Prompts Live on an Arc: Gaussian Curricula in Fisher--Rao Coordinates for Rollout-Efficient GRPO

תקציר מקורי באנגליתarXiv:2609.38018v1 Announce Type: new Abstract: Group relative policy optimization (GRPO) learns only from prompts whose sampled responses disagree: a group that is entirely correct or entirely incorrect has zero reward variance, contributes no gradient, and still consumes its rollouts. Prompt-selection methods reduce this waste by steering sampling toward intermediate pass rates, but they choose the target, its width, and the uncertainty model heuristically, in raw pass-rate or logit coordinates. We show that GRPO comes with a natural coordinate for pass rates: the arc length $\psi=\arcsin\sqrt{p}$ on the Bernoulli Fisher--Rao manifold. In arc length, the expected GRPO update is uniform up to two boundary ramps; the probability of a zero-variance group is bounded by two Gaussian boundary