THE CAPACITY OF THE KANERVA ASSOCIATIVE MEMORY IS EXPONENTIAL P. A. Chou CA 94305 ABSTRACT The capacity of an associative memory is defined as the maximum number of vords that can be stored and retrieved reliably by an address vithin a given sphere of attraction. It is shown by sphere packing arguments that as the address length increases. This exponential grovth in capacity can actually be achieved by the Kanerva associative memory. Formulas for these op.timal values are provided. The exponential grovth in capacity for the Kanerva associative memory contrasts sharply vith the sub-linear grovth in capacity for the Hopfield associative memory.

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DISTRIBUTED NEURAL INFORMATION PROCESSING IN THE VESTIBULO-OCULAR SYSTEM Clifford Lau Office of Naval Research Detach ment Pasadena, CA 91106 Vicente Honrubia* UCLA Division of Head and Neck Surgery Los Angeles, CA 90024 ABSTRACT A new distributed neural information-processing model is proposed to explain the response characteristics of the vestibulo-ocular system and to reflect more accurately the latest anatomical and neurophysiological data on the vestibular afferent fibers and vestibular nuclei. In this model, head motion is sensed topographically by hair cells in the semicircular canals. Hair cell signals are then processed by multiple synapses in the primary afferent neurons which exhibit a continuum of varying dynamics. The model is an application of the concept of "multilayered" neural networks to the description of findings in the bullfrog vestibular nerve, and allows us to formulate mathematically the behavior of an assembly of neurons whose physiological characteristics vary according to their anatomical properties. INTRODUCTION Traditionally the physiological properties of individual vestibular afferent neurons have been modeled as a linear time-invariant system based on Steinhausents description of cupular motion.

ABSTRACT The potential for presynaptic information processing within the arbor of a single axon will be discussed in this paper. Current knowledge about the activity dependence of the firing threshold, the conditions required for conduction failure, and the similarity of nodes along a single axon will be reviewed. An electronic circuit model for a site of low conduction safety in an axon will be presented. In response to single frequency stimulation the electronic circuit acts as a lowpass filter. I. INTRODUCTION The axon is often modeled as a wire which imposes a fixed delay on a propagating signal.

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.

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" networks

A"'ir Dembo Information Systems Laboratory, Stanford University Stanford, CA 94305 Ofer Zeitouni Laboratory for Information and Decision Systems MIT, Cambridge, MA 02139 ABSTRACT A class of high dens ity assoc iat ive memories is constructed, starting from a description of desired properties those should exhib it. These propert ies include high capac ity, controllable bas ins of attraction and fast speed of convergence. Fortunately enough, the resulting memory is implementable by an artificial Neural Net. I NfRODUCTION Most of the work on assoc iat ive memories has been structure oriented, i.e.. given a Neural architecture, efforts were directed towards the analysis of the resulting network. Issues like capacity, basins of attractions, etc. were the main objects to be analyzed cf., e.g.

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.

The neural network model is a discrete time system that can be represented by a weighted and undirected graph. There is a weight attached to each edge of the graph and a threshold value attached to each node (neuron) of the graph.

The high interconnectivity required by neural computers can be simply implemented in optics because channels for optical signals may be superimposed in three dimensions with little or no cross coupling. Since these channels may be formed holographically, optical neural systems can be designed to create and maintain interconnections very simply. Thus the optical system designer can to a large extent avoid the analytical and topological problems of determining individual interconnections for a given neural system and constructing physical paths for these interconnections. An archetypical design for a single layer of an optical neural computer is shown in Figure 1. Nonlinear thresholding elements, neurons, are arranged on two dimensional planes which are interconnected via the third dimension by holographic elements. The key concerns in implementing this design involve the need for suitable nonlinearities for the neural planes and high capacity, easily modifiable holographic elements. While it is possible to implement the neural function using entirely optical nonlinearities, for example using etalon arrays\ optoelectronic two dimensional spatial light modulators (2D SLMs) suitable for this purpose are more readily available.