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Rethinking Reward Models for Multi-Domain Test-Time Scaling

Dong Bok Lee, Seanie Lee, Sangwoo Park, Minki Kang, Jinheon Baek, Dongki Kim, Dominik Wagner, Jiongdao Jin, Heejun Lee, Tobias Bocklet, Jinyu Wang, Jingjing Fu, Sung Ju Hwang, Jiang Bian, Lei Song

TL;DR

This work systematically evaluates four reward-model variants for test-time scaling of LLMs across math and 14-domain datasets, challenging the assumption that fine-grained process supervision is always better. It shows that discriminative outcome reward models (dORM) can match discriminative process reward models (dPRM) in multi-domain settings, while generative PRMs underperform relative to generative ORMs due to long CoT length and label-noise effects. The authors provide theoretical log-error bounds illustrating how stepwise PRMs accumulate error with increased CoT length, and they empirically demonstrate that gORM offers the most robust gains across domains, with gPRM suffering from length distribution shifts caused by consensus filtering. The work culminates in practical guidelines and releases code, datasets, and checkpoints to foster future research in multi-domain TTS with verifiers.

Abstract

The reliability of large language models (LLMs) during test-time scaling is often assessed with \emph{external verifiers} or \emph{reward models} that distinguish correct reasoning from flawed logic. Prior work generally assumes that process reward models (PRMs), which score every intermediate reasoning step, outperform outcome reward models (ORMs) that assess only the final answer. This view is based mainly on evidence from narrow, math-adjacent domains. We present the first unified evaluation of four reward model variants, discriminative ORM and PRM (\DisORM, \DisPRM) and generative ORM and PRM (\GenORM, \GenPRM), across 14 diverse domains. Contrary to conventional wisdom, we find that (i) \DisORM performs on par with \DisPRM, (ii) \GenPRM is not competitive, and (iii) overall, \GenORM is the most robust, yielding significant and consistent gains across every tested domain. We attribute this to PRM-style stepwise scoring, which inherits label noise from LLM auto-labeling and has difficulty evaluating long reasoning trajectories, including those involving self-correcting reasoning. Our theoretical analysis shows that step-wise aggregation compounds errors as reasoning length grows, and our empirical observations confirm this effect. These findings challenge the prevailing assumption that fine-grained supervision is always better and support generative outcome verification for multi-domain deployment. We publicly release our code, datasets, and checkpoints at \href{https://github.com/db-Lee/Multi-RM}{\underline{\small\texttt{https://github.com/db-Lee/Multi-RM}}} to facilitate future research in multi-domain settings.

Rethinking Reward Models for Multi-Domain Test-Time Scaling

TL;DR

This work systematically evaluates four reward-model variants for test-time scaling of LLMs across math and 14-domain datasets, challenging the assumption that fine-grained process supervision is always better. It shows that discriminative outcome reward models (dORM) can match discriminative process reward models (dPRM) in multi-domain settings, while generative PRMs underperform relative to generative ORMs due to long CoT length and label-noise effects. The authors provide theoretical log-error bounds illustrating how stepwise PRMs accumulate error with increased CoT length, and they empirically demonstrate that gORM offers the most robust gains across domains, with gPRM suffering from length distribution shifts caused by consensus filtering. The work culminates in practical guidelines and releases code, datasets, and checkpoints to foster future research in multi-domain TTS with verifiers.

Abstract

The reliability of large language models (LLMs) during test-time scaling is often assessed with \emph{external verifiers} or \emph{reward models} that distinguish correct reasoning from flawed logic. Prior work generally assumes that process reward models (PRMs), which score every intermediate reasoning step, outperform outcome reward models (ORMs) that assess only the final answer. This view is based mainly on evidence from narrow, math-adjacent domains. We present the first unified evaluation of four reward model variants, discriminative ORM and PRM (\DisORM, \DisPRM) and generative ORM and PRM (\GenORM, \GenPRM), across 14 diverse domains. Contrary to conventional wisdom, we find that (i) \DisORM performs on par with \DisPRM, (ii) \GenPRM is not competitive, and (iii) overall, \GenORM is the most robust, yielding significant and consistent gains across every tested domain. We attribute this to PRM-style stepwise scoring, which inherits label noise from LLM auto-labeling and has difficulty evaluating long reasoning trajectories, including those involving self-correcting reasoning. Our theoretical analysis shows that step-wise aggregation compounds errors as reasoning length grows, and our empirical observations confirm this effect. These findings challenge the prevailing assumption that fine-grained supervision is always better and support generative outcome verification for multi-domain deployment. We publicly release our code, datasets, and checkpoints at \href{https://github.com/db-Lee/Multi-RM}{\underline{\small\texttt{https://github.com/db-Lee/Multi-RM}}} to facilitate future research in multi-domain settings.

Paper Structure

This paper contains 60 sections, 7 theorems, 34 equations, 40 figures, 4 tables.

Key Result

Theorem 4.1

Let $\epsilon\in\{\epsilon_d,\epsilon_g\}$ with $\epsilon_d \coloneqq \log \hat{f}_{\texttt{dORM}\xspace}(x) - \log f(x)$ and $\epsilon_g \coloneqq \log \hat{f}_{\texttt{gORM}\xspace}(x) - \log f(x)$. Define $\bar{m} \coloneqq \mathbb{E}[\epsilon\mid x], \bar{\xi} \coloneqq \epsilon - \bar{m}, \beta

Figures (40)

  • Figure 1: Evaluating CoTs usinggORMandgPRM.
  • Figure 2: Conceptual illustration of reward models: $r_2$ is the first incorrect step; the final answer is correct.
  • Figure 3: Outcome verification results on https://huggingface.co/datasets/Qwen/ProcessBench in the math domain.
  • Figure 4: Best-of-$N$ results using https://huggingface.co/Qwen/Qwen2.5-7B-Instruct on GSM8K and Math in the math domain.
  • Figure 5: Outcome verification results on MMLU-Pro in the multi-domain setting.
  • ...and 35 more figures

Theorems & Definitions (11)

  • Theorem 4.1: Log-error bound of dORM and gORM
  • Theorem 4.2: Log-error lower bound of dPRM
  • Theorem 4.3: Log-error lower bound of gPRM
  • Theorem A.1: Log-error lower bound of dPRM
  • Theorem A.2: Log-error bound of dORM or gORM
  • Theorem A.3: Log-error lower bound of gPRM
  • Theorem A.4: Log-error lower bound of mean-gPRM
  • proof
  • proof
  • proof
  • ...and 1 more