Several recurrent networks have been proposed as representations for the task of formal language learning. After training a recurrent network recognize aformal language or predict the next symbol of a sequence, the next logical step is to understand the information processing carried out by the network. Some researchers have begun to extracting finite state machines from the internal state trajectories of their recurrent networks. This paper describes how sensitivity to initial conditions and discrete measurements can trick these extraction methods to return illusory finite state descriptions.

Critical features of a domain (such as invariance under translation, rotation, and permu- Clustering with a Domain-Specific Distance Measure 103 tation) are captured within the clustering procedure, rather than reflected in the properties of feature sets created prior to clustering. The distance measure and learning problem are formally described as nested objective functions. We derive an efficient algorithm by using optimization techniques that allow us to divide up the objective function into parts which may be minimized in distinct phases. The algorithm has accurately recreated 10 prototypes from a randomly generated sample database of 100 images consisting of 20 points each in 120 experiments. Finally, by incorporating permutation invariance in our distance measure, we have a technique that we may be able to apply to the clustering of graphs. Our goal is to develop measures which will enable the learning of objects with shape or structure. Acknowledgements This work has been supported by AFOSR grant F49620-92-J-0465 and ONR/DARPA grant N00014-92-J-4048.

Given such a classification task in most cases it is not too difficult to devise a network architecture that is capable of learning the input-output relation as represented by a number of training examples.

An approach is presented to learning high dimensional functions in the case where the learning algorithm can affect the generation of new data. A local modeling algorithm, locally weighted regression, is used to represent the learned function. Architectural parameters of the approach, such as distance metrics, are also localized and become a function of the query point instead of being global. Statistical tests are given for when a local model is good enough and sampling should be moved to a new area. Our methods explicitly deal with the case where prediction accuracy requirements exist during exploration: By gradually shifting a "center of exploration" and controlling the speed of the shift with local prediction accuracy,a goal-directed exploration of state space takes place along the fringes of the current data support until the task goal is achieved.

In this procedure one transforms variables to a basis in which the covariance isdiagonal and then projects out the low variance directions. While application of PCA to remove input variables is useful in some cases (Leen et al., 1990), there is no guarantee that low variance variables have little effect on error. We propose a saliency measure, based on PCA, that identifies those variables that have the least effect on error. Our proposed Principal Components Pruning algorithm applies this measure to obtain a simple and cheap pruning technique in the context of supervised learning. Fast Pruning Using Principal Components 37 Special Case: PCP in Linear Regression In unbiased linear models, one can bound the bias introduced from pruning the principal degrees of freedom in the model.

We propose a new distance measure which is optimal for the task of local PCA. Our results with speech and image data indicate that the nonlinear techniques provide more accurate encodings than PCA. Our local linear algorithm produces more accurate encodings (except for one simulation with image data), and trains much faster than five layer auto-associative networks. Acknowledgments This work was supported by grants from the Air Force Office of Scientific Research (F49620-93-1-0253) and Electric Power Research Institute (RP8015-2). The authors are grateful to Gary Cottrell and David DeMers for providing their image database and clarifying their experimental results. We also thank our colleagues in the Center for Spoken Language Understanding at OGI for providing speech data.

We propose a method for improving the performance of any network designedto predict the next value of a time series. Vve advocate analyzing the deviations of the network's predictions from the data in the training set. This can be carried out by a secondary network trainedon the time series of these residuals. The combined system of the two networks is viewed as the new predictor. We demonstrate the simplicity and success of this method, by applying itto the sunspots data. The small corrections of the secondary network can be regarded as resulting from a Taylor expansion of a complex network which includes the combined system.

Moore School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213 Memory-based learning methods operate by storing all (or most) of the training data and deferring analysis of that data until "run time" (i.e., when a query is presented and a decision or prediction must be made). When a query is received, these methods generally answer the query by retrieving and analyzing a small subset of the training data-namely, data in the immediate neighborhood of the query point. In short, memory-based methods are "lazy" (they wait until the query) and "local" (they use only a local neighborhood). The purpose of this workshop was to review the state-of-the-art in memory-based methods and to understand their relationship to "eager" and "global" learning algorithms such as batch backpropagation. There are two essential components to any memory-based algorithm: the method for defining the "local neighborhood" and the learning method that is applied to the training examples in the local neighborhood.

This paper presents a formulation for unsupervised learning of clusters reflectingmultiple causal structure in binary data. Unlike the standard mixture model, a multiple cause model accounts for observed databy combining assertions from many hidden causes, each of which can pertain to varying degree to any subset of the observable dimensions.A crucial issue is the mixing-function for combining beliefs from different cluster-centers in order to generate data reconstructions whose errors are minimized both during recognition and learning. We demonstrate a weakness inherent to the popular weighted sum followed by sigmoid squashing, and offer an alternative formof the nonlinearity. Results are presented demonstrating the algorithm's ability successfully to discover coherent multiple causal representat.ions of noisy test data and in images of printed characters. 1 Introduction The objective of unsupervised learning is to identify patterns or features reflecting underlying regularities in data. Single-cause techniques, including the k-means algorithm andthe standard mixture-model (Duda and Hart, 1973), represent clusters of data points sharing similar patterns of Is and Os under the assumption that each data point belongs to, or was generated by, one and only one cluster-center; output activity is constrained to sum to 1. In contrast, a multiple-cause model permits more than one cluster-center to become fully active in accounting for an observed data vector. The advantage of a multiple cause model is that a relatively small number 27 28 Saund of hidden variables can be applied combinatorially to generate a large data set.

Data clustering amounts to a combinatorial optimization problem to reduce thecomplexity of a data representation and to increase its precision. Central and pairwise data clustering are studied in the maximum entropy framework.For central clustering we derive a set of reestimation equations and a minimization procedure which yields an optimal number ofclusters, their centers and their cluster probabilities. A meanfield approximation for pairwise clustering is used to estimate assignment probabilities. A se1fconsistent solution to multidimensional scaling and pairwise clustering is derived which yields an optimal embedding and clustering of data points in a d-dimensional Euclidian space. 1 Introduction A central problem in information processing is the reduction of the data complexity with minimal loss in precision to discard noise and to reveal basic structure of data sets. Data clustering addresses this tradeoff by optimizing a cost function which preserves the original data as complete as possible and which simultaneously favors prototypes with minimal complexity (Linde et aI., 1980; Gray, 1984; Chou et aI., 1989; Rose et ai., 1990). We discuss anobjective function for the joint optimization of distortion errors and the complexity of a reduced data representation.