Deep learning via message passing algorithms based on belief propagation

TL;DR

This paper introduces BP-based message-passing algorithms adapted for mini-batch GPU training, enabling neural networks with discrete weights to perform comparably to SGD and providing improved Bayesian predictions.

Contribution

It presents a novel BP-based training method for discrete neural networks, suitable for mini-batch GPU implementation and continual learning, with enhanced Bayesian inference capabilities.

Findings

Comparable performance to SGD-based methods on discrete neural networks

Effective in continual learning scenarios

Provides more accurate Bayesian marginal estimates

Abstract

Message-passing algorithms based on the Belief Propagation (BP) equations constitute a well-known distributed computational scheme. It is exact on tree-like graphical models and has also proven to be effective in many problems defined on graphs with loops (from inference to optimization, from signal processing to clustering). The BP-based scheme is fundamentally different from stochastic gradient descent (SGD), on which the current success of deep networks is based. In this paper, we present and adapt to mini-batch training on GPUs a family of BP-based message-passing algorithms with a reinforcement field that biases distributions towards locally entropic solutions. These algorithms are capable of training multi-layer neural networks with discrete weights and activations with performance comparable to SGD-inspired heuristics (BinaryNet) and are naturally well-adapted to continual learning. Furthermore, using these algorithms to estimate the marginals of the weights allows us to make approximate Bayesian predictions that have higher accuracy than point-wise solutions.