M2/n' for sufficiently large values of M. Here, Poo(error) denotes the probability of error in the infinite sample limit, and is at most twice the error of a Bayes classifier. Although the value of the coefficient a depends upon the underlying probability distributions, the exponent of M is largely distribution free. We thus obtain a concise relation between a classifier's ability to generalize from a finite reference sample and the dimensionality of the feature space, as well as an analytic validation of Bellman's well known "curse of dimensionality." 1 INTRODUCTION One of the primary tasks assigned to neural networks is pattern classification. Common applications include recognition problems dealing with speech, handwritten characters, DNA sequences, military targets, and (in this conference) sexual identity. Two fundamental concepts associated with pattern classification are generalization (how well does a classifier respond to input data it has never encountered before?) and scalability (how are a classifier's processing and training requirements affected by increasing the number of features that describe the input patterns?).

The in previ us face recognition systems (Ka R· na e, 19;)y' ......--.-.. scaled to the range [0 -. 8]. Part of the training set and its d' tances between facial elements.

Static correlations among spike trains obtained from simulations of large arrays of cells are in agreement with the predictions from these Hamiltonians, and dynamic correlat.ions

Function approximation on high-dimensional spaces is often thwarted by a lack of sufficient data to adequately "fill" the space, or lack of sufficient computational resources. The technique of local variable selection provides a partial solution to these problems by attempting to approximate functions locally using fewer than the complete set of input dimensions.

While the network loading problem for 2-layer threshold nets is NPhard when learning from examples alone (as with backpropagation), (Baum, 91) has now proved that a learner can employ queries to evade the hidden unit credit assignment problem and PACload nets with up to four hidden units in polynomial time. Empirical tests show that the method can also learn far more complicated functions such as randomly generated networks with 200 hidden units. The algorithm easily approximates Wieland's 2-spirals function using a single layer of 50 hidden units, and requires only 30 minutes of CPU time to learn 200-bit parity to 99.7% accuracy.

Spherical Units can be used to construct dynamic reconfigurable consequential regions, the geometric bases for Shepard's (1987) theory of stimulus generalization in animals and humans. We derive from Shepard's (1987) generalization theory a particular multi-layer network with dynamic (centers and radii) spherical regions which possesses a specific mass function (Cauchy). This learning model generalizes the configural-cue network model (Gluck & Bower 1988): (1) configural cues can be learned and do not require pre-wiring the power-set of cues, (2) Consequential regions are continuous rather than discrete and (3) Competition amoungst receptive fields is shown to be increased by the global extent of a particular mass function (Cauchy). We compare other common mass functions (Gaussian; used in models of Moody & Darken; 1989, Krushke, 1990) or just standard backpropogation networks with hyperplane/logistic hidden units showing that neither fare as well as models of human generalization and learning.

I have presented a qualitative approach to the problem of recovering object structure from motion information and discussed some of its computational, psychophysical and implementational aspects. The computation of qualitative shape, as represented by the sign of the Gaussian curvature, can be performed by a field of simple operators, in parallel over the entire image. The performance of a qualitative shape detection module, implemented by an artificial neural network, appears to be similar to the performance of human subjects in an identical task.

We present a large vocabulary, continuous speech recognition system based on Linked Predictive Neural Networks (LPNN's). The system uses neural networks as predictors of speech frames, yielding distortion measures which are used by the One Stage DTW algorithm to perform continuous speech recognition. The system, already deployed in a Speech to Speech Translation system, currently achieves 95%, 58%, and 39% word accuracy on tasks with perplexity 5, 111, and 402 respectively, outperforming several simple HMMs that we tested. We also found that the accuracy and speed of the LPNN can be slightly improved by the judicious use of hidden control inputs. We conclude by discussing the strengths and weaknesses of the predictive approach.

A neural network model of motion segmentation by visual cortex is described. The model clarifies how preprocessing of motion signals by a Motion Oriented Contrast Filter (MOC Filter) is joined to long-range cooperative motion mechanisms in a motion Cooperative Competitive Loop (CC Loop) to control phenomena such as as induced motion, motion capture, and motion aftereffects. The total model system is a motion Boundary Contour System (BCS) that is computed in parallel with a static BCS before both systems cooperate to generate a boundary representation for three dimensional visual form perception. The present investigations clarify how the static BCS can be modified for use in motion segmentation problems, notably for analyzing how ambiguous local movements (the aperture problem) on a complex moving shape are suppressed and actively reorganized into a coherent global motion signal. 1 INTRODUCTION: WHY ARE STATIC AND MOTION BOUNDARY CONTOUR SYSTEMS NEEDED? Some regions, notably MT, of visual cortex are specialized for motion processing. However, even the earliest stages of visual cortex processing, such as simple cells in VI, require stimuli that change through time for their maximal activation and are direction-sensitive. Why has evolution generated regions such as MT, when even VI is change-sensitive and direction-sensitive? What computational properties are achieved by MT that are not already available in VI?

There have been very few demonstrations ofthe application ofVLSI neural networks to real world problems. Yet there are many signal processing, pattern recognition or optimization problems where a large number of competing hypotheses need to be explored in parallel, most often in real time. The massive parallelism of VLSI neural network devices, with one multiplier circuit per synapse, is ideally suited to such problems. In this paper, we present preliminary results from our design for a real time robot navigation system based on VLSI neural network modules.