Spectral Dynamics of Learning Restricted Boltzmann Machines

Abstract

The Restricted Boltzmann Machine (RBM), an important tool used in machine learning in particular for unsupervized learning tasks, is investigated from the perspective of its spectral properties. Starting from empirical observations, we propose a generic statistical ensemble for the weight matrix of the RBM and characterize its mean evolution. This let us show how in the linear regime, in which the RBM is found to operate at the beginning of the training, the statistical properties of the data drive the selection of the unstable modes of the weight matrix. A set of equations characterizing the non-linear regime is then derived, unveiling in some way how the selected modes interact in later stages of the learning procedure and defining a deterministic learning curve for the RBM.

References in corpus (2)

• Mean-field message-passing equations in the Hopfield model and its generalizations
• Advanced Mean Field Theory of Restricted Boltzmann Machine

Cited by in corpus (5)

• Barriers and Dynamical Paths in Alternating Gibbs Sampling of Restricted Boltzmann Machines
• The unbearable lightness of Restricted Boltzmann Machines: Theoretical Insights and Biological Applications
• A Probability Density Theory for Spin-Glass Systems
• A relativistic extension of Hopfield neural networks via the mechanical analogy
• Nonequilibrium thermodynamics of self-supervised learning