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

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 Reward Model (Pairwise RM) combined with a knockout tournament for BoN sampling. Instead of assigning absolute scores, given one math problem, Pairwise RM evaluates two candidate solutions' correctness simultaneously. This approach eliminates the need for arbitrary scoring and enables cross-validation of solutions through parallel comparison. In the knockout tournament, Pairwise RM conducts pairwise comparisons between candidate solutions and eliminates the incorrect ones iteratively. We construct \ourdataset, a large-scale dataset of 443K pairwise comparisons derived from NumiaMath and annotated using \texttt{gemini-1.5-flash}, and train the Pairwise RM via supervised fine-tuning. Experiments on MATH-500 and the Olympiad Bench demonstrate significant improvements over traditional discriminative reward models. And a 40% to 60% relative improvement is achieved on the top 50% challenging problems.