fokker-planck-analyzer

Gibbs equilibrium verification compares your empirical weight distribution to the theoretical Gibbs distribution predicted by Fokker-Planck theory. This Skill analyzes training trajectories across loss landscapes and temperatures to confirm convergence to equilibrium, supporting mixing-time estimation and steady-state validation.

Mixing time is the duration required for a system to reach equilibrium under Langevin dynamics. This Skill approximates mixing time from Hessian eigenvalues or empirical convergence data, enabling you to predict how long training needs to stabilize at a given temperature.

KL divergence tracking measures how quickly your empirical weight distribution approaches the Gibbs distribution. This Skill monitors KL divergence over training epochs and validates gradient stability, reporting convergence metrics and steady-state assessments.

Yes. This Skill applies Fokker-Planck-based convergence checks across various loss landscapes and temperature settings. It computes Gibbs convergence metrics and validates steady-state behavior, supporting scenarios from low-temperature steep landscapes to high-temperature exploration regimes.

Hessian eigenvalues determine the local curvature of your loss landscape and directly influence mixing time under Langevin dynamics. This Skill uses the Hessian spectrum to estimate equilibrium convergence speed, helping you understand how landscape geometry affects training dynamics.