Two approaches are described which allow parallel computation of a model's nonlinear functions, parallel modification of a model's weights, and parallel propagation of a model's activation and error. Each approach also allows a model's interconnect structure to be physically dynamic. A Hopfield model is implemented with each approach at six sizes over the same number of CM processors to provide a performance comparison. INTRODUCflON Simulations of neural network models on digital computers perform various computations by applying linear or nonlinear functions, defined in a program, to weighted sums of integer or real numbers retrieved and stored by array reference. The numerical values are model dependent parameters like time averaged spiking frequency (activation), synaptic efficacy (weight), the error in error back propagation models, and computational temperature in thermodynamic models. The interconnect structure of a particular model is implied by indexing relationships between arrays defined in a program. On the Connection Machine (CM), these relationships are expressed in hardware processors interconnected by a 16-dimensional hypercube communication network. Mappings are constructed to defme higher dimensional interconnectivity between processors on top of the fundamental geometry of the communication network.

Using a simple Hebb-type learning rule in conjunction withthe cortical dynamics which emerge from the anatomical and physiological organization ofthe model, the simulations are capable of establishing cortical representations for different input patterns. The basis of these representations lies in the interaction of sparsely distributed, highly divergent/convergent interconnections between modeled neurons. We have shown that different representations can be stored with minimal interference.

Using one extracellular microelectrode to record from several neurons is one approach to studying the response properties of sets of adjacent and therefore likely related neurons. However, to do this, it is necessary to correctly classify the signals generated by these different neurons. This paper considers this problem of classifying the signals in such an extracellular recording, based upon their shapes, and specifically considers the classification of signals in the case when spikes overlap temporally. Introduction How single neurons in a network of neurons interact when processing information is likely to be a fundamental question central to understanding how real neural networks compute. In the mammalian nervous system we know that spatially adjacent neurons are, in general, more likely to interact, as well as receive common inputs.

In the past thirty years many researchers have studied the question of supervised learning in'neural'-like networks. Recently a learning algorithm called'back propagation

In this article we consider two aspects of computation with neural networks. Firstly we consider the problem of the complexity of the network required to compute classes of specified (structured) functions. We give a brief overview of basic known complexity theoremsfor readers familiar with neural network models but less familiar with circuit complexity theories. We argue that there is considerable computational and physiological justification for the thesis that shallow circuits (Le., networks with relatively few layers) are computationally more efficient. We hence concentrate on structured (as opposed to random) problems that can be computed in shallow (constant depth)circuits with a relatively few number (polynomial) of elements, and demonstrate classes of structured problems that are amenable to such low cost solutions. Wediscuss an allied problem-the complexity of learning-and close with some open problems and a discussion of the observed limitations of the theoretical approach. Wenext turn to a rigourous classification of how much a network of given structure can do; i.e., the computational capacity of a given construct.

In biological systems, it relates to such issues as classical and operant conditioning, temporal coordination of sensorimotor systems and temporal reasoning. In artificial systems, it addresses such real-world tasks as robot control, speech recognition, dynamic image processing, moving target detection by sonars or radars, EEG diagnosis, and seismic signal processing. Most of the processing elements used in neural network models for practical applications have been the formal neuronl or" its variations. These elements lack a memory flexible to temporal patterns,thus limiting most of the neural network models previously proposed to problems of spatial (or static) patterns. Some past solutions have been to convert the dynamic problems to static ones using buffer (or storage) neurons, or using a layered network with/without feedback.

LEARNING ON A GENERAL NETWORK Amir F. Atiya Department of Electrical Engineering California Institute of Technology Ca 91125 Abstract This paper generalizes the backpropagation method to a general network containing feedback t;onnections.The network model considered consists of interconnected groups of neurons, where each group could be fully interconnected (it could have feedback connections, with possibly asymmetricweights), but no loops between the groups are allowed. A stochastic descent algorithm is applied, under a certain inequality constraint on each intragroup weight matrix which ensures for the network to possess a unique equilibrium state for every input. Introduction Ithas been shown in the last few years that large networks of interconnected "neuron" -like elemp.nts One of the well-known neural network models is the backpropagation model [1]-[4]. It is an elegant way for teaching a layered feedforward network by a set of given input/output examples.

The Fifth Annual Theoretical Issues in Conceptual Information Processing Workshop took place in Washington, D.C. in June 1987. About 100 participants gathered to hear several invited talks and panels discussing the issues relating to artificial intelligence and cognitive science.

We built on previous work to develop an evaluation method that can be used to select expert system applications which are most likely to be successfully implemented. Both essential and desirable features of an expert system application are discussed. Essential features are used to ensure that the application does not require technology beyond the state of the art. Advice on helpful directions for evaluating candidate expert system applications is also given.

A novel approach is presented for the development of expert systems for structural design problems. This approach differs from the conventional expert systems in two fundamental respects. As an example of this approach, a prototype coupled expert system, the bridge truss expert (BTExpert), is presented for optimum design of bridge trusses subjected to moving loads. BTExpert was developed by interfacing an interactive optimization program developed in Fortran 77 to an expert system shell developed in Pascal.