I propose a learning algorithm for learning hierarchical models for object recognition.The model architecture is a compositional hierarchy that represents part-whole relationships: parts are described in the local contextof substructures of the object. The focus of this report is learning hierarchical models from data, i.e. inducing the structure of model prototypes from observed exemplars of an object. At each node in the hierarchy, a probability distribution governing its parameters must be learned. The connections between nodes reflects the structure of the object. The formulation of substructures is encouraged such that their parts become conditionally independent.

The first class of network adaptation algorithms start out with a redundant architecture and proceed by pruning away seemingly unimportant weights (Sietsma and Dow, 1988; Le Cun et aI, 1990). A second class of algorithms starts off with a sparse architecture and grows the network to the complexity required by the problem. Several algorithms have been proposed for growing feedforward networks. The upstart algorithm of Frean (1990) and the cascade-correlation algorithm of Fahlman (1990) are examples of this approach.

Center positions are continuously updated through soft competitive learning. The width of the radial basis functions is derived from the distance to topological neighbors. During the training the observed error is accumulated locally and used to determine where to insert the next unit. This leads (in case of classification problems) to the placement of units near class borders rather than near frequency peaks as is done by most existing methods. The resulting networks need few training epochs and seem to generalize very well. This is demonstrated by examples.

We show how an "Elman" network architecture, constructed from recurrently connected oscillatory associative memory network modules, canemploy selective "attentional" control of synchronization to direct the flow of communication and computation within the architecture to solve a grammatical inference problem. Previously we have shown how the discrete time "Elman" network algorithm can be implemented in a network completely described by continuous ordinary differential equations. The time steps (machine cycles)of the system are implemented by rhythmic variation (clocking) of a bifurcation parameter. In this architecture, oscillation amplitudecodes the information content or activity of a module (unit), whereas phase and frequency are used to "softwire" the network. Only synchronized modules communicate by exchanging amplitudeinformation; the activity of non-resonating modules contributes incoherent crosstalk noise. Attentional control is modeled as a special subset of the hidden modules with ouputs which affect the resonant frequencies of other hidden modules. They control synchrony among the other modules anddirect the flow of computation (attention) to effect transitions betweentwo subgraphs of a thirteen state automaton which the system emulates to generate a Reber grammar. The internal crosstalk noise is used to drive the required random transitions of the automaton.

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.

Thomas G. Dietterich Arris Pharmaceutical Corporation and Oregon State University Corvallis, OR 97331-3202 Ajay N. Jain Arris Pharmaceutical Corporation 385 Oyster Point Blvd., Suite 3 South San Francisco, CA 94080 Richard H. Lathrop and Tomas Lozano-Perez Arris Pharmaceutical Corporation and MIT Artificial Intelligence Laboratory 545 Technology Square Cambridge, MA 02139 Abstract In drug activity prediction (as in handwritten character recognition), thefeatures extracted to describe a training example depend on the pose (location, orientation, etc.) of the example. In handwritten characterrecognition, one of the best techniques for addressing thisproblem is the tangent distance method of Simard, LeCun and Denker (1993). Jain, et al. (1993a; 1993b) introduce a new technique-dynamic reposing-that also addresses this problem. Dynamicreposing iteratively learns a neural network and then reposes the examples in an effort to maximize the predicted output values.New models are trained and new poses computed until models and poses converge. This paper compares dynamic reposing to the tangent distance method on the task of predicting the biological activityof musk compounds.

In this paper, it is shown that the conventional back-propagation (BPP) algorithm for neural network regression is robust to leverages (datawith:n corrupted), but not to outliers (data with y corrupted). A robust model is to model the error as a mixture of normal distribution. The influence function for this mixture model is calculated and the condition for the model to be robust to outliers is given. EM algorithm [5] is used to estimate the parameter. The usefulness of model selection criteria is also discussed.

Four versions of a k-nearest neighbor algorithm with locally adaptive kare introduced and compared to the basic k-nearest neighbor algorithm (kNN). Locally adaptive kNN algorithms choose the value of k that should be used to classify a query by consulting the results of cross-validation computations in the local neighborhood of the query. Local kNN methods are shown to perform similar to kNN in experiments with twelve commonly used data sets. Encouraging resultsin three constructed tasks show that local methods can significantly outperform kNN in specific applications. Local methods can be recommended for online learning and for applications wheredifferent regions of the input space are covered by patterns solving different sub-tasks.

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.

Terence D. Sanger Jet Propulsion Laboratory MS 303-310 4800 Oak Grove Drive Pasadena, CA 91109 Abstract The Singular Value Decomposition (SVD) is an important tool for linear algebra and can be used to invert or approximate matrices. Although many authors use "SVD" synonymously with "Eigenvector Decomposition"or "Principal Components Transform", it is important to realize that these other methods apply only to symmetric matrices, while the SVD can be applied to arbitrary nonsquare matrices. This property is important for applications to signal transmission and control. I propose two new algorithms for iterative computation of the SVD given only sample inputs and outputs from a matrix. Although there currently exist many algorithms for Eigenvector Decomposition (Sanger1989, for example), these are the first true samplebased SVDalgorithms. 1 INTRODUCTION The Singular Value Decomposition (SVD) is a method for writing an arbitrary nons quare matrix as the product of two orthogonal matrices and a diagonal matrix.