title: STDP-Compatible Approximation of Backpropagation in an Energy-Based Model.
abstract: We show that Langevin Markov chain Monte Carlo 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, similar to backpropagation. The backpropagated error is with respect to output units that have received an outside driving force pushing them away from the stationary point. Backpropagated error gradients correspond to temporal derivatives with respect to the activation of hidden units. These lead to a weight update proportional to the product of the presynaptic firing rate and the temporal rate of change of the postsynaptic firing rate. Simulations and a theoretical argument suggest that this rate-based update rule is consistent with those associated with spike-timing-dependent plasticity. The ideas presented in this article could be an element of a theory for explaining how brains perform credit assignment in deep hierarchies as efficiently as backpropagation does, with neural computation corresponding to both approximate inference in continuous-valued latent variables and error backpropagation, at the same time.
authors.affiliation: Montreal Institute for Learning Algorithms, University of Montreal, Montreal H3T 1J4, Quebec, Canada, and Canadian Institute for Advanced Research yoshua.umontreal@gmail.com.
authors.forename: Yoshua
authors.initials: Y
authors.lastname: Bengio
authors.affiliation: Computer Science Department, École Normale Supérieure, Paris 75005, France thomas.mesnard@gmail.com.
authors.forename: Thomas
authors.initials: T
authors.lastname: Mesnard
authors.affiliation: Institute of Computer Science, University of Bonn, Bonn 53117, Germany asja.fischer@gmail.com.
authors.forename: Asja
authors.initials: A
authors.lastname: Fischer
authors.affiliation: Montreal Institute for Learning Algorithms, University of Montreal, Montreal H3T 1J4, Quebec, Canada saizhenglisa@gmail.com.
authors.forename: Saizheng
authors.initials: S
authors.lastname: Zhang
authors.affiliation: University of Toronto, Toronto, Ontario, M5S 1A1, Canada ywu@cs.toronto.edu.
authors.forename: Yuhuai
authors.initials: Y
authors.lastname: Wu