Efficient Prediction of Pass@k Scaling in Large Language Models

Assessing the capabilities and risks of frontier AI systems is a critical area of research; recent work has shown that repeated sampling can dramatically increase both. For instance, repeated sampling allows models to solve difficult math and coding problems, but it may also increase their risk of being jailbroken. Such results raise a crucial question: how can one accurately predict a model's behavior when scaled to a massive number of attempts, given a vastly smaller sampling budget? This question is directly relevant to model providers, who serve hundreds of millions of users daily, and to governmental regulators, who seek to prevent harms. To answer this question, we make three contributions. First, we find that standard methods for fitting these laws suffer from statistical shortcomings that hinder predictions, especially in data-limited scenarios. Second, we remedy these shortcomings by introducing a robust estimation framework, which uses a beta-binomial distribution to generate more accurate predictions from limited data. Third, we propose a dynamic sampling strategy that allocates a greater budget to harder problems. Combined, these innovations enable more reliable prediction of rare risks and capabilities at a fraction of the computational cost.