Coefficient Gradient Impact: Calibrating Executed Trust Regions in LLM RL

Trust-region mechanisms are ubiquitous in reinforcement learning for language-model reasoning, yet their control parameters inhabit incompatible geometries and say little about the intervention actually executed by training code. We introduce Coefficient Gradient Impact, an objective-aligned measure of the relative displacement of the token coefficients that form the policy gradient. Our analysis yields exact identities for hard removal and smooth reweighting, separates activation frequency from coefficient energy, and characterizes how coefficient-space interventions propagate to parameter gradients. Building on this measure, we develop a baseline-aware calibration procedure that maps heterogeneous trust-region mechanisms onto a common, baseline-declared reporting coordinate, together with a one-sided impact-capping rule that adapts the control threshold while preserving the underlying objective geometry. An immutable-trace protocol makes the measurement auditable across rollout, anchor, and current policies while preserving scoring and synchronization provenance. Multi-run experiments on physical servers across model scales and numerical precisions indicate that the framework enables calibrated comparison among otherwise incomparable mechanisms, tracks parameter-gradient change more faithfully than the tested alternatives, provides useful early warning of unstable training, and transfers across the tested execution settings. Across paired training runs, impact-guided control exhibits the strongest observed stability profile while maintaining comparable reasoning accuracy. Coefficient Gradient Impact therefore provides a principled interface between trust-region design, systems execution, and empirical evaluation, enabling more interpretable comparison and auditable control of language-model reinforcement learning.