Towards a Biologically Plausible Backprop

This work contributes several new elements to the quest for a biologically plausible implementation of backprop in brains. We introduce a very general and abstract framework for machine learning, in which the quantities of interest are defined implicitly through an energy function. In this framework, only one kind of neural computation is involved both for the first phase (when the prediction is made) and the second phase (after the target is revealed), like the contrastive Hebbian learning algorithm in the continuous Hopfield model for example. Contrary to automatic differentiation in computational graphs (i.e. standard backprop), there is no need for special computation in the second phase of our framework. One advantage of our framework over contrastive Hebbian learning is that the second phase corresponds to only nudging the first-phase fixed point towards a configuration that reduces prediction error. In the case of a multi-layer supervised neural network, the output units are slightly nudged towards their target, and the perturbation introduced at the output layer propagates backward in the network. The signal 'back-propagated' during this second phase actually contains information about the error derivatives, which we use to implement a learning rule proved to perform gradient descent with respect to an objective cost function.