Poster
Equilibrium and non-Equilibrium regimes in the learning of Restricted Boltzmann Machines
Aurélien Decelle · Cyril Furtlehner · Beatriz Seoane
Keywords: [ Generative Model ] [ Self-Supervised Learning ]
Abstract:
Training Restricted Boltzmann Machines (RBMs) has been challenging for a long time due to the difficulty of computing precisely the log-likelihood gradient. Over the past decades, many works have proposed more or less successful recipes but without studying systematically the crucial quantity of the problem: the mixing time i.e. the number of MCMC iterations needed to sample completely new configurations from a model. In this work, we show that this mixing time plays a crucial role in the behavior and stability of the trained model, and that RBMs operate in two well-defined distinct regimes, namely equilibrium and out-of-equilibrium, depending on the interplay between this mixing time of the model and the number of MCMC steps, , used to approximate the gradient. We further show empirically that this mixing time increases along the learning, which often implies a transition from one regime to another as soon as becomes smaller than this time.In particular, we show that using the popular (persistent) contrastive divergence approaches, with small, the dynamics of the fitted model are extremely slow and often dominated by strong out-of-equilibrium effects. On the contrary, RBMs trained in equilibrium display much faster dynamics, and a smooth convergence to dataset-like configurations during the sampling.Finally, we discuss how to exploit in practice both regimes depending on the task one aims to fulfill: (i) short s can be used to generate convincing samples in short learning times, (ii) large (or increasingly large) must be used to learn the correct equilibrium distribution of the RBM. Finally, the existence of these two operational regimes seems to be a general property of energy based models trained via likelihood maximization.
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