Thermodynamic Regulation of Finite-Time Gibbs Training in Energy-Based Models: A Restricted Boltzmann Machine Study
This work addresses the challenges of sampling collapse, negative-phase localization, and parameter drift in Restricted Boltzmann Machine (RBM) training under fixed-temperature finite-time Gibbs sampling. To overcome these issues, the authors propose an endogenous thermodynamic regulation framework that treats temperature as a dynamic state variable coupled with sampling statistics, thereby modeling RBM training as a controlled non-equilibrium dynamical process. By incorporating a thermodynamic self-regulation mechanism, the approach rigorously ensures global parameter boundedness under L2 regularization and local exponential stability of subsystems, effectively preventing inverse-temperature explosion and sampling freeze. Theoretical analysis leverages two-time-scale separation and local Lipschitz conditions. Experiments on MNIST demonstrate significantly improved normalized stability and effective sample size while preserving reconstruction performance, outperforming fixed-temperature baselines.