We open our eyes and we "see" the world in all its color, brightness, and movement. Yet, we have great difficulties when trying to endow our machines with similar abilities. In this paper we shall describe recent developments in the theory of early vision which lead from the formulation of the motion problem as an illposed oneto its solution by minimizing certain "cost" functions. These cost or energy functions can be mapped onto simple analog and digital resistive networks. Thus, we shall see how the optical flow can be computed by injecting currents into resistive networks and recording the resulting stationary voltage distribution at each node. These networks can be implemented in cMOS VLSI circuits and represent plausible candidates for biological vision systems. APERTURE PROBLEM AND SMOOTHNESS ASSUMPTION In this study, we use intensity-based schemes for recovering motion.

Box 150, Cheongryang, Seoul, Korea ABSTRACT Inverse matrix calculation can be considered as an optimization. We have demonstrated that this problem can be rapidly solved by highly interconnected simple neuron-like analog processors. A network for matrix inversion based on the concept of Hopfield's neural network was designed, and implemented with electronic hardware. With slight modifications, the network is readily applicable to solving a linear simultaneous equation efficiently. Notable features of this circuit are potential speed due to parallel processing, and robustness against variations of device parameters. INTRODUCTION Highly interconnected simple analog processors which mmnc a biological neural network are known to excel at certain collective computational tasks.

Previous work on nets with continuous-valued inputs led to generative procedures to construct convex decision regions with two-layer perceptrons (one hidden layer) and arbitrary decision regions with three-layer perceptrons (two hidden layers). Here we demonstrate that two-layer perceptron classifiers trained with back propagation can form both convex and disjoint decision regions. Such classifiers are robust, train rapidly, and provide good performance with simple decision regions. When complex decision regions are required, however, convergence time can be excessively long and performance is often no better than that of k-nearest neighbor classifiers. Three neural net classifiers are presented that provide more rapid training under such situations.

In the first a closed optical feedback loop is used to implement auto-associative image recall. In the second a perceptron-Iike learning algorithm is implemented with photorefractive holography.

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.

It is also possible to define a gradient over r such that a minimum in error would be sought.

Oregon Graduate Center, Beaverton, OR 97006 ABSTRACT The efficient realization, using current silicon technology, of Very Large Connection Networks (VLCN) with more than a billion connections requires that these networks exhibit a high degree of communication locality. Real neural networks exhibit significant locality, yet most connectionist/neural network models have little. In this paper, the connectivity requirements of a simple associative network are analyzed using communication theory. Several techniques based on communication theory are presented that improve the robustness ofthe network in the face of sparse, local interconnect structures. Also discussed are some potential problems when information is distributed too widely. INTRODUCTION Connectionist/neural network researchers are learning to program networks that exhibit a broad range of cognitive behavior.

Two hundred layer IT cells are used with 100 input (LOT) lines and 200 collateral axons; both the LOT and collateral axons flow caudally. LOT axons connect with rostral dendrites with a probability of 0.2, which decreases linearly to 0.05 by the caudal end of the model. The connectivity is arranged randomly, subject to the constraint that the number of contacts for axons and dendrites is fixed within certain narrow b01llldaries (in the most severe case, each axon forms 20 synapses and each dendrite receives 20 contacts). The resulting matrix is thus hypergeometric in both dimensions. There are 20 simulated inhibitory interneurons, such that the layer IT cells are arranged in 20 overlapping patches, each within the influence of one such inhibitory cell.

Learning algorithms for the neural network which search for the "most probable" member of P can then be designed. Statistical tests which decide if the "true" or environmental probability distribution is in P can also be developed. Example applications of the theory to the highly nonlinear back-propagation learning algorithm, and the networks of Hopfield and Anderson are discussed. INTRODUCTION A connectionist system is a network of simple neuron-like computing elements which can store and retrieve information, and most importantly make generalizations. Using terminology suggested by Rumelhart & McClelland 1, the computing elements of a connectionist system are called units, and each unit is associated with a real number indicating its activity level. The activity level of a given unit in the system can also influence the activity level of another unit. The degree of influence between two such units is often characterized by a parameter of the system known as a connection strength. During the information retrievalprocess some subset of the units in the system are activated, and these units in turn activate neighboring units via the inter-unit connection strengths.

Paolo Gaudiano Dept. of Aerospace Engineering Sciences, University of Colorado, Boulder CO 80309, USA January 5, 1988 Abstract Patterns of activity over real neural structures are known to exhibit timedependent behavior.It would seem that the brain may be capable of utilizing temporal behavior of activity in neural networks as a way of performing functions which cannot otherwise be easily implemented. These might include the origination of sequential behavior and the recognition of time-dependent stimuli. A model is presented here which uses neuronal populations with recurrent feedback connections inan attempt to observe and describe the resulting time-dependent behavior. Shortcomings and problems inherent to this model are discussed. Current models by other researchers are reviewed and their similarities and differences discussed. METHODS / PRELIMINARY RESULTS In previous papers,[2,3] computer models were presented that simulate a net consisting oftwo spatially organized populations of realistic neurons.