[2603.02525] Thermodynamic Regulation of Finite-Time Gibbs Training in Energy-Based Models: A Restricted Boltzmann Machine Study

Computer Science > Machine Learning arXiv:2603.02525 (cs) [Submitted on 3 Mar 2026] Title:Thermodynamic Regulation of Finite-Time Gibbs Training in Energy-Based Models: A Restricted Boltzmann Machine Study Authors:Görkem Can Süleymanoğlu View a PDF of the paper titled Thermodynamic Regulation of Finite-Time Gibbs Training in Energy-Based Models: A Restricted Boltzmann Machine Study, by G\"orkem Can S\"uleymano\u{g}lu View PDF HTML (experimental) Abstract:Restricted Boltzmann Machines (RBMs) are typically trained using finite-length Gibbs chains under a fixed sampling temperature. This practice implicitly assumes that the stochastic regime remains valid as the energy landscape evolves during learning. We argue that this assumption can become structurally fragile under finite-time training dynamics. This fragility arises because, in nonconvex energy-based models, fixed-temperature finite-time training can generate admissible trajectories with effective-field amplification and conductance collapse. As a result, the Gibbs sampler may asymptotically freeze, the negative phase may localize, and, without sufficiently strong regularization, parameters may exhibit deterministic linear drift. To address this instability, we introduce an endogenous thermodynamic regulation framework in which temperature evolves as a dynamical state variable coupled to measurable sampling statistics. Under standard local Lipschitz conditions and a two-time-scale separation regime, we establish global ...