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arxiv: 2606.02113 · v1 · pith:OZVF2K7Mnew · submitted 2026-06-01 · 💻 cs.CL · cs.AI

A Primer in Post-Training Reasoning Data: What We Know About How It Works

Yaoming Li , Guangxiang Zhao , Qilong Shi , Lin Sun , Xiangzheng Zhang , Tong Yang This is my paper

Pith reviewed 2026-06-28 14:38 UTC · model grok-4.3

classification 💻 cs.CL cs.AI
keywords post-trainingreasoning datalarge reasoning modelsdata constructionscalingreinforcement learningreward models
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The pith

A four-question framework organizes the literature on post-training reasoning data to enable attribution of model gains.

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

The paper synthesizes over 150 public studies and system reports on reasoning data used after initial training of large models. It groups the scattered work into four questions covering what data objects exist, what makes them useful, how they are constructed, and how they scale. This structure is presented as an attribution framework that links specific data choices to outcomes in post-training. A reader would care because post-training has become a primary driver of progress in reasoning capabilities, and scattered findings make it hard to design effective new datasets or recipes without such an organizing lens.

Core claim

This paper claims to be the first primer that pulls together more than 150 studies across dataset papers, reinforcement-learning recipes, reward-model work, benchmarks, and frontier reports, then organizes them around four questions on data objects, usefulness, construction, and scaling to supply an attribution framework for future reasoning-data releases and post-training recipes.

What carries the argument

The four-question attribution framework that maps existing work onto data objects, usefulness, construction, and scaling.

If this is right

  • New reasoning datasets can be released with explicit documentation against the four questions.
  • Post-training recipes can diagnose success or failure by tracing back to specific data properties.
  • Reward-model and benchmark papers can be compared using the same structure.
  • Frontier system reports can be used to update or refine the framework over time.

Where Pith is reading between the lines

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

  • The framework could be applied to test whether a proposed new dataset fills gaps across all four questions.
  • Similar four-question structures might be tested on post-training data for alignment or safety tasks.
  • Controlled experiments could check if data choices predicted to be useful by the framework actually produce larger gains.

Load-bearing premise

The selected set of over 150 studies is representative of the field and the four questions capture the load-bearing variables without omitting critical unexamined factors.

What would settle it

A new empirical study on post-training reasoning data whose results cannot be mapped to any of the four questions or whose outcomes contradict attributions made by the framework.

Figures

Figures reproduced from arXiv: 2606.02113 by Guangxiang Zhao, Lin Sun, Qilong Shi, Tong Yang, Xiangzheng Zhang, Yaoming Li.

Figure 1
Figure 1. Figure 1: Beyond prompt–response pairs. A reasoning-data item packages a problem or state, model behavior, judging feedback, and attribution metadata. The map previews four questions: objects, usefulness, construction, and gain attribution [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Verifier-anchored taxonomy. Verification contracts, rather than domains, define the native signal, trainable object, failure surface, and required audit fields of a reasoning sample. Judgment-required verification. When no de￾terministic verifier exists, the reusable unit is an au￾ditable judgment record. Medical, factuality, safety, and rubric-reward datasets attach criteria, evidence, risk, provenance, j… view at source ↗
Figure 4
Figure 4. Figure 4: Quality support matrix. No single field li￾censes all quality claims: correctness, difficulty, trace quality, and coverage each require different verifier, base, trajectory, and lineage evidence [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Two common quality traps: long trace ̸= good trace, hard item ̸= useful item. Trace quality de￾pends on validity and grounding, while useful difficulty lies between always-fail and always-pass regimes for a given base and sampling protocol. 3.1 Correctness Is Verifier-Relative Correctness is a versioned verifier contract, not an answer string. DeepMath-103K and DAPO show that extraction, normalization, rul… view at source ↗
Figure 6
Figure 6. Figure 6: Verifier families and failure surfaces. A reward channel is itself a data object: formal checkers, process verifiers, learned reward models, rubric judges, and implicit selectors expose different use cases, failure modes, and audit fields. pseudo-label accuracy can degrade as generated tasks harden (Wu et al., 2026; Huang et al., 2026a). AlphaEvolve illustrates the counter-pressure: dis￾covery is auditable… view at source ↗
Figure 7
Figure 7. Figure 7: Asymptote–efficiency decomposition. A scaling result can change what the data substrate makes reachable, how efficiently training approaches that fron￾tier, or both. 5.1 Asymptotes and Efficiency The useful commonality between the Khatri and Tan laws is the separation in [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Small-pool versus large-pool coverage. Small curated pools can be effective when they repeat￾edly sample the active band of a capable base; larger pools matter when useful gradients lie in the tail or must cover multiple bases, verifiers, or domains. behaviour when the base already supports the skill (Ye et al., 2025; Yue et al., 2025; Wu et al., 2026). OpenThoughts and Big-Math expose the opposite regime,… view at source ↗
read the original abstract

Post-training has become a primary driver of recent progress in large reasoning models, and reasoning data are often the key variable determining whether this stage succeeds. Work on post-training reasoning data has grown rapidly, yet this literature remains scattered across dataset papers, reinforcement-learning recipes, reward-model studies, benchmarks, and frontier system reports. This paper is the first primer to synthesize over 150 key public studies and system reports on post-training reasoning data. We organize the field around four questions: what data objects exist, what makes them useful, how they are constructed, and how they scale. Together, this organization provides an attribution framework for future reasoning-data releases and post-training recipes.

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 manuscript claims to be the first primer synthesizing over 150 key public studies and system reports on post-training reasoning data. It organizes the literature around four questions—what data objects exist, what makes them useful, how they are constructed, and how they scale—thereby providing an attribution framework for future reasoning-data releases and post-training recipes.

Significance. If the synthesis is accurate and representative and the four-question organization captures the dominant causal variables, the work would supply a structured overview of a rapidly expanding but scattered literature. This could help attribute performance gains in reasoning models to specific data choices and guide the design of future post-training pipelines. The breadth of coverage (over 150 studies) would be a notable strength if supported by transparent selection methods.

major comments (2)
  1. Introduction: The claim to synthesize 'over 150 key public studies' is presented without any disclosed literature search protocol, inclusion/exclusion criteria, or coverage audit. This is load-bearing for the central claim of delivering a representative attribution framework, because it leaves open whether studies on data contamination, multimodal reasoning data, or interactions with base-model pre-training distributions were systematically included or omitted.
  2. Four-question organization (sections describing data objects, usefulness, construction, and scaling): The framework does not explicitly examine interactions between post-training reasoning data and either the base model's pre-training distribution or reward-model specifics. If these interactions are load-bearing for reasoning performance, the attribution framework is incomplete by construction.
minor comments (1)
  1. Abstract and introduction: The target audience and the precise ways in which this primer differs from prior surveys on RLHF or general post-training could be stated more explicitly.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which identify opportunities to improve transparency and scope in our literature synthesis. We address each major comment below and will incorporate revisions accordingly.

read point-by-point responses

  1. Referee: Introduction: The claim to synthesize 'over 150 key public studies' is presented without any disclosed literature search protocol, inclusion/exclusion criteria, or coverage audit. This is load-bearing for the central claim of delivering a representative attribution framework, because it leaves open whether studies on data contamination, multimodal reasoning data, or interactions with base-model pre-training distributions were systematically included or omitted.

    Authors: We agree that the absence of an explicit literature search protocol is a limitation. In the revised manuscript we will add a dedicated appendix (or methods subsection) that describes the search strategy, primary sources (arXiv, ACL/NeurIPS/ICLR proceedings, and system reports), inclusion criteria centered on post-training reasoning data, and a brief coverage audit. We will also note areas such as multimodal reasoning data and contamination studies that were included opportunistically rather than through exhaustive systematic review. revision: yes

  2. Referee: Four-question organization (sections describing data objects, usefulness, construction, and scaling): The framework does not explicitly examine interactions between post-training reasoning data and either the base model's pre-training distribution or reward-model specifics. If these interactions are load-bearing for reasoning performance, the attribution framework is incomplete by construction.

    Authors: The four-question structure is intentionally scoped to the properties and behaviors of the reasoning data itself. Interactions with pre-training distributions and reward models are referenced where supported by existing studies (particularly within the scaling and usefulness sections), but we concur that a more explicit treatment would strengthen the attribution claims. We will add a concise subsection on cross-stage interactions, drawing on available evidence, while preserving the primer's focus on post-training data. revision: yes

Circularity Check

0 steps flagged

No circularity: synthesis paper with no derivations or self-referential reductions

full rationale

The paper is a literature review that synthesizes over 150 existing studies and organizes them around four questions (data objects, usefulness, construction, scaling) to provide an attribution framework. It contains no equations, fitted parameters, predictions, or derivations that could reduce to inputs by construction. No self-citation chains, ansatzes, or uniqueness theorems are invoked as load-bearing premises for any result. The central claim is the value of the organizational synthesis itself, which is independent of the paper's own inputs and does not match any of the enumerated circularity patterns. This is a self-contained review against external literature.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

As a literature synthesis, the paper introduces no new free parameters, axioms, or invented entities; all content is drawn from cited prior work.

pith-pipeline@v0.9.1-grok · 5649 in / 1025 out tokens · 22186 ms · 2026-06-28T14:38:32.210235+00:00 · methodology

discussion (0)

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Works this paper leans on

18 extracted references · 9 linked inside Pith · cited by 1 Pith paper

  1. [1]

    arXiv preprint arXiv:2505.13388

    R3: Robust rubric-agnostic reward models. arXiv preprint arXiv:2505.13388. Rahul K. Arora, Jason Wei, Rebecca Soskin Hicks, Pre- ston Bowman, Joaquin Quiñonero-Candela, Foivos Tsimpourlas, Michael Sharman, Meghan Shah, An- drea Vallone, Alex Beutel, Johannes Heidecke, and Karan Singhal. 2025. Healthbench: Evaluating large language models towards improved ...

    arXiv 2025

  2. [2]

    Distillation scaling laws.arXiv preprint arXiv:2502.08606. Mark Chen, Jerry Tworek, Heewoo Jun, Qiming Yuan, Henrique Ponde de Oliveira Pinto, Jared Kaplan, Harri Edwards, Yuri Burda, Nicholas Joseph, Greg Brockman, Alex Ray, Raul Puri, Gretchen Krueger, Michael Petrov, Heidy Khlaaf, Girish Sastry, Pamela Mishkin, Brooke Chan, Scott Gray, and 39 others

    arXiv

  3. [3]

    Yixing Chen, Yiding Wang, Siqi Zhu, Haofei Yu, Tao Feng, Muhan Zhang, Mostofa Patwary, and Jiaxuan You

    Evaluating large language models trained on code.arXiv preprint arXiv:2107.03374. Yixing Chen, Yiding Wang, Siqi Zhu, Haofei Yu, Tao Feng, Muhan Zhang, Mostofa Patwary, and Jiaxuan You. 2025. Multi-agent evolve: Llm self-improve through co-evolution.arXiv preprint arXiv:2510.23595. Zhiyu Chen, Wenhu Chen, Charese Smiley, Sameena Shah, Iana Borova, Dylan L...

    Pith/arXiv arXiv 2025

  4. [4]

    Ganqu Cui, Lifan Yuan, Ning Ding, Guanming Yao, Bingxiang He, Wei Zhu, Yuan Ni, Guotong Xie, Ruobing Xie, Yankai Lin, Zhiyuan Liu, and Maosong Sun

    Training verifiers to solve math word prob- lems.arXiv preprint arXiv:2110.14168. Ganqu Cui, Lifan Yuan, Ning Ding, Guanming Yao, Bingxiang He, Wei Zhu, Yuan Ni, Guotong Xie, Ruobing Xie, Yankai Lin, Zhiyuan Liu, and Maosong Sun. 2024. Ultrafeedback: Boosting language models with scaled ai feedback.arXiv preprint arXiv:2310.01377. Ganqu Cui, Lifan Yuan, Z...

    Pith/arXiv arXiv 2024

  5. [5]

    Yihong Dong, Xue Jiang, Yongding Tao, Huanyu Liu, Kechi Zhang, Lili Mou, Rongyu Cao, Yingwei Ma, 10 Jue Chen, Binhua Li, Zhi Jin, Fei Huang, Yongbin Li, and Ge Li

    Mind2web: Towards a generalist agent for the web.arXiv preprint arXiv:2306.06070. Yihong Dong, Xue Jiang, Yongding Tao, Huanyu Liu, Kechi Zhang, Lili Mou, Rongyu Cao, Yingwei Ma, 10 Jue Chen, Binhua Li, Zhi Jin, Fei Huang, Yongbin Li, and Ge Li. 2026. Rl-plus: Countering capability boundary collapse of llms in reinforcement learn- ing with hybrid-policy o...

    Pith/arXiv arXiv 2026

  6. [6]

    Yixiong Fang, Tianran Sun, Yuling Shi, Min Wang, and Xiaodong Gu

    Workarena: How capable are web agents at solving common knowledge work tasks?arXiv preprint arXiv:2403.07718. Yixiong Fang, Tianran Sun, Yuling Shi, Min Wang, and Xiaodong Gu. 2025. Lastingbench: Defend bench- marks against knowledge leakage.arXiv preprint arXiv:2506.21614. Kanishk Gandhi, Ayush Chakravarthy, Anikait Singh, Nathan Lile, and Noah D. Goodma...

    Pith/arXiv arXiv 2025

  7. [7]

    Seungju Han, Kavel Rao, Allyson Ettinger, Liwei Jiang, Bill Yuchen Lin, Nathan Lambert, Yejin Choi, and Nouha Dziri

    Rubrics as rewards: Reinforcement learn- ing beyond verifiable domains.arXiv preprint arXiv:2507.17746. Seungju Han, Kavel Rao, Allyson Ettinger, Liwei Jiang, Bill Yuchen Lin, Nathan Lambert, Yejin Choi, and Nouha Dziri. 2024. Wildguard: Open one-stop mod- eration tools for safety risks, jailbreaks, and refusals of llms.arXiv preprint arXiv:2406.18495. Zi...

    Pith/arXiv arXiv 2024

  8. [8]

    arXiv preprint arXiv:2602.00846

    Omni-rrm: Advancing omni reward modeling via automatic rubric-grounded preference synthesis. arXiv preprint arXiv:2602.00846. Masahiro Koreeda and Christopher Manning. 2021. Contractnli: A dataset for document-level natural language inference for contracts. InEMNLP. Nathan Lambert, Valentina Pyatkin, Jacob Morrison, LJ Miranda, Bill Yuchen Lin, Khyathi Ch...

    arXiv 2021

  9. [9]

    Stephanie Lin, Jacob Hilton, and Owain Evans

    Let’s verify step by step.arXiv preprint arXiv:2305.20050. Stephanie Lin, Jacob Hilton, and Owain Evans. 2022. Truthfulqa: Measuring how models mimic human falsehoods.arXiv preprint arXiv:2109.07958. Yong Lin, Shange Tang, Bohan Lyu, Ziran Yang, Jui- Hui Chung, Haoyu Zhao, Lai Jiang, Yihan Geng, Jiawei Ge, Jingruo Sun, Jiayun Wu, Jiri Gesi, Ximing Lu, Dav...

    Pith/arXiv arXiv 2022

  10. [10]

    arXiv preprint arXiv:2410.05229

    Gsm-symbolic: Understanding the limitations of mathematical reasoning in large language models. arXiv preprint arXiv:2410.05229. Mistral-AI, :, Abhinav Rastogi, Albert Q. Jiang, Andy Lo, Gabrielle Berrada, Guillaume Lample, Jason Rute, Joep Barmentlo, Karmesh Yadav, Kartik Khan- delwal, Khyathi Raghavi Chandu, Léonard Blier, Lu- cile Saulnier, Matthieu Di...

    Pith/arXiv arXiv

  11. [11]

    Kaixiang Mo, Yuxin Shi, Weiwei Weng, Zhiqiang Zhou, Shuman Liu, Haibo Zhang, and Anxiang Zeng

    Magistral.arXiv preprint arXiv:2506.10910. Kaixiang Mo, Yuxin Shi, Weiwei Weng, Zhiqiang Zhou, Shuman Liu, Haibo Zhang, and Anxiang Zeng. 2025. Mid-training of large language models: A survey. arXiv preprint arXiv:2510.06826. Ivan Moshkov, Darragh Hanley, Ivan Sorokin, Shubham Toshniwal, Christof Henkel, Benedikt Schifferer, Wei Du, and Igor Gitman. 2025....

    arXiv 2025

  12. [12]

    David Rein, Betty Li Hou, Asa Cooper Stickland, Jackson Petty, Richard Yuanzhe Pang, Julien Di- rani, Julian Michael, and Samuel R

    Androidworld: A dynamic benchmarking en- vironment for autonomous agents.arXiv preprint arXiv:2405.14573. David Rein, Betty Li Hou, Asa Cooper Stickland, Jackson Petty, Richard Yuanzhe Pang, Julien Di- rani, Julian Michael, and Samuel R. Bowman. 2023. Gpqa: A graduate-level google-proof q&a bench- mark.arXiv preprint arXiv:2311.12022. Z. Z. Ren, Zhihong S...

    Pith/arXiv arXiv 2023

  13. [13]

    arXiv preprint arXiv:2407.18901

    Appworld: A controllable world of apps and people for benchmarking interactive coding agents. arXiv preprint arXiv:2407.18901. George Tsatsaronis, Georgios Balikas, Prodromos Malakasiotis, Ioannis Partalas, Matthias Zschunke, Michael R. Alvers, Dirk Weissenborn, Anastasia Krithara, Sergios Petridis, Dimitris Polychronopou- los, Yannis Almirantis, John Pav...

    arXiv 2015

  14. [14]

    Xingyao Wang, Boxuan Li, Yufan Song, Frank F

    Math-shepherd: Verify and reinforce llms step- by-step without human annotations.arXiv preprint arXiv:2312.08935. Xingyao Wang, Boxuan Li, Yufan Song, Frank F. Xu, Xiangru Tang, Mingchen Zhuge, Jiayi Pan, Yueqi Song, Bowen Li, Jaskirat Singh, Hoang H. Tran, Fuqiang Li, Ren Ma, Mingzhang Zheng, Bill Qian, Yanjun Shao, Niklas Muennighoff, Yizhe Zhang, Binyu...

    Pith/arXiv arXiv 2025

  15. [15]

    Yang Yue, Zhiqi Chen, Rui Lu, Andrew Zhao, Zhaokai Wang, Yang Yue, Shiji Song, and Gao Huang

    Naturalreasoning: Reasoning in the wild with 2.8m challenging questions.arXiv preprint arXiv:2502.13124. Yang Yue, Zhiqi Chen, Rui Lu, Andrew Zhao, Zhaokai Wang, Yang Yue, Shiji Song, and Gao Huang. 2025. Does reinforcement learning really incentivize rea- soning capacity in llms beyond the base model? arXiv preprint arXiv:2504.13837. 16 Eric Zelikman, Yu...

    arXiv 2025

  16. [16]

    InThe Tenth In- ternational Conference on Learning Representations, ICLR 2022, Virtual Event, April 25-29, 2022

    minif2f: a cross-system benchmark for for- mal olympiad-level mathematics. InThe Tenth In- ternational Conference on Learning Representations, ICLR 2022, Virtual Event, April 25-29, 2022. Open- Review.net. Lucia Zheng, Neel Guha, Brandon R. Anderson, Peter Henderson, and Daniel E. Ho. 2021. When does pre- training help?: assessing self-supervised learning...

    2022

  17. [17]

    Fengbin Zhu, Wenqiang Lei, Youcheng Huang, Chao Wang, Shuo Zhang, Jiancheng Lv, Fuli Feng, and Tat-Seng Chua

    OpenReview.net. Fengbin Zhu, Wenqiang Lei, Youcheng Huang, Chao Wang, Shuo Zhang, Jiancheng Lv, Fuli Feng, and Tat-Seng Chua. 2021. Tat-qa: A question answering benchmark on a hybrid of tabular and textual content in finance.arXiv preprint arXiv:2105.07624. Lianghui Zhu, Xinggang Wang, and Xinlong Wang

    arXiv 2021

  18. [18]

    self-generated

    Judgelm: Fine-tuned large language models are scalable judges.arXiv preprint arXiv:2310.17631. Terry Yue Zhuo, Minh Chien Vu, Jenny Chim, Han Hu, Wenhao Yu, Ratnadira Widyasari, Imam Nur Bani Yusuf, Haolan Zhan, Junda He, Indraneil Paul, Simon Brunner, Chen Gong, Thong Hoang, Armel Randy Zebaze, Xiaoheng Hong, Wen-Ding Li, Jean Kad- dour, Ming Xu, Zhihan ...

    arXiv 2025