On the role of non-linear latent features in bipartite generative neural networks

Abstract

We investigate the phase diagram and memory retrieval capabilities of bipartite energy-based neural networks, namely Restricted Boltzmann Machines (RBMs), as a function of the prior distribution imposed on their hidden units - including binary, multi-state, and ReLU-like activations. Drawing connections to the Hopfield model and employing analytical tools from statistical physics of disordered systems, we explore how the architectural choices and activation functions shape the thermodynamic properties of these models. Our analysis reveals that standard RBMs with binary hidden nodes and extensive connectivity suffer from reduced critical capacity, limiting their effectiveness as associative memories. To address this, we examine several modifications, such as introducing local biases and adopting richer hidden unit priors. These adjustments restore ordered retrieval phases and markedly improve recall performance, even at finite temperatures. Our theoretical findings, supported by finite-size Monte Carlo simulations, highlight the importance of hidden unit design in enhancing the expressive power of RBMs.

23 pages, 5 figures

References in corpus (15)

• The physics of higher-order interactions in complex systems
• Mean-field message-passing equations in the Hopfield model and its generalizations
• Mean-field theory for the inverse Ising problem at low temperatures
• Spectral Dynamics of Learning Restricted Boltzmann Machines
• Equilibrium and non-Equilibrium regimes in the learning of Restricted Boltzmann Machines
• Replica symmetry breaking in dense neural networks
• Learning a Restricted Boltzmann Machine using biased Monte Carlo sampling
• Fundamental problems in statistical physics XIV: Lecture on Machine Learning
• Inferring effective couplings with Restricted Boltzmann Machines
• Hopfield model with planted patterns: a teacher-student self-supervised learning model
• The unbearable lightness of Restricted Boltzmann Machines: Theoretical Insights and Biological Applications
• Daydreaming Hopfield Networks and their surprising effectiveness on correlated data
• The effect of priors on Learning with Restricted Boltzmann Machines
• A fast and accurate algorithm for inferring sparse Ising models via parameters activation to maximize the pseudo-likelihood
• Inferring Higher-Order Couplings with Neural Networks