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.
翻译:基于信仰传播(BP)等式的信件传递算法构成了众所周知的分布式计算方法。它精确地存在于树类图形模型中,并且已证明在环状图(从推论到优化,从信号处理到集群)中界定的许多问题中有效。基于BP的算法与目前深层网络的成功所基于的随机梯度梯度(SGD)有根本的不同。在本文中,我们介绍并适应关于GPUs的小型批次培训,这是一种基于BP的邮件传递算法,其强化字段将分布偏向于本地的昆虫解决方案。这些算法能够培训具有离散重量的多层神经网络,并以与SGD所激发的超常力(BinaryNet)相似的性能激活多层神经网络,并且自然地适应于持续学习。此外,利用这些算法来估计重量的边缘值,使我们能够作出比点准解决方案更精确的近似巴伊西亚预测。