The Jacobian of the hand position vector is expressed as J(8) 8/(8)/88. Let Xd be the desired hand position and e Xd - X Xd - /(8) be the hand position error vector.

Zili Lin Rutgers University, Newark DaphnaWeinshall Hebrew University, Israel Abstract The learning of many visual perceptual tasks has been shown to be specific to practiced stimuli, while new stimuli require re-Iearning from scratch. Here we demonstrate generalization using a novel paradigm in motion discrimination where learning has been previously shownto be specific. We trained subjects to discriminate the directions of moving dots, and verified the previous results that learning does not transfer from the trained direction to a new one. However, by tracking the subjects' performance across time in the new direction, we found that their rate of learning doubled. Therefore, learning generalized in a task previously considered too difficult for generalization.

While it is unlikely that complete information from any macroscopic neural tissue will ever be available, some interesting insight can be obtained from simultaneously recorded cells in the cortex of behaving animals. The question we address in this study is the level of synergy, or the level of cooperation, among brain cells, as determined by the information they provide about the observed behavior of the animal.

We propose a new in-sample cross validation based method (randomized GACV) for choosing smoothing or bandwidth parameters that govern the bias-variance or fit-complexity tradeoff in'soft' classification. Soft classification refersto a learning procedure which estimates the probability that an example with a given attribute vector is in class 1 vs class O. The target for optimizing the the tradeoff is the Kullback-Liebler distance between the estimated probability distribution and the'true' probability distribution,representing knowledge of an infinite population.

I present a theory of mean field approximation based on information geometry. Thistheory includes in a consistent way the naive mean field approximation, as well as the TAP approach and the linear response theorem instatistical physics, giving clear information-theoretic interpretations to them. 1 INTRODUCTION Many problems of neural networks, such as learning and pattern recognition, can be cast into a framework of statistical estimation problem. How difficult it is to solve a particular problem depends on a statistical model one employs in solving the problem. For Boltzmann machines[ 1] for example, it is computationally very hard to evaluate expectations of state variables from the model parameters. Mean field approximation[2], which is originated in statistical physics, has been frequently used in practical situations in order to circumvent this difficulty.

We study the approximation of functions by two-layer feedforward neural networks,focusing on incremental algorithms which greedily add units, estimating single unit parameters at each stage. As opposed to standard algorithms for fixed architectures, the optimization at each stage is performed over a small number of parameters, mitigating many of the difficult numerical problems inherent in high-dimensional nonlinear optimization. Weestablish upper bounds on the error incurred by the algorithm, when approximating functions from the Sobolev class, thereby extending previous results which only provided rates of convergence for functions in certain convex hulls of functional spaces. By comparing our results to recently derived lower bounds, we show that the greedy algorithms arenearly optimal. Combined with estimation error results for greedy algorithms, a strong case can be made for this type of approach.

We show how t.o find people by finding putative body segments, and then construct.

In 1986, Tanner and Mead [1] implemented an interesting constraint satisfaction circuitfor global motion sensing in aVLSI. We report here a new and improved aVLSI implementation that provides smooth optical flow as well as global motion in a two dimensional visual field. The computation ofoptical flow is an ill-posed problem, which expresses itself as the aperture problem. However, the optical flow can be estimated by the use of regularization methods, in which additional constraints are introduced interms of a global energy functional that must be minimized. We show how the algorithmic constraints of Hom and Schunck [2] on computing smoothoptical flow can be mapped onto the physical constraints of an equivalent electronic network.

In previous work [6, 9, 10], we advanced a new technique for direct visual matching of images for the purposes of face recognition and image retrieval, using a probabilistic measure of similarity based primarily on a Bayesian (MAP) analysis of image differences, leadingto a "dual" basis similar to eigenfaces [13]. The performance advantage of this probabilistic matching technique over standard Euclidean nearest-neighbor eigenface matching was recently demonstrated using results from DARPA's 1996 "FERET" face recognition competition, in which this probabilistic matching algorithm was found to be the top performer. We have further developed a simple method of replacing the costly compution of nonlinear (online) Bayesian similarity measures by the relatively inexpensive computation of linear (offline) subspace projections and simple (online) Euclidean norms, thus resulting in a significant computational speedup for implementation with very large image databases as typically encountered in real-world applications.

Kernel PCA as a nonlinear feature extractor has proven powerful as a preprocessing step for classification algorithms. But it can also be considered asa natural generalization of linear principal component analysis. This gives rise to the question how to use nonlinear features for data compression, reconstruction, and de-noising, applications common in linear PCA. This is a nontrivial task, as the results provided by kernel PCAlive in some high dimensional feature space and need not have pre-images in input space. This work presents ideas for finding approximate pre-images,focusing on Gaussian kernels, and shows experimental results using these pre-images in data reconstruction and de-noising on toy examples as well as on real world data.