rank clipping threshold r_max = 100
    Eq. 7 and §4.1: chosen to maximize correlation. Table 5 shows r_max=50 gives 0.696, no clipping 0.700, r_max=500 0.822, so the reported 0.86 depends on this choice.
  • Zipf exponent alpha in simulation = 2.3
    A.6: 'based on a preliminary fit to reasoning data'; the simulated student distribution and the X_B pattern follow from this choice.
  • Simulation mixture masses M_A, M_B = 1,000,000 / 250,000
    A.6: hand-picked to define the mixture pi; controls how much mass the 'reasoning' mode has in the simulated student.
  • Surprisal-weighting aggregation scheme = weighted average (not top-30% filter)
    §3.4: Eq. 5 filtered average and Eq. 6 weighted average were compared; correlation differences (Table 5) drove adoption of weighted averaging. A method-structure choice selected on the same data.
assumptions (4)
  • domain assumption Trajectory suitability for SFT is fully captured by token-level probability and rank under the pre-trained base student, without considering optimization dynamics or post-training distribution shift.
    Central premise of RSR (§3.4, §4); never directly validated against intermediate-checkpoint or interaction-based suitability.
  • ad hoc to paper The student model's token-level prediction distribution is a mixture of two Zipf distributions with alpha=2.3 and mass ratio 4:1.
    A.6; this choice manufactures the X_B pattern (low probability, high rank) used to motivate RSR.
  • ad hoc to paper Tokens with higher surprisal have greater influence on downstream learning, justifying surprisal weighting.
    §3.4 'Empirically, we find...' rather than a derivation or controlled test.
  • domain assumption Average Acc@4 on AIME'25, AIME'24, AMC'23, and MATH500 is a valid proxy for post-training reasoning ability.
    Standard evaluation choice; the paper adds GPQA in one experiment, but the main correlation claim depends on these four math benchmarks.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Which Reasoning Trajectories Teach Students to Reason Better? A Simple Metric of Informative Alignment." pith.science (2026). https://pith.science/paper/R4XXJIEG

@misc{pith2026260114249,
  author       = {Pith},
  title        = {Pith review of: Which Reasoning Trajectories Teach Students to Reason Better? A Simple Metric of Informative Alignment},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/R4XXJIEG}},
  note         = {Machine review of arXiv:2601.14249}
}
read the original abstract

Long chain-of-thought (CoT) trajectories provide rich supervision signals for distilling reasoning from teacher to student LLMs. However, both prior work and our experiments show that trajectories from stronger teachers do not necessarily yield better students, highlighting the importance of data-student suitability in distillation. Existing methods assess suitability primarily through student likelihood, favoring trajectories that align closely with the student model's current behavior but overlooking more informative ones. Addressing this, we propose Rank-Surprisal Ratio (RSR), a simple metric that captures both alignment and informativeness to assess the suitability of a reasoning trajectory. RSR is motivated by the observation that effective trajectories typically balance learning signal strength and behavioral alignment by combining low absolute probability with relatively high-ranked tokens under the student model. Concretely, RSR is defined as the ratio of a trajectory's average token-wise rank to its average negative log-likelihood, and is straightforward to compute and interpret. Across five student models and reasoning trajectories from 11 diverse teachers, RSR strongly correlates with post-training reasoning performance (average Spearman 0.86), consistently outperforming existing metrics. We further demonstrate its practical utility in both trajectory selection and teacher selection.

Review history (2 revisions) →

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

55 extracted references · 20 linked inside Pith

  1. [1]

    Phi-4-reasoning technical report

    Marah Abdin, Sahaj Agarwal, Ahmed Awadallah, Vidhisha Balachandran, Harkirat Behl, Lingjiao Chen, Gustavo de Rosa, Suriya Gunasekar, Mojan Javaheripi, Neel Joshi, et al. Phi-4-reasoning technical report. arXiv preprint arXiv:2504.21318, 2025. 2.1

    arXiv 2025

  2. [2]

    On-policy distillation of language models: Learning from self-generated mistakes

    Rishabh Agarwal, Nino Vieillard, Yongchao Zhou, Piotr Stańczyk, Sabela Ramos, Matthieu Geist, and Olivier Bachem. On-policy distillation of language models: Learning from self-generated mistakes. In International Conference on Learning Representations, 2023. 6

    2023

  3. [3]

    gpt-oss-120b & gpt-oss-20b model card.arXiv preprint arXiv:2508.10925, 2025

    Sandhini Agarwal, Lama Ahmad, Jason Ai, Sam Altman, Andy Applebaum, Edwin Arbus, Rahul K Arora, Yu Bai, Bowen Baker, Haiming Bao, et al. gpt-oss-120b & gpt-oss-20b model card.arXiv preprint arXiv:2508.10925, 2025. 2.1

    arXiv 2025

  4. [4]

    Llama-nemotron: Efficient reasoning models.arXiv preprint arXiv:2505.00949, 2025

    Akhiad Bercovich, Itay Levy, Izik Golan, Mohammad Dabbah, Ran El-Yaniv, Omri Puny, Ido Galil, Zach Moshe, Tomer Ronen, Najeeb Nabwani, et al. Llama-nemotron: Efficient reasoning models.arXiv preprint arXiv:2505.00949, 2025. 2.1

    arXiv 2025

  5. [5]

    Retaining by doing: The role of on-policy data in mitigating forgetting.CoRR, abs/2510.18874, 2025

    Howard Chen, Noam Razin, Karthik Narasimhan, and Danqi Chen. Retaining by doing: The role of on-policy data in mitigating forgetting.CoRR, abs/2510.18874, 2025. 6

    arXiv 2025

  6. [6]

    Unveiling the key factors for distilling chain-of-thought 10 Which Reasoning Trajectories Teach Students to Reason Better? A Simple Metric of Informative Alignment reasoning

    Xinghao Chen, Zhijing Sun, Wenjin Guo, Miaoran Zhang, Yanjun Chen, Yirong Sun, Hui Su, Yijie Pan, Dietrich Klakow, Wenjie Li, and Xiaoyu Shen. Unveiling the key factors for distilling chain-of-thought 10 Which Reasoning Trajectories Teach Students to Reason Better? A Simple Metric of Informative Alignment reasoning. In Wanxiang Che, Joyce Nabende, Ekateri...

    2025

  7. [7]

    Pearson correlation coefficient.Noise reduction in speech processing, pages 1–4, 2009

    Israel Cohen, Yiteng Huang, Jingdong Chen, Jacob Benesty, Jacob Benesty, Jingdong Chen, Yiteng Huang, and Israel Cohen. Pearson correlation coefficient.Noise reduction in speech processing, pages 1–4, 2009. A.7

    2009

  8. [8]

    FlashAttention-2: Faster attention with better parallelism and work partitioning

    Tri Dao. FlashAttention-2: Faster attention with better parallelism and work partitioning. InInternational Conference on Learning Representations (ICLR), 2024. A.5

    2024

Show all 55 references
  1. [9]

    Micota: Bridgingthelearnabilitygapwithintermediatecotandteacherassistants.ArXiv, abs/2507.01887,

    Dongyi Ding, Tiannan Wang, Chenghao Zhu, Meiling Tao, Yuchen Eleanor Jiang, and Wangchunshu Zhou. Micota: Bridgingthelearnabilitygapwithintermediatecotandteacherassistants.ArXiv, abs/2507.01887,

    arXiv

  2. [10]

    Posterior-grpo: Rewarding reasoning processes in code generation.CoRR, abs/2508.05170, 2025

    Lishui Fan, Yu Zhang, Mouxiang Chen, and Zhongxin Liu. Posterior-grpo: Rewarding reasoning processes in code generation.CoRR, abs/2508.05170, 2025. B.1

    2025 arXiv

  3. [11]

    Roger B. Grosse, Juhan Bae, Cem Anil, Nelson Elhage, Alex Tamkin, Amirhossein Tajdini, Benoit Steiner, Dustin Li, Esin Durmus, Ethan Perez, Evan Hubinger, Kamile Lukosiute, Karina Nguyen, Nicholas Joseph, Sam McCandlish, Jared Kaplan, and Samuel R. Bowman. Studying large langu...

    2023 arXiv

  4. [12]

    Etash Kumar Guha, Ryan Marten, Sedrick Keh, Negin Raoof, Georgios Smyrnis, Hritik Bansal, Marianna Nezhurina, Jean Mercat, Trung Vu, Zayne Sprague, Ashima Suvarna, Benjamin Feuer, Liangyu Chen, Zaid Khan, Eric Frankel, Sachin Grover, Caroline Choi, Niklas Muennighoff, Shiye Su...

    2025 arXiv

  5. [13]

    Daya Guo, Dejian Yang, Haowei Zhang, Junxiao Song, Peiyi Wang, Qihao Zhu, Runxin Xu, Ruoyu Zhang, Shirong Ma, Xiao Bi, Xiaokang Zhang, Xingkai Yu, Yu Wu, Z. F. Wu, Zhibin Gou, Zhihong Shao, Zhuoshu Li, Ziyi Gao, Aixin Liu, Bing Xue, Bingxuan Wang, Bochao Wu, Bei Feng, Chengda ...

    2025

  6. [14]

    A probabilistic earley parser as a psycholinguistic model

    John Hale. A probabilistic earley parser as a psycholinguistic model. InLanguage Technologies 2001: The Second Meeting of the North American Chapter of the Association for Computational Linguistics, NAACL 2001, Pittsburgh, PA, USA, June 2-7, 2001. The Association for Computati...

    2001

  7. [15]

    Measuring mathematical problem solving with the math dataset.arXiv preprint arXiv:2103.03874, 2021

    Dan Hendrycks, Collin Burns, Saurav Kadavath, Akul Arora, Steven Basart, Eric Tang, Dawn Song, and Jacob Steinhardt. Measuring mathematical problem solving with the math dataset.arXiv preprint arXiv:2103.03874, 2021. 2.1

    2021 arXiv

  8. [16]

    Hinton, Oriol Vinyals, and Jeffrey Dean

    Geoffrey E. Hinton, Oriol Vinyals, and Jeffrey Dean. Distilling the knowledge in a neural network.CoRR, abs/1503.02531, 2015. 6

    2015 arXiv

  9. [17]

    Kaplan, Matteo Matteucci, Supriyo Chakraborty, and Irina Rish

    Prateek Humane, Paolo Cudrano, Daniel Z. Kaplan, Matteo Matteucci, Supriyo Chakraborty, and Irina Rish. Influence functions for efficient data selection in reasoning.CoRR, abs/2510.06108, 2025. 4.1, 6, B.3

    2025

  10. [18]

    What makes a good reasoning chain? uncovering structural patterns in long chain-of-thought reasoning

    Gangwei Jiang, Yahui Liu, Zhaoyi Li, Qi Wang, Fuzheng Zhang, Linqi Song, Ying Wei, and Defu Lian. What makes a good reasoning chain? uncovering structural patterns in long chain-of-thought reasoning. CoRR, abs/2505.22148, 2025. 6

    2025 arXiv

  11. [19]

    Distilling reasoning into student llms: Local naturalness for selecting teacher data.CoRR, abs/2510.03988, 2025

    Hoang Anh Just, Myeongseob Ko, and Ruoxi Jia. Distilling reasoning into student llms: Local naturalness for selecting teacher data.CoRR, abs/2510.03988, 2025. 1, 3.2, 4.1, 6

    2025 arXiv

  12. [20]

    Gonzalez, Hao Zhang, and Ion Stoica

    Woosuk Kwon, Zhuohan Li, Siyuan Zhuang, Ying Sheng, Lianmin Zheng, Cody Hao Yu, Joseph E. Gonzalez, Hao Zhang, and Ion Stoica. Efficient memory management for large language model serving with pagedattention. InProceedings of the ACM SIGOPS 29th Symposium on Operating Systems ...

  13. [21]

    Patil, Matei Zaharia, Joseph E

    Dacheng Li, Shiyi Cao, Tyler Griggs, Shu Liu, Xiangxi Mo, Eric Tang, Sumanth Hegde, Kourosh Hakhamaneshi, Shishir G. Patil, Matei Zaharia, Joseph E. Gonzalez, and Ion Stoica. Llms can eas- ily learn to reason from demonstrations structure, not content, is what matters!CoRR, ab...

    arXiv

  14. [22]

    Numinamath: The largest public dataset in ai4maths with 860k pairs of competition math problems and solutions.Hugging Face repository, 13(9):9, 2024

    Jia Li, Edward Beeching, Lewis Tunstall, Ben Lipkin, Roman Soletskyi, Shengyi Huang, Kashif Rasul, Longhui Yu, Albert Q Jiang, Ziju Shen, et al. Numinamath: The largest public dataset in ai4maths with 860k pairs of competition math problems and solutions.Hugging Face repositor...

    2024

  15. [23]

    Small models struggle to learn from strong reasoners

    Yuetai Li, Xiang Yue, Zhangchen Xu, Fengqing Jiang, Luyao Niu, Bill Yuchen Lin, Bhaskar Ramasubrama- nian, and Radha Poovendran. Small models struggle to learn from strong reasoners. In Wanxiang Che, Joyce Nabende, Ekaterina Shutova, and Mohammad Taher Pilehvar, editors,Findin...

    2025

  16. [24]

    Air: Post-training data selection for reasoning via attention head influence.arXiv preprint arXiv:2512.13279, 2025

    Jinrui Liu, Jeff Wu, Xuanguang Pan, Gavin Cheung, Shuai Ma, and Chongyang Tao. Air: Post-training data selection for reasoning via attention head influence.arXiv preprint arXiv:2512.13279, 2025. 6

    2025

  17. [25]

    Through the valley: Path to effective long cot training for small language models.CoRR, abs/2506.07712, 2025

    Renjie Luo, Jiaxi Li, Chen Huang, and Wei Lu. Through the valley: Path to effective long cot training for small language models.CoRR, abs/2506.07712, 2025. 6

    2025

  18. [26]

    Learning what reinforcement learning can’t: Interleaved online fine-tuning for hardest questions.CoRR, abs/2506.07527, 2025

    Lu Ma, Hao Liang, Meiyi Qiang, Lexiang Tang, Xiaochen Ma, Zhen Hao Wong, Junbo Niu, Chengyu Shen, Runming He, Bin Cui, and Wentao Zhang. Learning what reinforcement learning can’t: Interleaved online fine-tuning for hardest questions.CoRR, abs/2506.07527, 2025. 6

    2025

  19. [27]

    Zipf’s and heaps’ laws for tokens and llm-generated texts

    Nikolay Mikhaylovskiy. Zipf’s and heaps’ laws for tokens and llm-generated texts. InFindings of the Association for Computational Linguistics: EMNLP 2025, pages 15469–15481, 2025. 3.3

    2025

  20. [28]

    Improved knowledge distillation via teacher assistant

    Seyed Iman Mirzadeh, Mehrdad Farajtabar, Ang Li, Nir Levine, Akihiro Matsukawa, and Hassan Ghasemzadeh. Improved knowledge distillation via teacher assistant. InProceedings of the AAAI conference on artificial intelligence, volume 34, pages 5191–5198, 2020. 6

    2020

  21. [29]

    Candès, and Tatsunori Hashimoto

    Niklas Muennighoff, Zitong Yang, Weijia Shi, Xiang Lisa Li, Li Fei-Fei, Hannaneh Hajishirzi, Luke Zettle- moyer, Percy Liang, Emmanuel J. Candès, and Tatsunori Hashimoto. s1: Simple test-time scaling.CoRR, abs/2501.19393, 2025. 1, A.1 12 Which Reasoning Trajectories Teach Stud...

    2025 arXiv

  22. [30]

    Kakade, and Surbhi Goel

    Abhishek Panigrahi, Bingbin Liu, Sadhika Malladi, Sham M. Kakade, and Surbhi Goel. In good graces: Principled teacher selection for knowledge distillation.CoRR, abs/2511.02833, 2025. 4.1, 6, B.4, B.5

    2025

  23. [31]

    Instruction tuning with GPT-4.CoRR, abs/2304.03277, 2023

    Baolin Peng, Chunyuan Li, Pengcheng He, Michel Galley, and Jianfeng Gao. Instruction tuning with GPT-4.CoRR, abs/2304.03277, 2023. 6

    2023 arXiv

  24. [32]

    Adaswitch: Adaptive switching generation for knowledge distillation.ArXiv, abs/2510.07842,

    Jingyu Peng, Maolin Wang, Hengyi Cai, Yuchen Li, Kai Zhang, Shuaiqiang Wang, Dawei Yin, and Xiangyu Zhao. Adaswitch: Adaptive switching generation for knowledge distillation.ArXiv, abs/2510.07842,

  25. [33]

    Information-guided identification of training data imprint in (proprietary) large language models

    Abhilasha Ravichander, Jillian Fisher, Taylor Sorensen, Ximing Lu, Maria Antoniak, Bill Yuchen Lin, Niloofar Mireshghallah, Chandra Bhagavatula, and Yejin Choi. Information-guided identification of training data imprint in (proprietary) large language models. In Luis Chiruzzo,...

    2025

  26. [34]

    David Rein, Betty Li Hou, Asa Cooper Stickland, Jackson Petty, Richard Yuanzhe Pang, Julien Dirani, Julian Michael, and Samuel R. Bowman. GPQA: A graduate-level google-proof q&a benchmark. InFirst Conference on Language Modeling, 2024. C.4.2

    2024

  27. [35]

    Warm up before you train: Unlocking general reasoning in resource-constrained settings.CoRR, abs/2505.13718, 2025

    Safal Shrestha, Minwu Kim, Aadim Nepal, Anubhav Shrestha, and Keith Ross. Warm up before you train: Unlocking general reasoning in resource-constrained settings.CoRR, abs/2505.13718, 2025. 6

    2025

  28. [36]

    Harvard university press, 1978

    Lev Semenovich Vygotsky and Michael Cole.Mind in society: Development of higher psychological processes. Harvard university press, 1978. 1

    1978

  29. [37]

    Chain-of-thought prompting elicits reasoning in large language models.Advances in neural information processing systems, 35:24824–24837, 2022

    Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Fei Xia, Ed Chi, Quoc V Le, Denny Zhou, et al. Chain-of-thought prompting elicits reasoning in large language models.Advances in neural information processing systems, 35:24824–24837, 2022. 1, 6

    2022

  30. [38]

    Beyond scaling law: A data-efficient distillation framework for reasoning.CoRR, abs/2508.09883, 2025

    Xiaojun Wu, Xiaoguang Jiang, Huiyang Li, Jucai Zhai, Dengfeng Liu, Qiaobo Hao, Huang Liu, Zhiguo Yang, Ji Xie, Ninglun Gu, Jin Yang, Kailai Zhang, Yelun Bao, and Jun Wang. Beyond scaling law: A data-efficient distillation framework for reasoning.CoRR, abs/2508.09883, 2025. 6

    2025 arXiv

  31. [39]

    On the generalization of SFT: A reinforcement learning perspective with reward rectification.CoRR, abs/2508.05629, 2025

    Yongliang Wu, Yizhou Zhou, Zhou Ziheng, Yingzhe Peng, Xinyu Ye, Xinting Hu, Wenbo Zhu, Lu Qi, Ming-Hsuan Yang, and Xu Yang. On the generalization of SFT: A reinforcement learning perspective with reward rectification.CoRR, abs/2508.05629, 2025. 6

    2025

  32. [40]

    Le, Dhruv Madeka, Lei Li, William Yang Wang, Rishabh Agarwal, Chen-YuLee, andTomasPfister

    Wenda Xu, Rujun Han, Zifeng Wang, Long T. Le, Dhruv Madeka, Lei Li, William Yang Wang, Rishabh Agarwal, Chen-YuLee, andTomasPfister. Speculativeknowledgedistillation: Bridgingtheteacher-student gap through interleaved sampling. InThe Thirteenth International Conference on Lear...

    2025

  33. [41]

    Qwen3 technical report.CoRR, abs/2505.09388, 2025

    An Yang, Anfeng Li, Baosong Yang, Beichen Zhang, Binyuan Hui, Bo Zheng, Bowen Yu, Chang Gao, Chengen Huang, Chenxu Lv, Chujie Zheng, Dayiheng Liu, Fan Zhou, Fei Huang, Feng Hu, Hao Ge, Haoran Wei, Huan Lin, Jialong Tang, Jian Yang, Jianhong Tu, Jianwei Zhang, Jian Yang, Jiaxi ...

    2025 arXiv

  34. [42]

    Select2reason: Efficient instruction-tuning data selection for long-cot reasoning.CoRR, abs/2505.17266,

    Cehao Yang, Xueyuan Lin, Chengjin Xu, Xuhui Jiang, Xiaojun Wu, Honghao Liu, Hui Xiong, and Jian Guo. Select2reason: Efficient instruction-tuning data selection for long-cot reasoning.CoRR, abs/2505.17266,

  35. [43]

    Measuring data diversity for instruction tuning: A systematic analysis and A reliable metric

    Yuming Yang, Yang Nan, Junjie Ye, Shihan Dou, Xiao Wang, Shuo Li, Huijie Lv, Tao Gui, Qi Zhang, and Xuanjing Huang. Measuring data diversity for instruction tuning: A systematic analysis and A reliable metric. In Wanxiang Che, Joyce Nabende, Ekaterina Shutova, and Mohammad Tah...

    2025

  36. [44]

    Analyzing the effects of supervised fine-tuning on model knowledge from token and parameter levels

    Junjie Ye, Yuming Yang, Yang Nan, Shuo Li, Qi Zhang, Tao Gui, Xuan-Jing Huang, Peng Wang, Zhongchao Shi, and Jianping Fan. Analyzing the effects of supervised fine-tuning on model knowledge from token and parameter levels. InProceedings of the 2025 Conference on Empirical Meth...

    2025

  37. [45]

    LIMO: less is more for reasoning.CoRR, abs/2502.03387, 2025

    Yixin Ye, Zhen Huang, Yang Xiao, Ethan Chern, Shijie Xia, and Pengfei Liu. LIMO: less is more for reasoning.CoRR, abs/2502.03387, 2025. 4.1, 6, A.1, B.2

    2025 arXiv

  38. [46]

    Rethinking the generation of high-quality cot data from the perspective of llm-adaptive question difficulty grading.CoRR, abs/2504.11919, 2025

    Qianjin Yu, Keyu Wu, Zihan Chen, Chushu Zhang, Manlin Mei, Lingjun Huang, Fang Tan, Yongsheng Du, Kunlin Liu, and Yurui Zhu. Rethinking the generation of high-quality cot data from the perspective of llm-adaptive question difficulty grading.CoRR, abs/2504.11919, 2025. 6

    2025 arXiv

  39. [47]

    Spearman rank correlation.Encyclopedia of biostatistics, 7, 2005

    Jerrold H Zar. Spearman rank correlation.Encyclopedia of biostatistics, 7, 2005. A.7

    2005

  40. [48]

    Towards the law of capacity gap in distilling language models

    Chen Zhang, Qiuchi Li, Dawei Song, Zheyu Ye, Yan Gao, and Yao Hu. Towards the law of capacity gap in distilling language models. In Wanxiang Che, Joyce Nabende, Ekaterina Shutova, and Mohammad Taher Pilehvar, editors,Proceedings of the 63rd Annual Meeting of the Association fo...

    2025

  41. [49]

    The best instruction-tuning data are those that fit.CoRR, abs/2502.04194, 2025

    Dylan Zhang, Qirun Dai, and Hao Peng. The best instruction-tuning data are those that fit.CoRR, abs/2502.04194, 2025. 1, 3.2

    2025

  42. [50]

    What, how, where, and how well? A survey on test-time scaling in large language models.CoRR, abs/2503.24235, 2025

    Qiyuan Zhang, Fuyuan Lyu, Zexu Sun, Lei Wang, Weixu Zhang, Zhihan Guo, Yufei Wang, Irwin King, Xue Liu, and Chen Ma. What, how, where, and how well? A survey on test-time scaling in large language models.CoRR, abs/2503.24235, 2025. 1

    2025 arXiv

  43. [51]

    BREAD: branched rollouts from expert anchors bridge SFT & RL for reasoning.CoRR, abs/2506.17211, 2025

    Xuechen Zhang, Zijian Huang, Yingcong Li, Chenshun Ni, Jiasi Chen, and Samet Oymak. BREAD: branched rollouts from expert anchors bridge SFT & RL for reasoning.CoRR, abs/2506.17211, 2025. 6

    2025 arXiv

  44. [52]

    Llamafactory: Unified efficient fine-tuning of 100+ language models

    YaoweiZheng, RichongZhang, JunhaoZhang, YanhanYe, ZheyanLuo, ZhangchiFeng, andYongqiangMa. Llamafactory: Unified efficient fine-tuning of 100+ language models. InProceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 3: System Demonstra...

    2024

  45. [53]

    LIMA: less is more for alignment

    Chunting Zhou, Pengfei Liu, Puxin Xu, Srinivasan Iyer, Jiao Sun, Yuning Mao, Xuezhe Ma, Avia Efrat, Ping Yu, Lili Yu, Susan Zhang, Gargi Ghosh, Mike Lewis, Luke Zettlemoyer, and Omer Levy. LIMA: less is more for alignment. In Alice Oh, Tristan Naumann, Amir Globerson, Kate Sae...

    2023

  46. [54]

    Routledge,

    George Kingsley Zipf.The psycho-biology of language: An introduction to dynamic philology. Routledge,

  47. [55]

    Return your final response within \boxed{}

    Jiaru Zou, Ling Yang, Jingwen Gu, Jiahao Qiu, Ke Shen, Jingrui He, and Mengdi Wang. Reasonflux-prm: Trajectory-aware prms for long chain-of-thought reasoning in llms.CoRR, abs/2506.18896, 2025. 6 14 Which Reasoning Trajectories Teach Students to Reason Better? A Simple Metric ...

    2025

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.