What pass@k Cannot Measure: Evaluating Diversity and Capability Retention after Post-Training

Subham Rath, Raj Dandekar, Rajat Dandekar, Sreedath Panat

pass@$k$, the fraction of problems a model solves within $k$ sampled attempts, is the field's default protocol for deciding whether reinforcement-learning (RL) post-training on verifiable rewards improved a model. At the population level, pass@$k$ depends only on a problem's probability of a correct sample, with no term for how it is distributed across outputs. We show this gap is not academic. Training Qwen2.5-1.5B-Instruct on grade-school math with Group Relative Policy Optimization (GRPO) and with rejection-sampling fine-tuning (RFT, training on the model's own shortest verifier-passed rollout) moves three complementary diversity measures (token-level entropy, answer-level entropy, unique answers per prompt) in opposite directions, with zero overlap across three seeds per arm. The gap survives restricting to verifier-correct completions only (lexical diversity among correct solutions is 15% lower for GRPO, after controlling for length) and a count-controlled check isolating diversity among incorrect answers alone, ruling out that GRPO's higher accuracy alone explains it. Yet pass@8 and pass@32 show no consistent winner on GSM8K, and a hard MATH-500 subset shows the same…