We have presented a locally interconnected network which minimizes a function that is analogous to the log likelihood function near the global minimum. The results of simulations demonstrate that the network can successfully decode input sequences containing no noise at least as well as the globally connected Hopfield-Tank [6] decomposition network.Simulations also strongly support the conjecture that in the noiseless case, the network can be guaranteed to converge to the global minimum. In addition, for low error rates, the network can also decode noisy received sequences. We have been able to apply the Cohen-Grossberg proof of the stability of "oncenter off-surround"networks to show that each stage will maximize the desired local "likelihood" for noisy received sequences. We have also shown that, in the large gain limit, the network as a whole is stable and that the equilibrium points correspond to the MLSE decoder output.

One criticism of back-propagation is that it requires a teacher to specify the desired output vectors. It is possible to dispense with the teacher in the case of "encoder" networks2 in which the desired output vector is identical with the input vector (see Figure 1). The purpose of an encoder network is to learn good "codes" in the intermediate, hidden units. If for, example, there are less hidden units than input units, an encoder network will perform data-compression3.

Lateral inhibition operating in the surround of firing cells in each layer provides for unsupervised capture of excitation patterns presented by the previous layer. By presenting patterns of increasing complexity, in coordination with network selforganization, higherlevels of the hierarchy capture concepts implicit in the pattern set. INTRODUCTION A fundamental difficulty in self-organization of hierarchical, multi-layered, networks of simple neuron-like cells is the determination of the direction of adjustment of synaptic link weights between neural layers not directly connected to input or output patterns. Several different approaches have been used to address this problem. One is to provide teaching inputs to the cells in internal layers of the hierarchy.

Serial Order: A Parallel Distributed Processing Approach.

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.