arxiv: 2605.05226 · v1 · submitted 2026-04-19 · 💻 cs.LG · cs.AI· cs.CL

Recognition: unknown

Internalizing Outcome Supervision into Process Supervision: A New Paradigm for Reinforcement Learning for Reasoning

Fei Ding , Yongkang Zhang , Runhao Liu , Yuhao Liao , Zijian Zeng , Sibo Wang , Huiming Yang

Authors on Pith no claims yet

Pith reviewed 2026-05-10 06:09 UTC · model grok-4.3

classification 💻 cs.LG cs.AIcs.CL

keywords reinforcement learningreasoningprocess supervisionoutcome supervisioncredit assignmentself-supervisionlanguage models

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The pith

Reinforcement learning for reasoning works by internalizing outcome supervision into process supervision.

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

The paper argues that the core difficulty in RL for reasoning is not just sparse final rewards but the need to convert those into usable signals at each intermediate step. It reframes the task as internalizing outcome supervision into process supervision, so that the model itself locates errors in its own reasoning paths, fixes them, and reuses the corrected paths to create its own training signals. This produces finer credit assignment during policy updates while using only outcome-level feedback. The result is presented as a new paradigm in which the model continually generates and refines internal process supervision on its own during training.

Core claim

Reinforcement learning for reasoning can be understood as the problem of internalizing outcome supervision into process supervision. From this perspective, we introduce a supervision-internalization method for reinforcement learning for reasoning, enabling the model to automatically extract process-level learning signals through identifying, correcting, and reusing failed reasoning trajectories, thereby achieving finer-grained policy optimization under outcome-only supervision. We further abstract this idea into a new training paradigm, in which the model continually generates and refines its own internal process supervision during reinforcement learning.

What carries the argument

The supervision-internalization method, which lets the model identify, correct, and reuse failed reasoning trajectories to turn outcome supervision into process-level signals.

If this is right

Finer-grained policy optimization becomes possible using only outcome supervision.
The model generates and refines its own process supervision continuously during training.
Credit assignment no longer requires costly externally constructed process labels.
A self-sustaining loop emerges for improving reasoning step by step.

Where Pith is reading between the lines

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

Training cost for reasoning models could drop if the need for human-written process annotations is removed.
The same internalization loop might extend to other sequential decision tasks where only terminal feedback is cheap to obtain.
Performance would likely depend on how accurately the model spots its own errors before reusing them.

Load-bearing premise

Models can reliably identify, correct, and reuse failed reasoning trajectories to produce accurate process-level learning signals without external supervision or introducing new errors.

What would settle it

A controlled run in which the internalized process signals are extracted from outcome rewards alone yet produce no gain (or a loss) in final reasoning accuracy compared with standard outcome-only RL.

Figures

Figures reproduced from arXiv: 2605.05226 by Fei Ding, Huiming Yang, Runhao Liu, Sibo Wang, Yongkang Zhang, Yuhao Liao, Zijian Zeng.

**Figure 2.** Figure 2: Internalizing outcome supervision into process supervision. Existing paradigm [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

read the original abstract

The central challenge of reinforcement learning for reasoning lies not only in the sparsity of outcome-level supervision, but more fundamentally in how to transform feedback provided only at the end of a sequence into fine-grained learning signals that can guide intermediate reasoning steps. Existing approaches either rely on outcome-level rewards for sequence-level optimization, which makes precise credit assignment difficult, or depend on externally constructed process supervision, which is costly and difficult to scale sustainably. To address this, we propose a new perspective: reinforcement learning for reasoning can be understood as the problem of internalizing outcome supervision into process supervision. From this perspective, we introduce a supervision-internalization method for reinforcement learning for reasoning, enabling the model to automatically extract process-level learning signals through identifying, correcting, and reusing failed reasoning trajectories, thereby achieving finer-grained policy optimization under outcome-only supervision. We further abstract this idea into a new training paradigm, in which the model continually generates and refines its own internal process supervision during reinforcement learning, opening a new path for fine-grained credit assignment in reinforcement learning for reasoning that differs from externally provided process supervision.

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

A high-level reframing of RL for reasoning as self-internalized process supervision from failed trajectories, but it stays conceptual with no implementation or tests to back the central assumption.

read the letter

The paper's main pitch is that RL for reasoning should be seen as turning outcome-only rewards into internal process signals by having the model spot errors in its failed runs, correct them, and reuse those as training data. This leads to a training loop where the model keeps generating and refining its own finer-grained supervision without external labels. They position it as a distinct paradigm from both pure outcome RL and costly human-provided process supervision. That framing is clear and directly addresses a real pain point around scaling supervision for multi-step reasoning tasks. It gives credit to the limitations of existing approaches without overclaiming novelty beyond the internalization angle. What stands out is the emphasis on continual self-refinement during RL rather than one-shot external signals. The soft spot is the load-bearing assumption that the model can reliably localize which intermediate step caused a terminal failure and then produce a verifiably better correction, all using only the outcome signal. In branching reasoning domains, many different error locations produce the same bad outcome, so self-correction is underdetermined and risks reinforcing or inventing new mistakes. The abstract and proposal contain no equations, algorithm sketch, toy example, or experiment, so there is no evidence this mechanism works or avoids error amplification. The full text appears to stay at the perspective level. This is for people already working on credit assignment and self-improvement in reasoning models who want a new way to think about the supervision bottleneck. It could generate useful discussion in a reading group but does not yet deliver something citable or usable. I would send it for peer review as a conceptual piece if the authors add concrete details and at least small-scale validation; otherwise it risks remaining too vague to engage seriously.

Referee Report

2 major / 0 minor

Summary. The paper proposes reframing reinforcement learning for reasoning as the problem of internalizing outcome supervision into process supervision. It introduces a conceptual 'supervision-internalization method' that enables models to automatically extract process-level learning signals by identifying, correcting, and reusing failed reasoning trajectories under outcome-only supervision, and abstracts this into a new training paradigm of continual self-generation and refinement of internal process supervision.

Significance. If the internalization mechanism could be made reliable and scalable, the perspective would offer a promising route to fine-grained credit assignment in reasoning RL without the cost of external process annotations, potentially advancing self-supervised approaches in the field. However, the manuscript provides no formalization, algorithms, or empirical results, so its significance is currently speculative and depends entirely on future development of the core idea.

major comments (2)

[Abstract] Abstract: the claim that the model can 'automatically extract process-level learning signals through identifying, correcting, and reusing failed reasoning trajectories' is load-bearing for the entire proposal yet lacks any description of the localization, correction, or verification procedures. Without an external reference for per-step credit, this risks the error amplification noted in the stress-test, where multiple distinct failure points can produce the same negative outcome.
[Abstract] Abstract: no equations, pseudocode, training algorithm, or experimental protocol is supplied to instantiate the 'supervision-internalization method' or the 'new training paradigm,' leaving the central contribution at the level of an untested perspective rather than a verifiable contribution.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive review and for recognizing the potential significance of reframing reinforcement learning for reasoning through supervision internalization. We agree that the manuscript is a conceptual proposal rather than a fully instantiated method, and we address the specific concerns below while clarifying the intended scope of the work.

read point-by-point responses

Referee: [Abstract] Abstract: the claim that the model can 'automatically extract process-level learning signals through identifying, correcting, and reusing failed reasoning trajectories' is load-bearing for the entire proposal yet lacks any description of the localization, correction, or verification procedures. Without an external reference for per-step credit, this risks the error amplification noted in the stress-test, where multiple distinct failure points can produce the same negative outcome.

Authors: We acknowledge that the abstract presents the core idea at a high level without specifying concrete procedures for localizing failures within trajectories, correcting them, or verifying the resulting process signals. This is because the contribution is the paradigm of internalizing outcome supervision rather than a particular algorithmic realization. The concern about error amplification in the absence of external per-step credit is valid and merits explicit discussion; we will revise the manuscript to include a dedicated subsection on potential failure modes and mitigation approaches, such as iterative self-correction or consistency checks across multiple trajectories. Detailed localization and verification mechanisms remain topics for subsequent empirical work. revision: partial
Referee: [Abstract] Abstract: no equations, pseudocode, training algorithm, or experimental protocol is supplied to instantiate the 'supervision-internalization method' or the 'new training paradigm,' leaving the central contribution at the level of an untested perspective rather than a verifiable contribution.

Authors: The manuscript is deliberately framed as a perspective paper that introduces a new conceptual paradigm for transforming outcome supervision into internalized process supervision. Supplying specific equations or pseudocode at this stage would require committing to one implementation, which could narrow the generality of the proposed shift away from externally annotated process supervision. We will revise the paper to include a high-level conceptual outline of the training loop (continual generation, failure identification, and refinement of internal signals) to make the paradigm more tangible, while explicitly stating that concrete algorithms and protocols constitute future research directions. revision: yes

Circularity Check

0 steps flagged

No circularity: conceptual reframing with no self-referential derivation

full rationale

The paper advances a new perspective that RL for reasoning is the problem of internalizing outcome supervision into process supervision, implemented via a method where the model identifies, corrects, and reuses failed trajectories to generate internal process signals. This is presented as an innovative training paradigm rather than a mathematical derivation or fitted result. No equations, parameters, or predictions are shown that reduce to their own inputs by construction. No self-citations, uniqueness theorems, or ansatzes from prior author work are invoked to justify the core claim. The proposal is self-contained as a methodological suggestion; any implementation risks (e.g., error amplification) pertain to correctness, not circularity in the derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that failed trajectories contain recoverable process information that a model can reliably extract and reuse without external labels or error amplification.

axioms (1)

domain assumption Outcome-only supervision can be transformed into accurate process-level signals through model-driven identification and correction of failed trajectories
This is the core premise stated in the abstract that enables the entire internalization method.

pith-pipeline@v0.9.0 · 5508 in / 1261 out tokens · 28303 ms · 2026-05-10T06:09:20.358188+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

29 extracted references · 28 canonical work pages · 14 internal anchors

[1]

MathArena: Evaluating LLMs on Uncontaminated Math Competitions

Mislav Balunovi ´c, Jasper Dekoninck, Ivo Petrov, Nikola Jovanovi ´c, and Martin Vechev. MathArena: Evaluating LLMs on uncontaminated math competitions.arXiv preprint arXiv:2505.23281,

work page internal anchor Pith review arXiv
[2]

Process Reinforcement through Implicit Rewards

Ganqu Cui, Lifan Yuan, Zefan Wang, Hanbin Wang, Wendi Li, Bingxiang He, Yuchen Fan, Tianyu Yu, Qixin Xu, Weize Chen, et al. Process reinforcement through implicit rewards. arXiv preprint arXiv:2502.01456,

work page internal anchor Pith review arXiv
[3]

DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning

DeepSeek-AI, Daya Guo, Dejian Yang, Haowei Zhang, Junxiao Song, Ruoyu Zhang, Runxin Xu, Qihao Zhu, Shirong Ma, Peiyi Wang, Xiao Bi, et al. DeepSeek-R1: Incentivizing reasoning capability in LLMs via reinforcement learning.arXiv preprint arXiv:2501.12948,

work page internal anchor Pith review Pith/arXiv arXiv
[4]

InFindings of the Association for Computational Linguistics: ACL 2025, pages 18974–18988, Vienna, Austria

Alex Havrilla, Yuqing Du, Sharath Chandra Raparthy, Christoforos Nalmpantis, Jane Dwivedi-Yu, Maksym Zhuravinskyi, Eric Hambro, Sainbayar Sukhbaatar, and Roberta Raileanu. Teaching large language models to reason with reinforcement learning.arXiv preprint arXiv:2403.04642,

work page arXiv
[5]

LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code

Naman Jain, King Han, Alex Gu, Wen-Ding Li, Fanjia Yan, Tianjun Zhang, Sida Wang, Ar- mando Solar-Lezama, Koushik Sen, and Ion Stoica. LiveCodeBench: Holistic and contam- ination free evaluation of large language models for code.arXiv preprint arXiv:2403.07974,

work page internal anchor Pith review arXiv
[6]

Process reward models that think.arXiv preprint arXiv:2504.16828, 2025

Muhammad Khalifa, Rishabh Agarwal, Lajanugen Logeswaran, Jaekyeom Kim, Hao Peng, Moontae Lee, Honglak Lee, and Lu Wang. Process reward models that think.arXiv preprint arXiv:2504.16828,

work page arXiv
[7]

Training language models to self-correct via reinforcement learning.arXiv preprint arXiv:2409.12917, 2024

Aviral Kumar, Vincent Zhuang, Rishabh Agarwal, Yi Su, John D. Co-Reyes, Avi Singh, Kate Baumli, Shariq Iqbal, Colton Bishop, Rebecca Roelofs, Lei M. Zhang, Kay McKinney, Disha Shrivastava, Cosmin Paduraru, George Tucker, Doina Precup, Feryal Behbahani, and Aleksandra Faust. Training language models to self-correct via reinforcement learning. arXiv preprin...

work page arXiv
[8]

ReVISE: Learning to refine at test-time via intrinsic self-verification.arXiv preprint arXiv:2502.14565,

Hyunseok Lee, Seunghyuk Oh, Jaehyung Kim, Jinwoo Shin, and Jihoon Tack. ReVISE: Learning to refine at test-time via intrinsic self-verification.arXiv preprint arXiv:2502.14565,

work page arXiv
[9]

Learning from the irrecoverable: Error-localized policy optimization for tool-integrated llm reasoning

Qiao Liang, Yuke Zhu, Chao Ge, Lei Yang, Ying Shen, Bo Zheng, and Sheng Guo. Learn- ing from the irrecoverable: Error-localized policy optimization for tool-integrated LLM reasoning.arXiv preprint arXiv:2602.09598,

work page arXiv
[10]

Let's Verify Step by Step

Hunter Lightman, Vineet Kosaraju, Yura Burda, Harrison Edwards, Bowen Baker, Teddy Lee, Jan Leike, John Schulman, Ilya Sutskever, and Karl Cobbe. Let’s verify step by step. arXiv preprint arXiv:2305.20050,

work page internal anchor Pith review arXiv
[11]

Save the good prefix: Precise error penalization via process-supervised rl to enhance llm reasoning.arXiv preprint arXiv:2601.18984, 2026

Haolin Liu, Dian Yu, Sidi Lu, Yujun Zhou, Rui Liu, Zhenwen Liang, Haitao Mi, Chen-Yu Wei, and Dong Yu. Save the good prefix: Precise error penalization via process-supervised RL to enhance LLM reasoning.arXiv preprint arXiv:2601.18984,

work page arXiv
[12]

Improve Mathematical Reasoning in Language Models by Automated Process Supervision

Liangchen Luo, Yinxiao Liu, Rosanne Liu, Samrat Phatale, Meiqi Guo, Harsh Lara, Yunxuan Li, Lei Shu, Yun Zhu, Lei Meng, Jiao Sun, and Abhinav Rastogi. Improve mathemat- ical reasoning in language models by automated process supervision.arXiv preprint arXiv:2406.06592,

work page internal anchor Pith review arXiv
[13]

S 2r: Teaching llms to self-verify and self- correct via reinforcement learning,

Ruotian Ma, Peisong Wang, Cheng Liu, Xingyan Liu, Jiaqi Chen, Bang Zhang, Xin Zhou, Nan Du, and Jia Li. S 2R: Teaching LLMs to self-verify and self-correct via reinforcement learning.arXiv preprint arXiv:2502.12853,

work page arXiv
[14]

Self-Refine: Iterative Refinement with Self-Feedback

Aman Madaan, Niket Tandon, Prakhar Gupta, Skyler Hallinan, Luyu Gao, Sarah Wiegreffe, Uri Alon, Nouha Dziri, Shrimai Prabhumoye, Yiming Yang, et al. Self-Refine: Iterative refinement with self-feedback.arXiv preprint arXiv:2303.17651,

work page internal anchor Pith review arXiv
[15]

Under review

10 Preprint. Under review. Mathematical Association of America. 2024-25 AIME thresholds are available. https: //maa.org/aime-thresholds-are-available/,

2024
[16]

ATTNPO: Attention-Guided Process Supervision for Efficient Reasoning

Shuaiyi Nie, Siyu Ding, Wenyuan Zhang, Linhao Yu, Tianmeng Yang, Yao Chen, Tingwen Liu, Weichong Yin, Yu Sun, and Hua Wu. ATTNPO: Attention-guided process supervision for efficient reasoning.arXiv preprint arXiv:2602.09953,

work page internal anchor Pith review Pith/arXiv arXiv
[17]

Opencodereasoning: Advancing data distillation for competitive coding

Nishanth Dikkala, Jiayi Shi, Naman Jain, Shaikh Quader Hossain, Niklas Muennighoff, Yun- tian Tao, Jonathan Tow, Hailey Wang, Guowei Shen, Tushar Jain, et al. OpenCodeReason- ing: Advancing data distillation for competitive coding.arXiv preprint arXiv:2504.01943,

work page arXiv
[18]

Beyond outcome verification: Verifiable process reward models for structured reasoning.arXiv preprint arXiv:2601.17223,

Massimiliano Pronesti, Anya Belz, and Yufang Hou. Beyond outcome verification: Verifiable process reward models for structured reasoning.arXiv preprint arXiv:2601.17223,

work page arXiv
[19]

Direct Preference Optimization: Your Language Model is Secretly a Reward Model

Rafael Rafailov, Archit Sharma, Eric Mitchell, Stefano Ermon, Christopher D. Manning, and Chelsea Finn. Direct preference optimization: Your language model is secretly a reward model.arXiv preprint arXiv:2305.18290,

work page internal anchor Pith review arXiv
[20]

Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi, Haowei Zhang, Mingchuan Zhang, Y. K. Li, Y. Wu, et al. DeepSeekMath: Pushing the limits of mathemati- cal reasoning in open language models.arXiv preprint arXiv:2402.03300,

work page internal anchor Pith review Pith/arXiv arXiv
[21]

Reflexion: Language Agents with Verbal Reinforcement Learning

Noah Shinn, Federico Cassano, Edward Berman, Ashwin Gopinath, Karthik Narasimhan, and Shunyu Yao. Reflexion: Language agents with verbal reinforcement learning.arXiv preprint arXiv:2303.11366,

work page internal anchor Pith review arXiv
[22]

Peiyi Wang, Lei Li, Zhihong Shao, R. X. Xu, Damai Dai, Yifei Li, Deli Chen, Y. Wu, and Zhifang Sui. Math-Shepherd: Verify and reinforce LLMs step-by-step without human annotations.arXiv preprint arXiv:2312.08935,

work page internal anchor Pith review arXiv
[23]

Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs

Xumeng Wen, Zihan Liu, Shun Zheng, Zhijian Xu, Shengyu Ye, Zhirong Wu, Xiao Liang, Yang Wang, Junjie Li, Ziming Miao, et al. Reinforcement learning with verifiable rewards implicitly incentivizes correct reasoning in base LLMs.arXiv preprint arXiv:2506.14245,

work page internal anchor Pith review arXiv
[24]

Self-rewarding correction for mathematical reasoning

Wei Xiong, Hanning Zhang, Chenlu Ye, Lichang Chen, Nan Jiang, and Tong Zhang. Self- rewarding correction for mathematical reasoning.arXiv preprint arXiv:2502.19613,

work page arXiv
[25]

Beyond the first error: Process reward models for reflective mathematical reasoning

Zhaohui Yang, Chenghua He, Xiaowen Shi, Linjing Li, Qiyue Yin, Shihong Deng, and Daxin Jiang. Beyond the first error: Process reward models for reflective mathematical reasoning. arXiv preprint arXiv:2505.14391,

work page arXiv
[26]

PRL: Process Reward Learning Improves LLMs’ Reasoning Ability and Broadens the Reasoning Boundary.arXiv preprint arXiv:2601.10201, 2026

Jiarui Yao, Ruida Wang, and Tong Zhang. PRL: Process reward learning improves LLMs’ reasoning ability and broadens the reasoning boundary.arXiv preprint arXiv:2601.10201,

work page arXiv
[27]

arXiv preprint arXiv:2501.07301 , year=

Zhenru Zhang, Chujie Zheng, Yangzhen Wu, Beichen Zhang, Runji Lin, Bowen Yu, Dayiheng Liu, Jingren Zhou, and Junyang Lin. The lessons of developing process reward models in mathematical reasoning.arXiv preprint arXiv:2501.07301,

work page arXiv
[28]

Group Sequence Policy Optimization

Chujie Zheng, Shixuan Liu, Mingze Li, Xiong-Hui Chen, Bowen Yu, Chang Gao, Kai Dang, Yuqiong Liu, Rui Men, An Yang, Jingren Zhou, and Junyang Lin. Group sequence policy optimization.arXiv preprint arXiv:2507.18071,

work page internal anchor Pith review arXiv
[29]

arXiv preprint arXiv:2504.11456 , year=

Chujie Zheng, Jie Zhou, Zhoufan Meng, Yilun Fan, and Junyang Lin. DeepMath-103K: A large-scale, challenging, decontaminated, and verifiable mathematical dataset for advancing reasoning.arXiv preprint arXiv:2504.11456,

work page arXiv