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

TL;DR

A functional decomposition of DEEPTHINK systems is introduced and PRISM, a Process Reward Model (PRM)-guided inference algorithm that uses step-level verification to guide both population refinement and solution aggregation is proposed.

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.

Figures (22)

• Figure 1: Accuracy on AIME25, HMMT25, and GPQA Diamond.PRISM achieves competitive or superior performance relative to state-of-the-art DeepThink methods, enabling gpt-oss-20b to match or exceed gpt-oss-120b (see Table \ref{['tab:final_accuracy']} for more results).
• Figure 2: Functional taxonomy of DeepThink systems (top) and overview of PRISM (bottom). The top panel decomposes DeepThink into population creation, population enhancement, and solution aggregation. The bottom panel illustrates PRISM's refinement mechanism, which uses Process Reward Model (PRM)-defined scores to guide resampling and stochastic refinement within an energy-based population framework.
• Figure 3: Compute–accuracy tradeoff on GPQA Diamond (Pareto view). Each point represents a method configuration (enhancement + aggregation). The connected frontier marks Pareto-optimal configurations. Most refinement-heavy methods spend substantially more tokens for marginal or inconsistent gains, whereas PRISM stays among the best accuracy-to-compute tradeoffs.
• Figure 4: Population quality vs. refinement depth on GPQA Diamond. Non-PRM-based methods often oscillate or degrade with depth, whereas PRISM exhibits stable upward population dynamics.
• Figure 5: Directional correction across enhancement depth on GPQA Diamond. Bars show NetFlip aggregated over depth and averaged across questions. Positive values indicate more incorrect$\rightarrow$correct than correct$\rightarrow$incorrect transitions, reflecting genuine correction rather than "random-walk" reshuffling.