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Outline

Backpropagation through time: what it does and how to do it

1990, Proceedings of the IEEE

https://doi.org/10.1109/5.58337

Abstract

Backpropagation is now the most widely used tool in the field of artificial neural networks. At the core of backpropagation is a method for calculating derivatives exactly and efficiently in any large system made up of elementary subsystems or calculations which are represented by known, differentiable functions; thus, backpropagation has many applications which do not involve neural networks as such. This paper first reviews basic backpropagation, a simple method which is now being widely used in areas like pattern recognition and fault diagnosis. Next, it presents the basic equations for backpropagation through time, and discusses applications to areas like pattern recognition involving dynamic systems, systems identification, and control. Finally, it describes further extensions of this method, to deal with systems other than neural networks, systems involving simultaneous equations or true recurrent networks, and other practical issues which arise with this method. Pseudocode is provided to clarify the algorithms. The chain rule for ordered derivatives-the theorem which underlies backpropagation-is briefly discussed.

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  16. Paul J. Werbos received degrees from Har- vard University, Cambridge, MA, and the London School of Economics, London, England, that emphasized mathematical physics, international political economy, and economics. He developed backprop- agation for the Ph.D. degree in applied mathematics at Harvard. He iscurrently Program Director for Neu- roengineering and Emerging Technology Initiation at the National Science Founda- tion (NSF) and Secretary of the International Neural Network Soci- ety. While an Assistant Professor at the University of Maryland, he developed advanced adaptive critic designs for neurocontrol. Before joining the hlSF in 1989, he worked nine years at the Energy Information Administration (EIA) of DOE, where he variously held lead responsibility for evaluating long-range forecasts (under Charles Smith), and for building models of industrial, transpor- tation, and commercial demand, and natural gas supply using backpropagation as one among several methods. In previous years, he was Regional Director and Washington representative of the L-5 Society, a predecessor to the National Space Society, and an organizer of the Global Futures Roundtable. He has worked on occasion with the National Space Society, the Global Tomorrow Coalition, the Stanford Energy Modeling Forum, and Adelphi Friends Meeting. He also retains an active interest in fuel cells for transportation and in the foundations of physics.