Unsupervised generative modeling based on Markov chains out of equilibrium

This thesis investigates steady-state Markov Machines (ssMMs), a class of unsupervised generative models where visible and hidden variables interact through independently parameterized transition matrices. Unlike Restricted Boltzmann Machines, ssMMs enable the system to operate intrinsically out of equilibrium and develop persistent latent-state cycles. The study, using MNIST as the dataset, provides the derivation of the model's log-likelihood gradient and analyzes its non-equilibrium dynamics, characterized by entropy production and probability currents. A central focus of this work is the one-hot encoded latent space, where we introduce specific strategies to prevent latent-state collapse and ensure systematic utilization of all hidden units. Our results show that operating far from equilibrium, together with other regularization techniques, allows the model to reproduce the empirical class distribution with excellent performance that stays consistent across independent training runs.