# Discovering Process-Outcome Credit in Multi-Step LLM Reasoning

arXiv: https://arxiv.org/abs/2602.01034 · HTML: https://mlsanity.com/paper/2602.01034/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 13 of its 40 references that are in the map.
- First posted on arXiv 1 Feb 2026.

## Placed in

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

## Builds on (most cited first, 13 of 13)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Reinforced Self-Training (ReST) for Language Modeling](https://mlsanity.com/paper/2308.08998/) (2023)
- [MM-Eureka: Exploring the Frontiers of Multimodal Reasoning with Rule-based Reinforcement Learning](https://mlsanity.com/paper/2503.07365/) (2025)
- [GDPO: Group reward-Decoupled Normalization Policy Optimization for Multi-reward RL Optimization](https://mlsanity.com/paper/2601.05242/) (2026)
- [Language Models are Hidden Reasoners: Unlocking Latent Reasoning Capabilities via Self-Rewarding](https://mlsanity.com/paper/2411.04282/) (2024)
- [G1: Bootstrapping Perception and Reasoning Abilities of Vision-Language Model via Reinforcement Learning](https://mlsanity.com/paper/2505.13426/) (2025)

## Built on by (most cited first, 3 of 3)

- [SkillFlow: Flow-Driven Recursive Skill Evolution for Agentic Orchestration](https://mlsanity.com/paper/2605.14089/) (2026)
- [TACO: Tool-Augmented Credit Optimization for Agentic Tool Use](https://mlsanity.com/paper/2606.30251/) (2026)
- [FiRe: Fine-grained Multimodal Reasoning for Enhanced Image Generation](https://mlsanity.com/paper/2604.13491/) (2026)

## Abstract (arXiv)

Reinforcement learning (RL) has become a widely used paradigm for improving the reasoning abilities of large language models (LLMs) and Vision-language models (VLMs). Sparse binary outcome rewards, however, score only final correctness and cannot identify which intermediate steps contributed to it; in multimodal tasks, they may also reward answers driven by linguistic priors rather than visual evidence. Process reward models (PRMs) densify supervision but usually require process annotations, auxiliary models, or inference-time search. In this paper, we introduce Stepwise Marginal Information Gain (MIG), an intrinsic process reward computed from the policy itself. MIG measures how each structured reasoning prefix changes the length-normalized, teacher-forced log-likelihood of the reference answer. A monotonic historical watermark rewards only new likelihood maxima, avoiding duplicate credit after sub-record detours. We combine this signal with outcome and format rewards and a gated self-distillation objective that retains only structurally valid and correct trajectories. For VLMs, a real-versus-blank likelihood gate down-weights rewards when answers remain predictable without the image. Across eight task-specific benchmarks, the full method exceeds outcome-only GRPO in every single-run comparison. In broad-data transfer, it improves average accuracy by up to 4.8 points over binary-reward training and gains 12.6 points on MathVerse. At 7B, it exceeds an external PRM-BoN@16 baseline by 12.9 points on vision-language transfer without inference-time reranking. These results support policy-derived stepwise credit as an annotation-free alternative to explicit process reward modeling.