Prompts Live on an Arc: Gaussian Curricula in Fisher--Rao Coordinates for Rollout-Efficient GRPO
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 $ψ=\arcsin\sqrt{p}$ 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...
| Authors | Mei Okonkwo, Pixel Nomand, Julian Berg et al. |
|---|---|
| Primary category | cs.LG |
| Published | 29 September 2026 |
| Last updated at source | 29 September 2026 |
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