Solve-Detect-Verify: Inference-Time Scaling with Flexible Generative Verifier

TL;DR

This work tackles the accuracy-efficiency dilemma in LLM reasoning by proposing FlexiVe, a flexible generative verifier that dynamically allocates verification budget across fast and slow thinking modes. Paired with the Solve-Detect-Verify pipeline, it enables intelligent, inference-time scaling by holistically evaluating reasoning traces $S_{trace}$ and triggering targeted verification at completion points, guided by the first error index $idx_{pred}$. Trained with Group Relative Policy Optimization on a mistake-detection objective, FlexiVe can balance speed and precision using a budgeted approach based on an agreement metric $R_{agreement}$ and threshold $\tau$. Across ProcessBench and challenging math benchmarks such as AIME (2024/2025) and CNMO, the method yields stronger accuracy and token efficiency compared with self-consistency and other baselines, underscoring its potential for scalable, reliable LLM reasoning in test-time settings.

Abstract

Large Language Model (LLM) reasoning for complex tasks inherently involves a trade-off between solution accuracy and computational efficiency. The subsequent step of verification, while intended to improve performance, further complicates this landscape by introducing its own challenging trade-off: sophisticated Generative Reward Models (GenRMs) can be computationally prohibitive if naively integrated with LLMs at test-time, while simpler, faster methods may lack reliability. To overcome these challenges, we introduce FlexiVe, a novel generative verifier that flexibly balances computational resources between rapid, reliable fast thinking and meticulous slow thinking using a Flexible Allocation of Verification Budget strategy. We further propose the Solve-Detect-Verify pipeline, an efficient inference-time scaling framework that intelligently integrates FlexiVe, proactively identifying solution completion points to trigger targeted verification and provide focused solver feedback. Experiments show FlexiVe achieves superior accuracy in pinpointing errors within reasoning traces on ProcessBench. Furthermore, on challenging mathematical reasoning benchmarks (AIME 2024, AIME 2025, and CNMO), our full approach outperforms baselines like self-consistency in reasoning accuracy and inference efficiency. Our system offers a scalable and effective solution to enhance LLM reasoning at test time.

Figures (15)

• Figure 1: Performance Scaling Analysis. (Left) On the AIME2024 benchmark, our inference-time scaling framework, Solve-Detect-Verify , achieves higher accuracy while requiring approximately 4x fewer solutions compared to baseline approaches. Since DeepSeek-R1-Distill-Qwen-14B does not report performance from $k=2...32$, we connect two dots with a dotted straight line. (Right) On the Math benchmark, our verifier FlexiVe (specifically with the Flex@8 configuration) attains a higher F1 score while generating approximately 3x fewer tokens than the baseline.
• Figure 2: Empirical motivation for efficient verification and generation strategies. (Left) Comparison of error precision and token usage between NoThinking and Thinking verification on GSM8K and Math (ProcessBench). While NoThinking significantly reduces tokens, its error precision is substantially lower, sugguesting high false positive rate. (Right) Accuracy and token usage comparison between generating a full solution (Full Thinking) and halting generation early upon detecting a complete intermediate solution (First Solution) on AIME 2024 and AIME 2025. Early detection offers significant token reduction with comparable accuracy.
• Figure 3: The NoThinking mechanism bypasses explicit thought generation, using a template to fill the thinking phase.
• Figure 4: Comparison of verification mechanisms. Standard GenRMs holistically assess a trace. GenPRMs often verify step-by-step. FlexiVe (Ours) uses an adaptive approach on the entire trace, with initial parallel fast evaluations deciding if deeper, slow verification is needed.
• Figure 5: F1 score vs. verification tokens on GSM8K (left) and MATH (right). FlexiVe (Flex@k, green circles) demonstrates higher F1 for similar token costs than DeepSeek-R1-Distill-Qwen-14B (blue triangles, baseline verifier), both outperforming the token-efficient FlexiVe (NoThinking variant, red squares). X-axis denote the number of token generated across the entire test set.