Deep learning via message passing algorithms based on belief propagation

Fabrizio Pittorino, Carlo Lucibello, Gabriele Perugini, Riccardo Zecchina

Keywords: belief propagation, neural networks, graphical models, gradient-free algorithms, discrete neural networks

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.

One-sentence Summary: Deep learning via message passing algorithms based on belief propagation.

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2110.14583/code)