A serious problem of unwanted spontaneous oscillation often arises with these circuits and renders them unusable in practice. This paper reports a design approach that guarantees such a system will be stable, even though the values of designed elements and parasitic elements in the resistive grid may be unknown. The method is based on a rigorous, somewhat novel mathematical analysis using Tellegen's theorem and the idea of Popov multipliers from control theory. It is thoroughly practical because the criteria are local in the sense that no overall analysis of the interconnected system is required, empirical in the sense that they involve only measurable frequency response data on the individual cells, and robust in the sense that unmodelled parasitic resistances and capacitances in the interconnection networkcannot affect the analysis. I. INTRODUCTION The term "lateral inhibition" first arose in neurophysiology to describe a common form of neural circuitry in which the output of each neuron in some population is used to inhibit the response of each of its neighbors. Perhaps the best understood example is the horizontal cell layer in the vertebrate retina, in which lateral inhibition simultaneously enhances intensity edges and acts as an automatic lain control to extend the dynamic range of the retina as a whole. The principle has been used in the design of artificial neural system algorithms by Kohonen2 and others and in the electronic design of neural chips by Carver Mead et.

The generalization replaces two state neurons by neurons taking a richer set of values. Two classes of neuron input output relations are developed guaranteeing convergence to stable states. The first is a class of "continuous" relations andthe second is a class of allowed quantization rules for the neurons.

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.

To illustrate the extent of this additional complexity, Fig. Input 6ashows a schematized circuit for a computational unit of method V-r

This relationship takes the form of a sigmoid curve, that describes normalized pulse-output for normalized wave input. The curve is fitted using nonlinear regression and is described by its slope and maximum value. Measurements were made for both excitatory and inhibitory neurons in the cortex. These neurons are known to form a monosynaptic negative feedback loop. Both classes of cells can be described by the same parameters. The sigmoid curve is asymmetric in that the region of maximal slope is displaced toward the excitatory side.

This paper focuses on the issue of learning in these networks especially with regard to their implementation in an electronic system. Learning phenomena that have been studied include associative memoryllJ.

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.

The algorithm, which resembles anew lightness algorithm recently proposed by Land, is approximately equivalent to filtering the image through a center-surround receptive field in individual chromatic channels.The synthesizing technique, optimal linear estimation, requires only one assumption, that the operator that transforms input into output is linear. This assumption is true for a certain class of early vision algorithms that may therefore be synthesized in a similar way from examples. Other methods of synthesizing algorithms from examples, or "learning", such as backpropagation, do not yield a significantly different orbetter lightness algorithm in the Mondrian world. The linear estimation and backpropagation techniques both produce simultaneous brightness contrast effects. The problems that a visual system must solve in decoding two-dimensional images into three-dimensional scenes (inverse optics problems) are difficult: the information supplied by an image is not sufficient by itself to specify a unique scene. To reduce the number of possible interpretations of images, visual systems, whether artificial or biological, must make use of natural constraints, assumptions about the physical properties of surfaces and lights. Computational vision scientists have derived effective solutions for some inverse optics problems (such as computing depth from binocular disparity) by determining the appropriate natural constraints and embedding them in algorithms. How might a visual system discover and exploit natural constraints on its own? We address a simpler question: Given only a set of examples of input images and desired output solutions, can a visual system synthesize.

Thecomputer 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. INTRODUCTION Neural networks are capable of many types of computation. However, the majority of researchers are currently limiting their studies to various forms of mapping systems; such as content addressable memories, expert system engines, and artificial retinas.

W. Scott Stornetta Stanford University, Physics Department, Stanford, Ca., 94305 Tad Hogg and B. A. Huberman Xerox Palo Alto Research Center, Palo Alto, Ca. 94304 ABSTRACT Recognizing patterns with temporal context is important for such tasks as speech recognition, motion detection and signature verification. We propose an architecture in which time serves as its own representation, and temporal context is encoded in the state of the nodes. We contrast this with the approach of replicating portions of the architecture to represent time. As one example of these ideas, we demonstrate an architecture with capacitive inputs serving as temporal feature detectors in an otherwise standard back propagation model. Experiments involving motion detection and word discrimination serve to illustrate novel features of the system.