Cheng Gui

Best-of-N inference returns the candidate with the highest proxy reward, so a larger budget reads the extreme tail of the reward distribution rather than its average ranking quality. The work writes the BoN value as a Beta-weighted integral of conditional true reward over within-prompt score quantiles, showing that BoN depends on scores only through their ranks and can decline only when the calibration curve in the tail turns downward. On public candidate pools, negative tail excess concentrates in code generation, and a cross-fitted tail statistic predicts whether a budget cap pays off on held-out data about as well as rank accuracy.

Best-of-N inference returns the candidate with the highest proxy reward, so a larger budget reads the extreme tail of the reward distribution rather than its average ranking quality. The work writes the BoN value as a Beta-weighted integral of conditional true reward over within-prompt score quantiles, showing that BoN depends on scores only through their ranks and can decline only when the calibration curve in the tail turns downward. On public candidate pools, negative tail excess concentrates in code generation, and a cross-fitted tail statistic predicts whether a budget cap pays off on held-out data about as well as rank accuracy.