The algorithm presented performs gradient descent on the weight space of an Artificial Neural Network (ANN), using a finite difference to approximate the gradient The method is novel in that it achieves a computational complexity similar to that of Node Perturbation, O(N3), but does not require access to the activity of hidden or internal neurons. This is possible due to a stochastic relation between perturbations at the weights and the neurons of an ANN. The algorithm is also similar to Weight Perturbation in that it is optimal in terms of hardware requirements when used for the training ofVLSI implementations of ANN's.

These results show how combinatorial structure can be based on the spatial nature of networks, and not just on their emulation of logical structure.

IR is typically a sigmoidal function such as (1.2) but other choices than (1.2) are possible and of interest.

The algorithm presented performs gradient descent on the weight space of an Artificial Neural Network (ANN), using a finite difference to approximate the gradient The method is novel in that it achieves a computational complexitysimilar to that of Node Perturbation, O(N3), but does not require access to the activity of hidden or internal neurons. This is possible due to a stochastic relation between perturbations at the weights and the neurons of an ANN. The algorithm is also similar to Weight Perturbation in that it is optimal in terms of hardware requirements whenused for the training ofVLSI implementations of ANN's.

These devices are implanted and perform three types of actions: l.monitor the heart 2.to pace the heart 3.to apply high energy/high voltage electric shock 1bey sense the electrical activity of the heart through leads attached to the heart tissue. Two types of sensing are commooly used: Single Chamber: Lead attached to the Right Ventricular Apex (RVA) Dual Chamber: An additional lead is attached to the High Right Atrium (HRA). The actions performed by defibrillators are based on the outcome of a classification procedure based on the heart rhythms of different heart diseases (abnormal rhythms or "arrhythmias").

This paper is concerned with the problem of learning in networks where some or all of the functions involved are not smooth. Examples of such networks are those whose neural transfer functions are piecewise-linear and those whose error function is defined in terms of the 100 norm. Up to now, networks whose neural transfer functions are piecewise-linear have received very little consideration in the literature, but the possibility of using an error function defined in terms of the 100 norm has received some attention. In this paper we draw upon some recent results from the field of nonsmooth optimization (NSO) to present an algorithm for the non smooth case. Our motivation for this work arose out of the fact that we have been able to show that, in backpropagation, an error function based upon the 100 norm overcomes the difficulties which can occur when using the 12 norm. 1 INTRODUCTION This paper is concerned with the problem of learning in networks where some or all of the functions involved are not smooth.

Connections between spline approximation, approximation with rational functions, and feedforward neural networks are studied. The potential improvement in the degree of approximation in going from single to two hidden layer networks is examined. Some results of Birman and Solomjak regarding the degree of approximation achievable when knot positions are chosen on the basis of the probability distribution of examples rather than the function values are extended.

We present a framework for programming tbe bidden unit representations of simple recurrent networks based on the use of hint units (additional targets at the output layer). We present two ways of analysing a network trained within this framework: Input patterns act as operators on the information encoded by the context units; symmetrically, patterns of activation over tbe context units act as curried functions of the input sequences. Simulations demonstrate that a network can learn to represent three different functions simultaneously and canonical discriminant analysis is used to investigate bow operators and curried functions are represented in the space of bidden unit activations.

Connections between spline approximation, approximation with rational functions, and feedforward neural networks are studied. The potential improvement in the degree of approximation in going from single to two hidden layer networks is examined. Some results of Birman and Solomjak regarding the degree of approximation achievable when knot positions are chosen on the basis of the probability distribution of examples rather than the function values are extended.

In this paper, a tree based neural network viz. MARS (Friedman, 1991) for the modelling of the yield strength of a steel rolling plate mill is described. The inputs to the time series model are temperature, strain, strain rate, and interpass time and the output is the corresponding yield stress. It is found that the MARSbased model reveals which variable's functional dependence is nonlinear, and significant. The results are compared with those obta.ined