This work follows Bengio and Fischer (2015) in which theoretical foundations were laid to show how iterative inference can backpropagate error signals. Neurons move their activations towards configurations corresponding to lower energy and smaller prediction error: a new observation creates a perturbation at visible neurons that propagates into hidden layers, with these propagated perturbations corresponding to the back-propagated gradient. This avoids the need for a lengthy relaxation in the positive phase of training (when both inputs and targets are observed), as was believed with previous work on fixed-point recurrent networks. We show experimentally that energy-based neural networks with several hidden layers can be trained at discriminative tasks by using iterative inference and an STDP-like learning rule. The main result of this paper is that we can train neural networks with 1, 2 and 3 hidden layers on the permutation-invariant MNIST task and get the training error down to 0.00%. The results presented here make it more biologically plausible that a mechanism similar to back-propagation may take place in brains in order to achieve credit assignment in deep networks. The paper also discusses some of the remaining open problems to achieve a biologically plausible implementation of backprop in brains.

介绍Equilibrium Propagation-一种学习能量模型的框架，该模型仅涉及一种神经计算，并在两个阶段中执行，通过Local perturbations，使预测从一个配置微调到减少预测误差的配置，并且在第二阶段向后传播的信号编码错误导数的梯度。

平衡传播：弥合基于能量模型与反向传播之间的鸿沟