Deep learning via message passing algorithms based on belief propagation
This work addresses the challenge of training discrete neural networks efficiently, offering a novel alternative to SGD for applications like continual learning, though it is incremental in adapting existing message-passing techniques.
The paper tackles training multi-layer neural networks with discrete weights and activations using belief propagation-based message-passing algorithms, achieving performance comparable to SGD-inspired methods like BinaryNet and enabling approximate Bayesian predictions with higher accuracy than point-wise solutions.
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.