Predictable GRPO: A Closed-Form Model of Training Dynamics
We develop a first-principles reduced-order model of these dynamics. Under a single mean-field assumption that summarizes the policy by its expected reward, we reduce the GRPO update to a stochastically-forced damped oscillator whose mass, damping, and stiffness are fixed in closed form by the optimizer hyperparameters together with a single measured curvature scale -- momentum supplies the inertia, off-policy lag erodes the damping, and the group size enters, to leading order, as a noise temperature. The reduction has three consequences. First, it subsumes the empirical single-exponential saturation law as its overdamped limit, recasting the fitted plateau, timescale, and size exponent a...
| Authors | Rajat Ghosh, Datta Nimmaturi, Aryan Singhal et al. |
|---|---|
| Primary category | cs.LG |
| Published | 29 June 2026 |
| Last updated at source | 1 July 2026 |
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