PairJudge RM: Perform Best-of-N Sampling with Knockout Tournament

Abstract

Best-of-N (BoN) sampling, a common strategy for test-time scaling of Large Language Models (LLMs), relies on reward models to select the best candidate solution from multiple generations. However, traditional reward models often assign arbitrary and inconsistent scores, limiting their effectiveness. To address this, we propose a Pairwise Judge Reward Model (PariJudge RM) combined with a knockout tournament for BoN sampling. Instead of assigning absolute scores, given one math problem, PariJudge RM judges two candidate solutions' correctness with chain-of-thought reasoning simultaneously. This approach eliminates the need for scoring and enables cross-validation of solutions through parallel judgment. In the knockout tournament, PariJudge RM conducts pairwise Judgment between candidate solutions and eliminates the incorrect ones iteratively. We construct PairJudge-432K, a large-scale dataset of 432K pairwise judgments derived from NumiaMath and annotated using \texttt{gemini-1.5-flash}, and train the PariJudge RM via supervised fine-tuning. Experiments on MATH-500 and the Olympiad Bench demonstrate significant improvements over baseline reward models. And a 40\% to 60\% relative improvement is achieved on the top 50\% challenging problems.