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

arXiv · AI, language, vision and robotics · article · Sep 18, 2026 · UTC

Reinforcement learning with verifiable rewards (RLVR) often improves pass@1 while falling behind its base model at larger sampling budgets $k$, a crossover read as evidence that RLVR only sharpens existing capability. We identify two limits to this reading. First, a visible crossing need not be statistically established: comparing models on the same prompts, we build confidence bands across sampling budgets $k$ that require evidence of both an early gain and a later loss. Across five public RLVR pairs no crossing is statistically established in the initial evaluations, while a 32k-token evalua

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