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

TL;DR

This paper analyzes how the choice of hidden unit priors and architectural modifications in bipartite energy-based neural networks, specifically RBMs, affect their phase diagram and memory retrieval capabilities, revealing ways to improve their associative memory performance.

Contribution

It provides a theoretical analysis linking hidden unit priors to the thermodynamic properties of RBMs and proposes modifications to enhance their memory retrieval abilities.

Findings

Binary RBMs have limited critical capacity.

Introducing biases and richer priors improves retrieval performance.

Theoretical results are supported by Monte Carlo simulations.

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.