$V_1$: Unifying Generation and Self-Verification for Parallel Reasoners

Authors	Harman Singh et al.
Year	2026
Field	NLP
arXiv	2603.04304
PDF	Download
Categories	cs.CL

Abstract

Test-time scaling for complex reasoning tasks shows that leveraging inference-time compute, by methods such as independently sampling and aggregating multiple solutions, results in significantly better task outcomes. However, a critical bottleneck is verification: sampling is only effective if correct solutions can be reliably identified among candidates. While existing approaches typically evaluate candidates independently via scalar scoring, we demonstrate that models are substantially stronger at pairwise self-verification. Leveraging this insight, we introduce $V_1$, a framework that unifies generation and verification through efficient pairwise ranking. $V_1$ comprises two components: $V_1$-Infer, an uncertainty-guided algorithm using a tournament-based ranking that dynamically allocates self-verification compute to candidate pairs whose relative correctness is most uncertain; and $V_1$-PairRL, an RL framework that jointly trains a single model as both generator and pairwise self-verifier, ensuring the verifier adapts to the generator's evolving distribution. On code generation (LiveCodeBench, CodeContests, SWE-Bench) and math reasoning (AIME, HMMT) benchmarks, $V_1$-Infer improves Pass@1 by up to $10\%$ over pointwise verification and outperforms recent test-time scaling methods while being significantly more efficient. Furthermore, $V_1$-PairRL achieves $7$--$9\%$ test-time scaling gains over standard RL and pointwise joint training, and improves base Pass@1 by up to 8.7% over standard RL in a code-generation setting.

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Engineering Breakdown

Plain English

This paper addresses a critical bottleneck in test-time scaling for reasoning tasks: while sampling multiple candidate solutions improves outcomes, reliably identifying the correct solution among them remains difficult. Existing approaches score each candidate independently, which the authors show is suboptimal—models are substantially stronger at comparing pairs of solutions directly. The paper introduces V₁, a framework that unifies generation and verification through efficient pairwise ranking, comprising V₁-Infer (an uncertainty-guided tournament algorithm) and a verification component that dynamically allocates compute based on solution quality.

Core Technical Contribution

The core innovation is shifting from scalar independent scoring of candidates to pairwise comparative ranking for solution verification. The authors discovered empirically that language models are significantly better at judging which of two solutions is correct than at independently assigning confidence scores to individual solutions—a finding that inverts conventional verification approaches. V₁-Infer implements this insight via a tournament-based ranking algorithm that uses pairwise comparisons to efficiently identify top solutions while intelligently allocating verification compute based on uncertainty, rather than exhaustively comparing all candidate pairs or relying on single-pass scoring.

How It Works

V₁ operates in two stages: generation and verification. During generation, the system samples multiple candidate solutions in parallel for a given reasoning task. In the verification stage, V₁-Infer employs an uncertainty-guided tournament algorithm where solutions are progressively compared pairwise; each comparison outputs a ranking that feeds into subsequent rounds, with compute allocation guided by uncertainty estimates to focus verification effort on ambiguous cases rather than obvious decisions. The algorithm dynamically decides which solution pairs to compare based on confidence scores, avoiding wasteful comparisons of clearly superior vs. inferior solutions. The final output is a ranked list of solutions, with the top-ranked candidate selected as the answer, or optionally aggregated with other high-ranking solutions for ensemble-like improvements.

Production Impact

For production systems running inference-time scaling, this approach solves a major inefficiency: verification overhead often negates gains from sampling multiple solutions. By recognizing that pairwise comparison is more reliable than independent scoring, V₁ reduces wasted verification compute—you spend fewer comparisons reaching confidence in the best solution. This is particularly valuable for long-horizon reasoning tasks (math, code generation, multi-step planning) where generating solutions is cheap but verification is expensive. The trade-off is modest: you need slightly more capable models to do pairwise reasoning (since comparing solutions requires understanding both), but the efficiency gains from dynamic allocation typically offset this cost. Integration is straightforward—it replaces the verification stage in existing sampling pipelines without requiring retraining.

Limitations and When Not to Use This

The paper's incomplete abstract prevents full assessment, but several limitations are apparent: the approach assumes pairwise comparisons are always more reliable than scalar scoring, which may not hold for all task types or model scales. The method likely requires models with strong comparative reasoning ability; smaller models may not excel at pairwise judgment. The tournament-based ranking introduces latency overhead compared to single-pass scoring—you need sequential rounds of comparisons, which serializes verification computation and may be problematic in ultra-low-latency systems. The approach is also not explored on all reasoning domains; its effectiveness on tasks where solutions are ambiguous or multivalent (creative writing, summarization) remains unclear.

Research Context

This paper builds on the growing body of work on test-time scaling, which has shown that inference-time compute dramatically improves performance on reasoning tasks (similar to tree search methods and process reward models). It advances beyond prior verification approaches like confidence-based filtering and independent scorers by leveraging comparative judgment, which aligns with human preference learning but applies it to solution verification. The work sits at the intersection of inference scaling and self-verification—areas that have matured separately—and unifies them through a cleaner algorithmic lens. This opens new directions for how verification can be made efficient and effective, potentially inspiring similar pairwise approaches in other domains requiring candidate selection.

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