We have produced a VLSI circuit capable of learning to approximate arbitrary smooth of a single variable using a technique closely related to splines. The circuit effectively has 512 knots space on a uniform grid and has full support for learning. The circuit also can be used to approximate multi-variable functions as sum of splines. An interesting, and as of yet, nearly untapped set of applications for VLSI implementation of neural network learning systems can be found in adaptive control and nonlinear signal processing. In most such applications, the learning task consists of approximating a real function of a small number of continuous variables from discrete data points.

Viewing n-variable boolean functions as vectors in'R'2", we invoke tools from linear algebra and linear programming to derive new results on the realizability of boolean functions using threshold gat.es. Using this approach, one can obtain: (1) upper-bounds on the number of spurious memories in HopfielJ networks, and on the number of functions implementable by a depth-d threshold circuit; (2) a lower bound on the number of ort.hogonal input.

Joseph E. Collard Martingale Research Corporation 100 Allentown Pkwy., Suite 211 Allen, Texas 75002 Abstract An Artificial Neural Network (ANN) is trained to recognize a buy/sell (long/short) pattern for a particular commodity future contract. The Back Propagation of errors algorithm was used to encode the relationship between the Long/Short desired output and 18 fundamental variables plus 6 (or 18) technical variables into the ANN. Trained on one year of past data the ANN is able to predict long/short market positions for 9 months in the future that would have made $10,301 profit on an investment of less than $1000. 1 INTRODUCTION An Artificial Neural Network (ANN) is trained to recognize a long/short pattern for a particular commodity future contract. The Back-Propagation of errors algorithm was used to encode the relationship between the Long/Short desired output and 18 fundamental variables plus 6 (or 18) technical variables into the ANN. 2 NETWORK ARCHITECTURE The ANNs used were simple, feed forward, single hidden layer networks with no input units, N hidden units and one output unit. N varied from six (6) through sixteen (16) hidden units.

In salamander retina, the response of On-Off ganglion cells to a central flash is reduced by movement in the receptive field surround. Through computer simulation of a 2-D model which takes into account their anatomical and physiological properties, we show that interactions between four neuron types (two bipolar and two amacrine) may be responsible for the generation and lateral conductance of this change sensitive inhibition. The model shows that the four neuron circuit can account for previously observed movement sensitive reductions in ganglion cell sensitivity and allows visualization and prediction of the spatiotemporal pattern of activity in change sensitive retinal cells.

In response to a puff of wind, the American cockroach turns away and runs. The circuit underlying the initial turn of this escape response consists of three populations of individually identifiable nerve cells and appears to employ distributed representations in its operation. We have reconstructed several neuronal and behavioral properties of this system using simplified neural network models and the backpropagation learning algorithm constrained by known structural characteristics of the circuitry. In order to test and refine the model, we have also compared the model's responses to various lesions with the insect's responses to similar lesions.

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We describe a computational model of the development and regeneration ofspecific eye-brain circuits. The model comprises a self-organizing map-forming network which uses local Hebb rules, constrained by (genetically determined) molecular markers. Various simulations of the development and regeneration of eye-brain maps in fish and frogs are described, in particular successful simulations of experiments by Schmidt-Cicerone-Easter; Meyer; and Yoon. 1 INTRODUCTION In a previous paper published in last years proceedings (Cowan & Friedman 1990) we outlined a new computational model for the development and regeneration of eye-brain maps. We indicated that such a model can simulate the results of a number of the more complicated surgical manipulations carried out on the visual pathways of goldfish and frogs. In this paper we describe in more detail some of these experiments, and our simulations of them.

James M. Bower Computation and Neural Systems Caltech 216-76 Pasadena, CA 91125 Combining neuropharmacological experiments with computational modeling, wehave shown that cholinergic modulation may enhance associative memory function in piriform (olfactory) cortex. We have shown that the acetylcholine analogue carbachol selectively suppresses synaptic transmission betweencells within piriform cortex, while leaving input connections unaffected. When tested in a computational model of piriform cortex, this selective suppression, applied during learning, enhances associative memory performance.

A massively parallel, all-digital, stochastic architecture - TlnMAN N - is described which performs competitive and Kohonen types of learning. A VLSI design is shown for a TlnMANN neuron which fits within a small, inexpensive MOSIS TinyChip frame, yet which can be used to build larger networks of several hundred neurons. The neuron operates at a speed of 15 MHz which allows the network to process 290,000 training examples per second. Use of level sensitive scan logic provides the chip with 100% fault coverage, permitting very reliable neural systems to be built.

In response to a puff of wind, the American cockroach turns away and runs. The circuit underlying the initial turn of this escape response consists of three populations of individually identifiable nerve cells and appears to employ distributedrepresentations in its operation. We have reconstructed several neuronal and behavioral properties of this system using simplified neural network models and the backpropagation learning algorithm constrained byknown structural characteristics of the circuitry. In order to test and refine the model, we have also compared the model's responses to various lesions with the insect's responses to similar lesions.