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

arXiv: https://arxiv.org/abs/2605.05226 · HTML: https://mlsanity.com/paper/2605.05226/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 23 of its 28 references that are in the map.
- First posted on arXiv 19 Apr 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 23 of 23)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [Training Language Models to Self-Correct via Reinforcement Learning](https://mlsanity.com/paper/2409.12917/) (2024)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs](https://mlsanity.com/paper/2506.14245/) (2025)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [Teaching Large Language Models to Reason with Reinforcement Learning](https://mlsanity.com/paper/2403.04642/) (2024)
- [Process Reward Models That Think](https://mlsanity.com/paper/2504.16828/) (2025)
- [OpenCodeReasoning: Advancing Data Distillation for Competitive Coding](https://mlsanity.com/paper/2504.01943/) (2025)
- [Self-rewarding correction for mathematical reasoning](https://mlsanity.com/paper/2502.19613/) (2025)
- [ReVISE: Learning to Refine at Test-Time via Intrinsic Self-Verification](https://mlsanity.com/paper/2502.14565/) (2025)
- [Beyond Outcome Verification: Verifiable Process Reward Models for Structured Reasoning](https://mlsanity.com/paper/2601.17223/) (2026)
- [Save the Good Prefix: Precise Error Penalization via Process-Supervised RL to Enhance LLM Reasoning](https://mlsanity.com/paper/2601.18984/) (2026)
- [ATTNPO: Attention-Guided Process Supervision for Efficient Reasoning](https://mlsanity.com/paper/2602.09953/) (2026)
- [Learning from the Irrecoverable: Error-Localized Policy Optimization for Tool-Integrated LLM Reasoning](https://mlsanity.com/paper/2602.09598/) (2026)

## Abstract (arXiv)

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.