Another class of nonlinear algorithms, exemplified by CART (Breiman, Friedman, Olshen, & Stone, 1984) and MARS (Friedman, 1990), generalizes classicaltechniques by partitioning the training data into non-overlapping regions and fitting separate models in each of the regions. These two classes of algorithms extendlinear techniques in essentially independent directions, thus it seems worthwhile to investigate algorithms that incorporate aspects of both approaches to model estimation. Such algorithms would be related to CART and MARS as multilayer neural networks are related to linear statistical techniques.

Automated monitoring of vigilance in attention intensive tasks such as air traffic control or sonar operation is highly desirable. As the operator monitorsthe instrument, the instrument would monitor the operator, insuring against lapses. We have taken a first step toward this goal by using feedforwardneural networks trained with backpropagation to interpret event related potentials (ERPs) and electroencephalogram (EEG) associated withperiods of high and low vigilance. The accuracy of our system on an ERP data set averaged over 28 minutes was 96%, better than the 83% accuracy obtained using linear discriminant analysis. Practical vigilance monitoring will require prediction over shorter time periods. We were able to average the ERP over as little as 2 minutes and still get 90% correct prediction of a vigilance measure. Additionally, we achieved similarly good performance using segments of EEG power spectrum as short as 56 sec.

Learning is posed as a problem of function estimation, for which two principles ofsolution are considered: empirical risk minimization and structural risk minimization. These two principles are applied to two different statements ofthe function estimation problem: global and local. Systematic improvements in prediction power are illustrated in application to zip-code recognition.

We derive criteria for training adaptive classifier networks to perform unsupervised dataanalysis. The first criterion turns a simple Gaussian classifier into a simple Gaussian mixture analyser. The second criterion, which is much more generally applicable, is based on mutual information.

Stephen M. Omohundro International Computer Science Institute 1947 CenteJ' Street, Suite 600 Berkeley, California 94704 Abstract "Best-first model merging" is a general technique for dynamically choosing the structure of a neural or related architecture while avoiding overfitting.It is applicable to both leaming and recognition tasks and often generalizes significantly better than fixed structures. We demonstrate theapproach applied to the tasks of choosing radial basis functions for function learning, choosing local affine models for curve and constraint surface modelling, and choosing the structure of a balltree or bumptree to maximize efficiency of access. 1 TOWARD MORE COGNITIVE LEARNING Standard backpropagation neural networks learn in a way which appears to be quite different fromhuman leaming. Viewed as a cognitive system, a standard network always maintains acomplete model of its domain. This model is mostly wrong initially, but gets gradually better and better as data appears. The net deals with all data in much the same way and has no representation for the strength of evidence behind a certain conclusion. The network architecture is usually chosen before any data is seen and the processing is much the same in the early phases of learning as in the late phases.

The localized linear discriminant network (LLDN) has been designed to address classification problems containing relatively closely spaced data from different classes (encounter zones [1], the accuracy problem [2]). Locally trained hyperplane segmentsare an effective way to define the decision boundaries for these regions [3]. The LLD uses a modified perceptron training algorithm for effective discovery of separating hyperplane/sigmoid units within narrow boundaries. The basic unit of the network is the discriminant receptive field (DRF) which combines the LLD function with Gaussians representing the dispersion of the local training data with respect to the hyperplane. The DRF implements a local distance measure [4],and obtains the benefits of networks oflocalized units [5]. A constructive algorithm for the two-class case is described which incorporates DRF's into the hidden layer to solve local discrimination problems. The output unit produces a smoothed, piecewise linear decision boundary. Preliminary results indicate the ability of the LLDN to efficiently achieve separation when boundaries are narrow and complex, in cases where both the "standard" multilayer perceptron (MLP) and k-nearest neighbor (KNN) yield high error rates on training data. 1 The LLD Training Algorithm and DRF Generation The LLD is defined by the hyperplane normal vector V and its "midpoint" M (a translated origin [1] near the center of gravity of the training data in feature space). Incremental corrections to V and M accrue for each training token feature vector Yj in the training set, as iIlustrated in figure 1 (exaggerated magnitudes).

We then regard gradient descent with momentum as a dynamic system and explore a non quadratic error surface, showing that saturation of the error accounts for a variety of effects observed in simulations and justifies some popular heuristics. 1 INTRODUCTION Gradient descent is the bread-and-butter optimization technique in neural networks. Some people build special purpose hardware to accelerate gradient descent optimization ofbackpropagation networks. Understanding the dynamics of gradient descent on such surfaces is therefore of great practical value. Here we briefly review the known results in the convergence of batch gradient descent; showthat second-order momentum does not give any speedup; simulate a real network and observe some effect not predicted by theory; and account for these effects by analyzing gradient descent with momentum on a saturating error surface.

Stochastic gradient descent is a general algorithm which includes LMS, online backpropagation, and adaptive k-means clustering as special cases.

After a decade of fundamental interdisciplinary research in machine learning, the spadework in this field has been done; the 1990s should see the widespread exploitation of knowledge discovery as an aid to assembling knowledge bases. The contributors to the AAAI Press book Knowledge Discovery in Databases were excited at the potential benefits of this research. The editors hope that some of this excitement will communicate itself to "AI Magazine readers of this article.

An effective to develop an abstract UI model which solution to this problem must have three encompasses the essence of those systems.