The Weakest Link Tells It All: Outcome-Supervised Process Reward Modeling via Learnable Credit Assignment

arXiv:2606.27739v2 Announce Type: replace Abstract: Process reward models (PRMs) enhance the reasoning capabilities of large language models (LLMs) by providing fine-grained feedback, yet training PRMs typically requires expensive stepwise annotations. Outcome-supervised PRMs offer a scalable alternative by learning from final-answer correctness alone, but this introduces a fundamental credit assignment challenge, i.e., attributing outcomes to responsible reasoning steps. Existing approaches rely on either uniform or causal assignment, both of which fail to anchor credit in step correctness and thus hinder process error identification. In this work, we propose Outcome-Supervised Process Reward Modeling via Learnable Credit Assignment (LCA), an outcome-supervised PRM framework that jointly learns credit assignment and reward modeling under the principle of Weakest Link Assignment: a reasoning chain is as strong as its weakest link. To address mutual dependence between credit assignment and reward modeling, we formalize outcome-supervised PRM as a Multiple Instance Learning (MIL) problem and introduce Softmax-Weighted-Sum (SWS) pooling, an MIL pooling technique tailored for strong dependence and redundancy among reasoning states. We establish instance-level Bayes consistency of the resulting learning objective under mild assumptions. Extensive experiments demonstrate that LCA outperforms state-of-the-art outcome-supervised PRMs across multiple tasks and backbones. Code is available at https://github.com/JiaTianyu20031016/MIL.git.

Abstract:Process reward models (PRMs) enhance the reasoning capabilities of large language models (LLMs) by providing fine-grained feedback, yet training PRMs typically requires expensive stepwise annotations. Outcome-supervised PRMs offer a scalable alternative by learning from final-answer correctness alone, but this introduces a fundamental credit assignment challenge, i.e., attributing outcomes to responsible reasoning steps. Existing approaches rely on either uniform or causal assignment, both of which fail to anchor credit in step correctness and thus hinder process error identification. In this work, we propose Outcome-Supervised Process Reward Modeling via Learnable Credit Assignment (LCA), an outcome-supervised PRM framework that jointly learns credit assignment and reward modeling under the principle of Weakest Link Assignment: a reasoning chain is as strong as its weakest link. To address mutual dependence between credit assignment and reward modeling, we formalize outcome-supervised PRM as a Multiple Instance Learning (MIL) problem and introduce Softmax-Weighted-Sum (SWS) pooling, an MIL pooling technique tailored for strong dependence and redundancy among reasoning states. We establish instance-level Bayes consistency of the resulting learning objective under mild assumptions. Extensive experiments demonstrate that LCA outperforms state-of-the-art outcome-supervised PRMs across multiple tasks and backbones. Code is available at this https URL.

Accepted to EMNLP 2026 (Oral). Camera-ready version. Code: this https URL

Machine Learning (cs.LG)

arXiv:2606.27739 [cs.LG]

(or arXiv:2606.27739v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2606.27739 Focus to learn more arXiv-issued DOI via DataCite

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The Weakest Link Tells It All: Outcome-Supervised Process Reward Modeling via Learnable Credit Assignment

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