Early Inference in Energy-Based Models Approximates Back-Propagation

TL;DR

This paper demonstrates that early inference steps in energy-based models approximate back-propagation, providing insights into potential neural mechanisms for credit assignment in the brain.

Contribution

It reveals that Langevin MCMC inference in energy-based models naturally performs error propagation similar to back-propagation during early inference steps.

Findings

Early inference steps correspond to propagating error gradients.

Error signals relate to temporal derivatives of hidden unit activations.

Potential neural basis for credit assignment in deep hierarchies.

Abstract

We show that Langevin MCMC inference in an energy-based model with latent variables has the property that the early steps of inference, starting from a stationary point, correspond to propagating error gradients into internal layers, similarly to back-propagation. The error that is back-propagated is with respect to visible units that have received an outside driving force pushing them away from the stationary point. Back-propagated error gradients correspond to temporal derivatives of the activation of hidden units. This observation could be an element of a theory for explaining how brains perform credit assignment in deep hierarchies as efficiently as back-propagation does. In this theory, the continuous-valued latent variables correspond to averaged voltage potential (across time, spikes, and possibly neurons in the same minicolumn), and neural computation corresponds to approximate inference and error back-propagation at the same time.