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

This paper first reviews basic backpropagation, a simple method which is now being widely used in areas like pattern recognition and fault diagnosis, and 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.

Abstract

Basic backpropagation, which is a simple method now being widely used in areas like pattern recognition and fault diagnosis, is reviewed. The basic equations for backpropagation through time, and applications to areas like pattern recognition involving dynamic systems, systems identification, and control are discussed. 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 arising with the method are described. Pseudocode is provided to clarify the algorithms. The chain rule for ordered derivatives-the theorem which underlies backpropagation-is briefly discussed. The focus is on designing a simpler version of backpropagation which can be translated into computer code and applied directly by neutral network users.>