Santosh S. Venkatesh Electrical Engineering University of Pennsylvania Philadelphia, PA 19104 If patterns are drawn from an n-dimensional feature space according to a probability distribution that obeys a weak smoothness criterion, we show that the probability that a random input pattern is misclassified by a nearest-neighbor classifier using M random reference patterns asymptotically satisfies a PM(error) "" Poo(error) 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.

We describe a multi-network, or modular, connectionist architecture that captures that fact that many tasks have structure at a level of granularity intermediate to that assumed by local and global function approximation schemes. The main innovation of the architecture is that it combines associative and competitive learning in order to learn task decompositions. A task decomposition is discovered by forcing the networks comprising the architecture to compete to learn the training patterns. As a result of the competition, different networks learn different training patterns and, thus, learn to partition the input space. The performance of the architecture on a "what" and "where" vision task and on a multi-payload robotics task are presented.

The main point of this paper is that stochastic neural networks have a mathematical structure that corresponds quite closely with that of quantum field theory. Neural network Liouvillians and Lagrangians can be derived, just as can spin Hamiltonians and Lagrangians in QFf. It remains to show the efficacy of such a description.

We propose a new parallel-hierarchical neural network model to enable motor learning for simultaneous control of both trajectory and force.

Previous work has shown the ability of Multilayer Perceptrons (MLPs) to estimate emission probabilities for Hidden Markov Models (HMMs). The advantages of a speech recognition system incorporating both MLPs and HMMs are the best discrimination and the ability to incorporate multiple sources of evidence (features, temporal context) without restrictive assumptions of distributions or statistical independence. This paper presents results on the speaker-dependent portion of DARPA's English language Resource Management database. Results support the previously reported utility of MLP probability estimation for continuous speech recognition. An additional approach we are pursuing is to use MLPs as nonlinear predictors for autoregressive HMMs. While this is shown to be more compatible with the HMM formalism, it still suffers from several limitations. This approach is generalized to take account of time correlation between successive observations, without any restrictive assumptions about the driving noise. 1 INTRODUCTION We have been working on continuous speech recognition using moderately large vocabularies (1000 words) [1,2].

A recurrent back-propagation neural network architecture was then designed to numerically estimate the parameters of an optimal nonlinear control law for landing the aircraft. The performance of the network was then evaluated.

We formulate the problem of optimizing the sampling of natural images using an array of linear filters. Optimization of information capacity is constrained by the noise levels of the individual channels and by a penalty for the construction of long-range interconnections in the array. At low signal-to-noise ratios the optimal filter characteristics correspond to bound states of a Schrodinger equation in which the signal spectrum plays the role of the potential. The resulting optimal filters are remarkably similar to those observed in the mammalian visual cortex and the retinal ganglion cells of lower vertebrates. The observed scale invariance of natural images plays an essential role in this construction.

We describe a computational model of the development and regeneration of specific eye-brain circuits. The model comprises a self-organizing map-forming network which uses local Hebb rules, constrained by (genetically determined) molecular markers. Various simulations of the development and regeneration of eye-brain maps in fish and frogs are described, in particular successful simulations of experiments by Schmidt-Cicerone-Easter; Meyer; and Y oon. 1 INTRODUCTION In a previous paper published in last years proceedings (Cowan & Friedman 1990) we outlined a new computational model for the development and regeneration of eye-brain maps. We indicated that such a model can simulate the results of a number of the more complicated surgical manipulations carried out on the visual pathways of goldfish and frogs. In this paper we describe in more detail some of these experiments, and our simulations of them.

Diagnosis of faults in complex, real-time control systems is a complicated task that has resisted solution by traditional methods. We have shown that neural networks can be successfully employed to diagnose faults in digitally controlled powertrain systems. This paper discusses the means we use to develop the appropriate databases for training and testing in order to select the optimum network architectures and to provide reasonable estimates of the classification accuracy of these networks on new samples of data.

A novel unsupervised neural network for dimensionality reduction which seeks directions emphasizing multimodality is presented, and its connection to exploratory projection pursuit methods is discussed. This leads to a new statistical insight to the synaptic modification equations governing learning in Bienenstock, Cooper, and Munro (BCM) neurons (1982). The importance of a dimensionality reduction principle based solely on distinguishing features, is demonstrated using a linguistically motivated phoneme recognition experiment, and compared with feature extraction using back-propagation network. 1 Introduction Due to the curse of dimensionality (Bellman, 1961) it is desirable to extract features from a high dimensional data space before attempting a classification. How to perform this feature extraction/dimensionality reduction is not that clear. A first simplification is to consider only features defined by linear (or semi-linear) projections of high dimensional data. This class of features is used in projection pursuit methods (see review in Huber, 1985). Even after this simplification, it is still difficult to characterize what interesting projections are, although it is easy to point at projections that are uninteresting. A statement that has recently been made precise by Diaconis and Freedman (1984) says that for most high-dimensional clouds, most low-dimensional projections are approximately normal. This finding suggests that the important information in the data is conveyed in those directions whose single dimensional projected distribution is far from Gaussian, especially at the center of the distribution.