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

TL;DR

This paper introduces $V_1$, a unified framework combining generation and pairwise self-verification to improve reasoning tasks, achieving significant test-time scaling improvements in code and math benchmarks.

Contribution

The paper presents a novel pairwise ranking framework, $V_1$, that unifies generation and verification, and introduces RL training for adaptive self-verification.

Findings

$V_1$-Infer improves Pass@1 by up to 10% over pointwise verification.

$V_1$-PairRL achieves 7-9% test-time scaling gains over standard RL.

The methods outperform recent test-time scaling approaches in benchmarks.

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.