What Fixed-Rollout pass@k Evaluations Can Identify
Repeated-sampling evaluations increasingly extrapolate pass@k far beyond the number n of samples collected per problem. We show that, in the pooled/random-task conditional-Binomial model, fixed-n success counts identify only the n free moments of the latent per-task success distribution. Consequently, direct pass@k is identified for k n, even with arbitrarily many exchangeable tasks at the same rollout budget....
Repeated-sampling evaluations increasingly extrapolate pass@k far beyond the number n of samples collected per problem. We show that, in the pooled/random-task conditional-Binomial model, fixed-n success counts identify only the n free moments of the latent per-task success distribution. Consequently, direct pass@k is identified for k n, even with arbitrarily many exchangeable tasks at the same rollout budget....