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A sign law for entropy drift: your RLVR sampler, not your loss, decides whether the policy sharpens or flattens

AspireAI community · arXiv
In reinforcement learning with verifiable rewards, whether entropy rises or falls can hinge on choices that look irrelevant under exact sampling, such as whether over-length responses are masked or counted as failures. This paper traces that instability to sampler mismatch, where rollouts are drawn with top-k or top-p truncation or at a temperature the learner does not itself apply, and proves that a constant advantage shift then changes the entropy of a softmax policy to first order with a sign fixed by the sampler. Positive shifts sharpen the policy under top-k, top-p, min-p and sub-unit temperatures and flatten it under flatter samplers, and in group-based RLVR with token-level losses the baseline-dependent part of the drift is set by the token-weighted net advantage, which masking and failing push in opposite directions. On a 2B model the entropy slope is linear in net-advantage shifts under truncated sampling, so this is a practical knob rather than a curiosity, though it is a single-model result.
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