DCPS' memory scheme is a modified version of the Random Receptors method [5]. The symbol space is the set of all triples over a 25 letter alphabet. Units have fixed-size receptive fields organized as 6 x 6 x 6 subspaces. Patterns are manipulated to minimize the variance in pattern size across symbols.

The method allows the fully distributed representation of symbolic structures: the roles in the structures, as well as the fillers for those roles, can be arbitrarily non-local. Fully and partially localized special cases reduce to existing cases of connectionist representations of structured data; the tensor product representation generalizes these and the few existing examples of fuUy distributed representations of structures. The representation saturates gracefully as larger structures are represented; it pennits recursive construction of complex representations from simpler ones; it respects the independence of the capacities to generate and maintain multiple bindings in parallel; it extends naturally to continuous structures and continuous representational patterns; it pennits values to also serve as variables; it enables analysis of the interference of symbolic structures stored in associative memories; and it leads to characterization of optimal distributed representations of roles and a recirculation algorithm for learning them. Introduction Any model of complex infonnation processing in networks of simple processors must solve the problem of representing complex structures over network elements. Connectionist models of realistic natural language processing, for example, must employ computationally adequate representations of complex sentences. Many connectionists feel that to develop connectionist systems with the computational power required by complex tasks, distributed representations must be used: an individual processing unit must participate in the representation of multiple items, and each item must be represented as a pattern of activity of multiple processors. Connectionist models have used more or less distributed representations of more or less complex structures, but little if any general analysis of the problem of distributed representation of complex infonnation has been carried out This paper reports results of an analysis of a general method called the tensor product representation.

Yaser S. Abu-Mostafa California Institute of Technology Pasadena, CA 91125 ABSTRACT How does the connectivity of a neural network (number of synapses per neuron) relate to the complexity of the problems it can handle (measured by the entropy)? Switching theory would suggest no relation at all, since all Boolean functions can be implemented using a circuit with very low connectivity (e.g., using two-input NAND gates). However, for a network that learns a problem from examples using a local learning rule, we prove that the entropy of the problem becomes a lower bound for the connectivity of the network. INTRODUCTION The most distinguishing feature of neural networks is their ability to spontaneously learnthe desired function from'training' samples, i.e., their ability to program themselves. Clearly, a given neural network cannot just learn any function, there must be some restrictions on which networks can learn which functions.

The designed networks exhibit the desired associative memory function: perfect storage and retrieval of pieces of information and/or sequences of information of any complexity. INTRODUCTION In the field of information processing, an important class of potential applications of neural networks arises from their ability to perform as associative memories. Since the publication of J. Hopfield's seminal paper1, investigations of the storage and retrieval properties of recurrent networks have led to a deep understanding of their properties. The basic limitations of these networks are the following: - their storage capacity is of the order of the number of neurons; - they are unable to handle structured problems; - they are unable to classify non-linearly separable data. American Institute of Physics 1988 234 In order to circumvent these limitations, one has to introduce additional non-linearities. This can be done either by using "hidden", nonlinear units, or by considering multi-neuron interactions2. This paper presents learning rules for networks with multiple interactions, allowing the storage and retrieval, either of static pieces of information (autoassociative memory), or of temporal sequences (associative memory), while preventing an explosive growth of the number of synaptic coefficients. AUTOASSOCIATIVEMEMORY The problem that will be addressed in this paragraph is how to design an autoassociative memory with a recurrent (or feedback) neural network when the number p of prototypes is large as compared to the number n of neurons. We consider a network of n binary neurons, operating in a synchronous mode, with period t.

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.

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 cortex2 . 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. ASINGLE LAYER NETWORK AND THE MEAN FIELD APPROXIMATION We consider a receive signals from the layer (Figure 1).

Centric Models of the Orientation Map in Primary Visual Cortex William Baxter of Computer Science, S.U.N.Y. at Buffalo, NY 14620Department Bruce Dow Department of Physiology, S.U.N.Y. at Buffalo, NY 14620 Abstract the visual cortex of the monkey the horizontal organization of the preferredIn of orientation-selective cells follows two opposing rules: 1) neighbors tendorientations Several orientation models which satisfy these constraints are found in the spacing and the topological index of their singularities. Using the rateto differ of orientation change as a measure, the models are compared to published experimental results. Introduction It has been known for some years that there exist orientation-sensitive neurons in the visual cortex of cats and mOnkeysl,2. These cells react to highly specific patterns of light occurring in narrowly circumscribed regiOns of the visual field, i.e., the cell's receptive field. The best patterns for such cells are typically not diffuse levels of but elongated bars or edges oriented at specific angles.

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 andE-set recognition is improved by focusing attention. Recognition accuracies are better than 98% for both vocabularies when implemented with a single layer perceptron. INTRODUCTION Artificial neural networks perform well on simple pattern recognition tasks.

Fernando J. Pineda Applied Physics Laboratory, Johns Hopkins University Johns Hopkins Rd., Laurel MD 20707 Abstract A general method for deriving backpropagation algorithms for networks with recurrent and higher order networks is introduced. The propagation of activation in these networks is determined by dissipative differential equations. The error signal is backpropagated by integrating an associated differential equation. The method is introduced by applying it to the recurrent generalization of the feedforward backpropagation network. The method is extended to the case of higher order networks and to a constrained dynamical system for training a content addressable memory. The essential feature of the adaptive algorithms is that adaptive equation has a simple outer product form.

Please address all further correspondence to: John Y. Cheung School of EECS 202 W. Boyd, CEC 219 Norman, OK 73019 (405)325-4721 November,1987 American Institute of Physics 1988 165 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.