A general method, the tensor product representation, is described for the distributed representation of value/variable bindings. 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 penn its 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.

THE SIGMOID NONLINEARITY IN PREPYRIFORM CORTEX Frank H. Eeckman University of California, Berkeley, CA 94720 ABSlRACT We report a study ·on the relationship between EEG amplitude values and unit spike output in the prepyriform cortex of awake and motivated rats. 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.

LEARNING BY ST ATE RECURRENCE DETECfION Bruce E. Rosen, James M. Goodwint, and Jacques J. Vidal University of California, Los Angeles, Ca. 90024 ABSTRACT This research investigates a new technique for unsupervised learning of nonlinear control problems. The approach is applied both to Michie and Chambers BOXES algorithm and to Barto, Sutton and Anderson's extension, the ASE/ACE system, and has significantly improved the convergence rate of stochastically based learning automata. Recurrence learning is a new nonlinear reward-penalty algorithm. It exploits information found during learning trials to reinforce decisions resulting in the recurrence of nonfailing states. Recurrence learning applies positive reinforcement during the exploration of the search space, whereas in the BOXES or ASE algorithms, only negative weight reinforcement is applied, and then only on failure. Simulation results show that the added information from recurrence learning increases the learning rate. Our empirical results show that recurrence learning is faster than both basic failure driven learning and failure prediction methods. Although recurrence learning has only been tested in failure driven experiments, there are goal directed learning applications where detection of recurring oscillations may provide useful information that reduces the learning time by applying negative, instead of positive reinforcement.

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

This paper describes an approach to 2-dimensional object recognition. Complex-log conformal mapping is combined with a distributed associative memory to create a system which recognizes objects regardless of changes in rotation or scale. Recalled information from the memorized database is used to classify an object, reconstruct the memorized version of the object, and estimate the magnitude of changes in scale or rotation. The system response is resistant to moderate amounts of noise and occlusion. Several experiments, using real, gray scale images, are presented to show the feasibility of our approach. Introduction The challenge of the visual recognition problem stems from the fact that the projection of an object onto an image can be confounded by several dimensions of variability such as uncertain perspective, changing orientation and scale, sensor noise, occlusion, and nonuniform illumination.

A general method, the tensor product representation, is described for the distributed representation of value/variable bindings. 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 penn its 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.

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.

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.

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.

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.