Closed‑Form Theory Predicts GRPO Training Dynamics and Stability
The paper derives a first‑principles closed‑form model for Group Relative Policy Optimization (GRPO) training dynamics, turning heuristic reward fits into a mechanistic framework. It predicts group‑size invariance, a stability threshold, and an overdamped‑to‑oscillatory transition, offering diagnostics that separate reward hacking from genuine instability. Experiments on multiple models achieve R² ≥ 0.91 and validate the predictions.