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.

DISCOVERING STRUCfURE FROM MOTION IN MONKEY, MAN AND MACHINE Ralph M. Siegel· The Salk Institute of Biology, La Jolla, Ca. 92037 ABSTRACT The ability to obtain three-dimensional structure from visual motion is important for survival of human and nonhuman primates. Using a parallel processing model, the current work explores how the biological visual system might solve this problem and how the neurophysiologist might go about understanding the solution. In the present work, much effort has been expended mimicking the visual system. This was done for one main reason: the model was designed to help direct physiological experiments in the primate. It was hoped that if an approach for understanding the model could be developed, the approach could then be directed at the primate's visual system.

ABSTRACT A single cell theory for the development of selectivity and ocular dominance in visual cortex has been presented previously by Bienenstock, Cooper and Munrol. This has been extended to a network applicable to layer IV of visual cortex 2. In this paper we present a mean field approximation that captures in a fairly transparent manner the qualitative, and many of the quantitative, results of the network theory. Finally, we consider the application of this theory to artificial neural networks and show that a significant reduction in architectural complexity is possible. A SINGLE LAYER NETWORK AND THE MEAN FIELD APPROXIMATION We consider a single layer network of ideal neurons which receive signals from outside of the layer and from cells within the layer (Figure 1). The activity of the ith cell in the network is c' - m' d J d is a vector of afferent signals to the network. Each cell receives input from n fibers outside of the cortical network through the matrix of synapses mi' Intra-layer input to each cell is then transmitted through the matrix of cortico-cortical synapses L. Light circles are the LGN -cortical synapses.

The nets are also described as parallel distributed systems!, connectionist models

ABSTRACT Artificial neural networks (ANNs) are capable of accurate recognition of simple speech vocabularies such as isolated digits [1]. This paper looks at two more difficult vocabularies, the alphabetic E-set and a set of polysyllabic words. The E-set is difficult because it contains weak discriminants and polysyllables are difficult because of timing variation. Polysyllabic word recognition is aided by a time pre-alignment technique based on dynamic programming and E-set recognition is improved by focusing attention. Recognition accuracies are better than 98% for both vocabularies when implemented with a single layer perceptron.

Please address all further correspondence to: John Y. Cheung School of EECS 202 W. Boyd, CEC 219 Norman, OK 73019 (405)325-4721 MATHEMATICAL ANALYSIS OF LEARNING BEHAVIOR OF NEURONAL MODELS John Y. Cheung and Massoud Omidvar School of Electrical Engineering and Computer Science ABSTRACT In this paper, we wish to analyze the convergence behavior of a number of neuronal plasticity models. Recent neurophysiological research suggests that the neuronal behavior is adaptive. In particular, memory stored within a neuron is associated with the synaptic weights which are varied or adjusted to achieve learning. A number of adaptive neuronal models have been proposed in the literature. Three specific models will be analyzed in this paper, specifically the Hebb model, the Sutton-Barto model, and the most recent trace model.

CYCLES: A Simulation Tool for Studying Cyclic Neural Networks Michael T. Gately Texas Instruments Incorporated, Dallas, TX 75265 ABSTRACT A computer program has been designed and implemented to allow a researcher to analyze the oscillatory behavior of simulated neural networks with cyclic connectivity. The computer program, implemented on the Texas Instruments Explorer / Odyssey system, and the results of numerous experiments are discussed. The program, CYCLES, allows a user to construct, operate, and inspect neural networks containing cyclic connection paths with the aid of a powerful graphicsbased interface. Numerous cycles have been studied, including cycles with one or more activation points, non-interruptible cycles, cycles with variable path lengths, and interacting cycles. The final class, interacting cycles, is important due to its ability to implement time-dependent goal processing in neural networks.

The operator also produces simultaneous brightness contrast, as expected from the shape and sign of its surround. The output reflectance it computes for a patch of fixed input reflectance decreases linearly with increasing average irradiance of the input test vector in which the patch appears. Similarly, to us, a dark patch appears darker when against a light background than against a dark one.

There are three existing connection::;t models in which network states are assigned a computational energy.

THE CAPACITY OF THE KANERVA ASSOCIATIVE MEMORY IS EXPONENTIAL P. A. Chou CA 94305 ABSTRACT The capacity of an associative memory is defined as the maximum number of vords that can be stored and retrieved reliably by an address vithin a given sphere of attraction. It is shown by sphere packing arguments that as the address length increases. This exponential grovth in capacity can actually be achieved by the Kanerva associative memory. Formulas for these op.timal values are provided. The exponential grovth in capacity for the Kanerva associative memory contrasts sharply vith the sub-linear grovth in capacity for the Hopfield associative memory.