cs.AIMar 3, 2026
SavePRISM: Pushing the Frontier of Deep Think via Process Reward Model-Guided Inference
Organizations: Virginia Tech
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 & tables
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 5 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 correct than correct incorrect transitions, reflecting genuine correction rather than “random-walk” reshuffling.
Figure 6: GPQA performance conditioned on initial population quality. Each column groups problems by how many correct solutions appear in the initial candidate pool, and each cell reports the final accuracy after refinement and majority voting. While most methods struggle when few correct candidates are present at the start, PRISM maintains substantially higher accuracy in these low-correctness regimes, which shows stronger resilience to weak initial populations.
Appendix figures & tables16 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 7: Compute–accuracy tradeoff on AIME25 (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 8: Compute–accuracy tradeoff on HMMT25 (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.
Figure 9: Population quality vs. refinement depth on AIME25. Non-PRM-based methods often oscillate or degrade with depth, whereas PRISM exhibits stable upward population dynamics.
Figure 10: Population quality vs. refinement depth on HMMT25. Non-PRM-based methods often oscillate or degrade with depth, whereas PRISM exhibits stable upward population dynamics.
Figure 11: Directional correction across enhancement depth on AIME25. Bars show NetFlip aggregated over depth and averaged across questions. Positive values indicate more incorrect correct than correct incorrect transitions, reflecting genuine correction rather than “random-walk” reshuffling.
Figure 12: Directional correction across enhancement depth on HMMT25. Bars show NetFlip aggregated over depth and averaged across questions. Positive values indicate more incorrect correct than correct incorrect transitions, reflecting genuine correction rather than “random-walk” reshuffling.
Figure 13: AIME25 performance conditioned on initial population quality. Each column groups problems by how many correct solutions appear in the initial candidate pool, and each cell reports the final accuracy after refinement and majority voting. While most methods struggle when few correct candidates are present at the start, PRISM maintains substantially higher accuracy in these low-correctness regimes, which shows stronger resilience to weak initial populations.
Figure 14: HMMT25 performance conditioned on initial population quality. Each column groups problems by how many correct solutions appear in the initial candidate pool, and each cell reports the final accuracy after refinement and majority voting. While most methods struggle when few correct candidates are present at the start, PRISM maintains substantially higher accuracy in these low-correctness regimes, which shows stronger resilience to weak initial populations.
Figure 15: AIME25 results on Qwen3 across model sizes. The bar chart compares zero-shot, Recursive Self-Aggregation, and PRISM across Qwen3-1.7B, 4B, 14B, and 30B-A3B. PRISM consistently improves over zero-shot performance across model sizes, with the largest gains observed for smaller models.
Figure 16: HMMT25 results on Qwen3 across model sizes. The bar chart compares zero-shot, Recursive Self-Aggregation, and PRISM across Qwen3-1.7B, 4B, 14B, and 30B-A3B. PRISM consistently improves over zero-shot performance across model sizes, with the largest gains observed for smaller models.
Figure 17: GPQA Diamond results on Qwen3 across model sizes. The bar chart compares zero-shot, Recursive Self-Aggregation, and PRISM across Qwen3-1.7B, 4B, 14B, and 30B-A3B. PRISM consistently improves over zero-shot performance across model sizes, with the largest gains observed for smaller models.
Figure 18: AIME25 compute–accuracy tradeoff on Qwen3. Each point corresponds to a method (color) and model size (marker shape), with the x-axis showing average tokens per question (log scale) and the y-axis showing accuracy. The Pareto frontier highlights that PRISM remains competitive under fixed compute budgets, which indicates that its gains are not driven solely by increased token usage.
Figure 19: HMMT25 compute–accuracy tradeoff on Qwen3. Each point corresponds to a method (color) and model size (marker shape), with the x-axis showing average tokens per question (log scale) and the y-axis showing accuracy. The Pareto frontier highlights that PRISM remains competitive under fixed compute budgets, which indicates that its gains are not driven solely by increased token usage.
Figure 20: GPQA Diamond compute–accuracy tradeoff on Qwen3. Each point corresponds to a method (color) and model size (marker shape), with the x-axis showing average tokens per question (log scale) and the y-axis showing accuracy. The Pareto frontier highlights that PRISM remains competitive under fixed compute budgets, which indicates that its gains are not driven solely by increased token usage.
Figure 21: Cross generator–verifier scaling on Qwen3. Bars report PRISM accuracy when the generator is fixed and the verifier varies, comparing self-verification (V=G) with cross-verification using different verifier sizes. Performance improves as verifier strength increases, with the largest gains occurring when the verifier is larger than the generator.
Figure 22: Model-type comparison on Qwen3-4B: Base vs. Instruct vs. Thinking variants. Bars compare zero-shot and PRISM across closely related variants for each dataset. PRISM consistently improves performance, with larger gains on weaker variants, thereby narrowing the gap to stronger tuned models.
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