RLVR is a Kernel, Not a Function: Statistical Inference for pass@$k$ Crossovers
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 evaluation on fresh prompts locates a reversal with first loss between 11 and 61 samples; power analysi...
| Authors | Chen Yang, Jun Chen |
|---|---|
| Primary category | stat.ML |
| Published | 18 September 2026 |
| Last updated at source | 25 September 2026 |
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