PRISM: Pushing the Frontier of Deep Think via Process Reward Model-Guided Inference

TL;DR

PRISM introduces a process reward model-guided inference method that enhances reasoning accuracy by refining candidate solutions through step-level verification, outperforming existing methods on mathematical and scientific benchmarks.

Contribution

This paper presents PRISM, a novel inference algorithm that uses step-level verification to improve population refinement in DEEPTHINK systems, addressing reliability issues during reasoning.

Findings

PRISM achieves state-of-the-art accuracy on multiple benchmarks.

PRISM maintains diversity while focusing on higher-quality solutions.

PRISM is reliable even with few correct initial candidates.

Abstract

DEEPTHINK methods improve reasoning by generating, refining, and aggregating populations of candidate solutions, which enables strong performance on complex mathematical and scientific tasks. However, existing frameworks often lack reliable correctness signals during inference, which creates a population-enhancement bottleneck where deeper deliberation amplifies errors, suppresses correct minority solutions, and yields weak returns to additional compute. In this paper, we introduce a functional decomposition of DEEPTHINK systems and propose PRISM, a Process Reward Model (PRM)-guided inference algorithm that uses step-level verification to guide both population refinement and solution aggregation. During refinement, PRISM treats candidate solutions as particles in a PRM-defined energy landscape and reshapes the population through score-guided resampling and stochastic refinement, which concentrates probability mass on higher-quality reasoning while preserving diversity. Across mathematics and science benchmarks, PRISM is competitive with or outperforms existing DEEPTHINK methods, reaching 90.0%, 75.4%, and 71.4% with gpt-oss-20b on AIME25, HMMT25, and GPQA Diamond, respectively, while matching or exceeding gpt-oss-120b. Additionally, our analysis shows that PRISM produces consistent net-directional correction during refinement, remains reliable when the initial population contains few correct candidates, and often lies on the compute-accuracy Pareto frontier.