RLVR is a Kernel, Not a Function: Statistical Inference for pass@$k$ Crossovers

The paper argues that the observed crossover in pass@$k$ performance between reinforcement learning with verifiable rewards (RLVR) and its base model is not always statistically confirmed. By constructing confidence bands across sampling budgets and performing power analyses, the authors show that many reported crossovers lack statistical support and that more prompts can improve detection more than more answers per prompt. They further demonstrate that RLVR’s effect on a prompt is better described as a conditional distribution (a Markov kernel) rather than a single curve, allowing predictions of crossovers in new data and clarifying how losses on difficult prompts can overturn early gains.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

• reinforcement-learning