The learning time of a simple neural network model is obtained through an analytic computation of the eigenvalue spectrum for the Hessian matrix, which describes the second order properties of the cost function in the space of coupling coefficients. The form of the eigenvalue distribution suggests new techniques for accelerating the learning process, and provides a theoretical justification for the choice of centered versus biased state variables.

Second order properties of cost functions for recurrent networks are investigated. We analyze a layered fully recurrent architecture, the virtue of this architecture is that it features the conventional feedforward architecture as a special case. A detailed description of recursive computation of the full Hessian of the network cost function isprovided. We discuss the possibility of invoking simplifying approximations of the Hessian and show how weight decays iron the cost function and thereby greatly assist training. We present tentative pruningresults, using Hassibi et al.'s Optimal Brain Surgeon, demonstrating that recurrent networks can construct an efficient internal memory. 1 LEARNING IN RECURRENT NETWORKS Time series processing is an important application area for neural networks and numerous architectures have been suggested, see e.g.

Second order properties of cost functions for recurrent networks are investigated. We analyze a layered fully recurrent architecture, the virtue of this architecture is that it features the conventional feedforward architecture as a special case. A detailed description of recursive computation of the full Hessian of the network cost function is provided. We discuss the possibility of invoking simplifying approximations of the Hessian and show how weight decays iron the cost function and thereby greatly assist training. We present tentative pruning results, using Hassibi et al.'s Optimal Brain Surgeon, demonstrating that recurrent networks can construct an efficient internal memory. 1 LEARNING IN RECURRENT NETWORKS Time series processing is an important application area for neural networks and numerous architectures have been suggested, see e.g. (Weigend and Gershenfeld, 94). The most general structure is a fully recurrent network and it may be adapted using Real Time Recurrent Learning (RTRL) suggested by (Williams and Zipser, 89). By invoking a recurrent network, the length of the network memory can be adapted to the given time series, while it is fixed for the conventional lag-space net (Weigend et al., 90). In forecasting, however, feedforward architectures remain the most popular structures; only few applications are reported based on the Williams&Zipser approach.

Second order properties of cost functions for recurrent networks are investigated. We analyze a layered fully recurrent architecture, the virtue of this architecture is that it features the conventional feedforward architecture as a special case. A detailed description of recursive computation of the full Hessian of the network cost function is provided. We discuss the possibility of invoking simplifying approximations of the Hessian and show how weight decays iron the cost function and thereby greatly assist training. We present tentative pruning results, using Hassibi et al.'s Optimal Brain Surgeon, demonstrating that recurrent networks can construct an efficient internal memory. 1 LEARNING IN RECURRENT NETWORKS Time series processing is an important application area for neural networks and numerous architectures have been suggested, see e.g. (Weigend and Gershenfeld, 94). The most general structure is a fully recurrent network and it may be adapted using Real Time Recurrent Learning (RTRL) suggested by (Williams and Zipser, 89). By invoking a recurrent network, the length of the network memory can be adapted to the given time series, while it is fixed for the conventional lag-space net (Weigend et al., 90). In forecasting, however, feedforward architectures remain the most popular structures; only few applications are reported based on the Williams&Zipser approach.

Holmdel, NJ 07733, USA The learning time of a simple neural network model is obtained through an analytic computation of the eigenvalue spectrum for the Hessian matrix, which describes the second order properties of the cost function in the space of coupling coefficients. The form of the eigenvalue distribution suggests new techniques for accelerating the learning process, and provides a theoretical justification for the choice of centered versus biased state variables.

The learning time of a simple neural network model is obtained through an analytic computation of the eigenvalue spectrum for the Hessian matrix, which describes the second order properties of the cost function in the space of coupling coefficients. The form of the eigenvalue distribution suggests new techniques for accelerating the learning process, and provides a theoretical justification for the choice of centered versus biased state variables.

The learning time of a simple neural network model is obtained through an analytic computation of the eigenvalue spectrum for the Hessian matrix, which describes the second order properties of the cost function in the space of coupling coefficients. The form of the eigenvalue distribution suggests new techniques for accelerating the learning process, and provides a theoretical justification for the choice of centered versus biased state variables.