Equivalence of Backpropagation and Contrastive Hebbian Learning in a Layered Network

Backpropagation and contrastive Hebbian learning are two methods of training networks with hidden neurons. Backpropagation computes an error signal for the output neurons and spreads it over the hidden neurons. Contrastive Hebbian learning involves clamping the output neurons at desired values and letting the effect spread through feedback connections over the entire network. To investigate the relationship between these two forms of learning, we consider a special case in which they are identical: a multilayer perceptron with linear output units, to which weak feedback connections have been added. In this case, the change in network state caused by clamping the output neurons turns out to be the same as the error signal spread by backpropagation, except for a scalar prefactor. This suggests that the functionality of backpropagation can be realized alternatively by a Hebbian-type learning algorithm, which is suitable for implementation in biological networks.

[1]  Stephen Grossberg,et al.  Absolute stability of global pattern formation and parallel memory storage by competitive neural networks , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[2]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[3]  Geoffrey E. Hinton,et al.  A Learning Algorithm for Boltzmann Machines , 1985, Cogn. Sci..

[4]  Geoffrey E. Hinton,et al.  Learning representations by back-propagating errors , 1986, Nature.

[5]  Geoffrey E. Hinton,et al.  Learning internal representations by error propagation , 1986 .

[6]  D. Rumelhart.  Learning Internal Representations by Error Propagation, Parallel Distributed Processing , 1986 .

[7]  James L. McClelland,et al.  Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations , 1986 .

[8]  Carsten Peterson,et al.  A Mean Field Theory Learning Algorithm for Neural Networks , 1987, Complex Syst..

[9]  J J Hopfield,et al.  Learning algorithms and probability distributions in feed-forward and feed-back networks. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[10]  Geoffrey E. Hinton,et al.  Learning Representations by Recirculation , 1987, NIPS.

[11]  Richard A. Andersen,et al.  A back-propagation programmed network that simulates response properties of a subset of posterior parietal neurons , 1988, Nature.

[12]  Francis Crick,et al.  The recent excitement about neural networks , 1989, Nature.

[13]  Michael I. Jordan,et al.  A more biologically plausible learning rule for neural networks. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[14]  Michael I. Jordan,et al.  A more biologically plausible learning rule than backpropagation applied to a network model of cortical area 7a. , 1991, Cerebral cortex.

[15]  Pierre Baldi,et al.  Contrastive Learning and Neural Oscillations , 1991, Neural Computation.

[16]  Javier R. Movellan,et al.  Contrastive Hebbian Learning in the Continuous Hopfield Model , 1991 .

[17]  Randall C. O'Reilly,et al.  Biologically Plausible Error-Driven Learning Using Local Activation Differences: The Generalized Recirculation Algorithm , 1996, Neural Computation.

[18]  Alexander J. Smola,et al.  Neural Information Processing Systems , 1997, NIPS 1997.

[19]  Michael I. Jordan,et al.  Deterministic Boltzmann Learning Performs Steepest Descent in Weight-Space , 2001 .

[20]  Robert M. French,et al.  Self-refreshing memory in artificial neural networks: learning temporal sequences without catastrophic forgetting , 2004, Connect. Sci..

[21]  R. Krishnan.  SPINAL CORD INJURY: REVERSING THE INCORRECT CORTICAL MAPS BY INDUCTIVE LABILITY PROCEDURE , 2004, The International journal of neuroscience.