Emergence of Nonequilibrium Latent Cycles in Unsupervised Generative Modeling

TL;DR

This paper demonstrates that nonequilibrium dynamics in unsupervised generative models can lead to the spontaneous formation of latent cycles, improving data distribution modeling by breaking detailed balance.

Contribution

It introduces a novel model that incorporates nonequilibrium steady states with latent cycles, enhancing generative performance over equilibrium models like RBMs.

Findings

Latent cycles emerge spontaneously during training.

Models with nonequilibrium dynamics avoid low-likelihood regimes.

Breaking detailed balance improves data distribution reproduction.

Abstract

We show that nonequilibrium dynamics can play a constructive role in unsupervised machine learning by inducing the spontaneous emergence of latent-state cycles. We introduce a model in which visible and hidden variables interact through two independently parametrized transition matrices, defining a Markov chain whose steady state is intrinsically out of equilibrium. Likelihood maximization drives this system toward nonequilibrium steady states with finite entropy production, reduced self-transition probabilities, and persistent probability currents in the latent space. These cycles are not imposed by the architecture but arise from training, and models that develop them avoid the low-log-likelihood regime associated with nearly reversible dynamics while more faithfully reproducing the empirical distribution of data classes. Compared with equilibrium approaches such as restricted Boltzmann machines, our model breaks the detailed balance between the forward and backward conditional transitions and relies on a log-likelihood gradient that depends explicitly on the last two steps of the Markov chain. Hence, this exploration of the interface between nonequilibrium statistical physics and modern machine learning suggests that introducing irreversibility into latent-variable models can enhance generative performance.