A biologically-plausible learning rule using reciprocal feedback connections

Artificial neural networks are frequently used to model neural systems, and have been shown to recapitulate features of biological networks, including in the hippocampus [1] and visual cortex [2] [3].
However, despite it’s success in neural modelling, the predominant learning algorithm, backpropagation, has long been considered biologically implausible [4]. One reason is the weight-transport problem - or the problem of how a global error signal can be accurately transmitted across the network to minimize the error resulting from each layer’s parameters. Previous solutions to the weight-transport problem have proposed using a separate, error-feedback network to transport an error signal across layers [5]. However, more recent experimental work indicates that cortical feedback connections are more likely to be involved in reconstructing lower-level activity based on activity from higher layers, rather than being exclusively used to transmit top-level error [6] [7] [8]. Under the predictive coding framework, the bidirectional, cortical processing hierarchy is more appropriately modeled as a multi-layered autoencoder [9]. Here, we attempt to unify these two views by showing how autoencoder-like, inverse feedback connections may be used to minimize top-level error in neural networks. Our proposed mechanism, Reciprocal Feedback, consists of two contributions: first we show how a modification of the Recirculation autoencoder algorithm [10] is equivalent to learning the Moore-Penrose pseudoinverse. Then, we will show how, using a Newton-like method [11], locally-learned pseudoinverse feedback connections may be used to facilitate an alternative, more biologically-realistic optimization method to gradient descent, by relying on the reciprocal of the forward network rather than its gradient. Overall, we provide a mathematical framework for understanding how the hierarchical, autoencoder-like feedback connections observed in the layers of the cortex may additionally be used as a mechanism for minimizing a global error signal, using only local activity.