In this work we describe a new method that adjusts time-delays and the widths of time-windows in artificial neural networks automatically. The input of the units are weighted by a gaussian input-window over time which allows the learning rules for the delays and widths to be derived in the same way as it is used for the weights. Our results on a phoneme classification task compare well with results obtained with the TDNN by Waibel et al., which was manually optimized for the same task.

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.

"vector quantization", and "unsupervised learning" are all words which descn'be the same process: assigning a few exemplars to represent a large set of samples. Perfonning that process is the subject of a substantial body of literature. In this paper, we are concerned with the comparison of various clustering techniques to a particular, practical application: color clustering. The color clustering problem is as follows: an image is recorded in full color -- that is, three components, RED, GREEN, and BLUE, each of which has been measured to 8 bits of precision. Thus, each pixel is a 24 bit quantity. We must find a representation in which 2563 possible colors are represented by only 8 bits per pixel. That is, for a problem with 256000 variables (512 x 512) variables, assign each variable to one of only 256 classes. The color clustering problem is currently of major economic interest since millions of display systems are sold each year which can only store 8 bits per pixel, but on which users would like to be able to display "true" color (or at least as near true color as possible). In this study, we have approached the problem using the standard techniques from the literature (including k-means -- ISODATA clustering[1,3,61, LBG[4]), competitive learning (referred to as CL herein) [2], and Kohonen feature maps [5,7,9].

Seven different neural network and conventional pattern classifiers were compared using artificial and speech recognition tasks. High order polynomial GMDH classifiers typically provided intermediate error rates and often required long training times and large amounts of memory. In addition, the decision regions formed did not generalize well to regions of the input space with little training data. Radial basis function classifiers generalized well in high dimensional spaces, and provided low error rates with training times that were much less than those of back-propagation classifiers (Lee and Lippmann, 1989). Gaussian mixture classifiers provided good performance when the numbers and types of mixtures were selected carefully to model class densities well. Linear tree classifiers were the most computationally ef- 976 Ng and Lippmann ficient but performed poorly with high dimensionality inputs and when the number of training patterns was small. KD-tree classifiers reduced classification time by a factor of four over conventional KNN classifiers for low 2-input dimension problems. They provided little or no reduction in classification time for high 22-input dimension problems. Improved condensed KNN classifiers reduced memory requirements over conventional KNN classifiers by a factor of two to fifteen for all problems, without increasing the error rate significantly.

Viewing n-variable boolean functions as vectors in'R'2", we invoke tools from linear algebra and linear programming to derive new results on the realizability of boolean functions using threshold gat.es. Using this approach, one can obtain: (1) upper-bounds on the number of spurious memories in HopfielJ networks, and on the number of functions implementable by a depth-d threshold circuit; (2) a lower bound on the number of ort.hogonal input.

The three problems that concern us are identifying a natural domain of pattern classification applications of feed forward neural networks, selecting an appropriate feedforward network architecture, and assessing the tradeoff between network complexity, training set size, and statistical reliability as measured by the probability of incorrect classification. We close with some suggestions, for improving the bounds that come from Vapnik Chervonenkis theory, that can narrow, but not close, the chasm between theory and practice. Neural networks are appropriate as pattern classifiers when the pattern sources are ones of which we have little understanding, beyond perhaps a nonparametric statistical model, but we have been provided with classified samples of features drawn from each of the pattern categories. Neural networks should be able to provide rapid and reliable computation of complex decision functions. The issue in doubt is their statistical response to new inputs.

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.

Since Kendrew & Perutz solved the first protein structures, myoglobin and hemoglobin, and explained from the discovered structures how these proteins perform their function, it has been widely recognized that protein function is intimately linked with protein structure[l]. Within the last two decades X-ray crystallographers have solved the 3-dimensional (3D) structures of a steadily increasing number of proteins in the crystalline state, and recently 2D-NMR spectroscopy has emerged as an alternative method for small proteins in solution. Today approximately three hundred 3D structures have been solved by these methods, although only about half of them can be considered as truly different, and only around a hundred of them are solved at high resolution (that is, less than 2A). The number of protein sequences known today is well over 20,000, and this number seems to be growing at least one order of magnitude faster than the number of known 3D protein structures. Obviously, it is of great importance to develop tools that can predict structural aspects of proteins on the basis of knowledge acquired from known 3D structures.

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.

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.