The back propagation algorithm has been modified to work without any multiplications and to tolerate comput.ations

The back propagation algorithm has been modified to work without any multiplications and to tolerate comput.ations

Learning to recognize or predict sequences using long-term context has many applications. However, practical and theoretical problems are found in training recurrent neural networks to perform tasks in which input/output dependencies span long intervals. Starting from a mathematical analysis of the problem, we consider and compare alternative algorithms and architectures on tasks for which the span of the input/output dependencies can be controlled. Results on the new algorithms show performance qualitatively superior to that obtained with backpropagation. 1 Introduction Recurrent neural networks have been considered to learn to map input sequences to output sequences. Machines that could efficiently learn such tasks would be useful for many applications involving sequence prediction, recognition or production. However, practical difficulties have been reported in training recurrent neural networks to perform tasks in which the temporal contingencies present in the input/output sequences span long intervals. In fact, we can prove that dynamical systems such as recurrent neural networks will be increasingly difficult to train with gradient descent as the duration of the dependencies to be captured increases. A mathematical analysis of the problem shows that either one of two conditions arises in such systems.

This fact provides a theoretical justification of the widely observed excellent robustness properties of the LMS and backpropagation algorithms. We further discuss some implications of these results.

Learning to recognize or predict sequences using long-term context has many applications. However, practical and theoretical problems are found in training recurrent neural networks to perform tasks in which input/output dependencies span long intervals. Starting from a mathematical analysis of the problem, we consider and compare alternative algorithms and architectures on tasks for which the span of the input/output dependencies can be controlled. Results on the new algorithms show performance qualitatively superior to that obtained with backpropagation. 1 Introduction Recurrent neural networks have been considered to learn to map input sequences to output sequences. Machines that could efficiently learn such tasks would be useful for many applications involving sequence prediction, recognition or production. However, practical difficulties have been reported in training recurrent neural networks to perform tasks in which the temporal contingencies present in the input/output sequences span long intervals. In fact, we can prove that dynamical systems such as recurrent neural networks will be increasingly difficult to train with gradient descent as the duration of the dependencies to be captured increases. A mathematical analysis of the problem shows that either one of two conditions arises in such systems.

This fact provides a theoretical justification of the widely observed excellent robustness properties of the LMS and backpropagation algorithms. We further discuss some implications of these results. 1 Introduction The LMS algorithm was originally conceived as an approximate recursive procedure that solves the following problem (Widrow and Hoff, 1960): given a sequence of n x 1 input column vectors {hd, and a corresponding sequence of desired scalar responses { di

The back propagation algorithm has been modified to work without anymultiplications and to tolerate comput.ations

Learning to recognize or predict sequences using long-term context hasmany applications. However, practical and theoretical problems are found in training recurrent neural networks to perform tasksin which input/output dependencies span long intervals. Starting from a mathematical analysis of the problem, we consider and compare alternative algorithms and architectures on tasks for which the span of the input/output dependencies can be controlled. Results on the new algorithms show performance qualitatively superior tothat obtained with backpropagation. 1 Introduction Recurrent neural networks have been considered to learn to map input sequences to output sequences. Machines that could efficiently learn such tasks would be useful for many applications involving sequence prediction, recognition or production.

TJ of the gradient updates is held constant (simple backpropagation).

TJ of the gradient updates is held constant (simple backpropagation).