By applying a likelihood splitting criteria to each expert in the HME we "grow" the tree adaptively during training. Secondly, by considering only the most probable path through the tree we may "prune" branches away, either temporarily, or permanently if they become redundant. We demonstrate results for the growing and path pruning algorithms which show significant speed ups and more efficient use of parameters over the standard fixed structure in discriminating between two interlocking spirals and classifying 8-bit parity patterns. INTRODUCTION The HME (Jordan & Jacobs 1994) is a tree structured network whose terminal nodes are simple function approximators in the case of regression or classifiers in the case of classification. The outputs of the terminal nodes or experts are recursively combined upwards towards the root node, to form the overall output of the network, by "gates" which are situated at the non-terminal nodes.

Over the last few years the Fourier Transform (FT) representation of boolean functions has been an instrumental tool in the computational learning theory community. It has been used mainly to demonstrate the learnability of various classes of functions with respect to the uniform distribution.

We propose a new learning method, "Generalized Learning Vector Quantization (GLVQ)," in which reference vectors are updated based on the steepest descent method in order to minimize the cost function. The cost function is determined so that the obtained learning rule satisfies the convergence condition. We prove that Kohonen's rule as used in LVQ does not satisfy the convergence condition and thus degrades recognition ability. Experimental results for printed Chinese character recognition reveal that GLVQ is superior to LVQ in recognition ability.

In this paper we examine a perceptron learning task. The task is realizable since it is provided by another perceptron with identical architecture. Both perceptrons have nonlinear sigmoid output functions. The gain of the output function determines the level of nonlinearity of the learning task. It is observed that a high level of nonlinearity leads to overfitting. We give an explanation for this rather surprising observation and develop a method to avoid the overfitting. This method has two possible interpretations, one is learning with noise, the other cross-validated early stopping.

A Bayesian-Kullback learning scheme, called Ying-Yang Machine, is proposed based on the two complement but equivalent Bayesian representations for joint density and their Kullback divergence. Not only the scheme unifies existing major supervised and unsupervised learnings, including the classical maximum likelihood or least square learning, the maximum information preservation, the EM & em algorithm and information geometry, the recent popular Helmholtz machine, as well as other learning methods with new variants and new results; but also the scheme provides a number of new learning models. 1 INTRODUCTION Many different learning models have been developed in the literature. We may come to an age of searching a unified scheme for them. With a unified scheme, we may understand deeply the existing models and their relationships, which may cause cross-fertilization on them to obtain new results and variants; We may also be guided to develop new learning models, after we get better understanding on which cases we have already studied or missed, which deserve to be further explored. Recently, a Baysian-Kullback scheme, called the YING-YANG Machine, has been proposed as such an effort(Xu, 1995a). It bases on the Kullback divergence and two complement but equivalent Baysian representations for the joint distribution of the input space and the representation space, instead of merely using Kullback divergence for matching un-structuralized joint densities in information geometry type learnings (Amari, 1995a&b; Byrne, 1992; Csiszar, 1975).

Search for the largest (or the smallest) among a number of input data, Le., the winner-take-all (WTA) action, is an essential part of intelligent data processing such as data retrieval in associative memories [3], vector quantization circuits [4], Kohonen's self-organizing maps [5] etc. In addition to the maximum or minimum search, data sorting also plays an essential role in a number of signal processing such as median filtering in image processing, evolutionary algorithms in optimizing problems [6] and so forth.

We propose an active learning method with hidden-unit reduction.

Most studies of attention have focused on the selection process of incoming sensory cues (Posner et al., 1980; Koch et al., 1985; Desimone et al., 1995). Emphasis was placed on the phenomena of causing different percepts for the same sensory stimuli. However, the selection of sensory input itself is not the final goal of attention. We consider attention as a means for goal-directed behavior and survival of the animal. In this view, dynamical properties of attention are crucial. While attention has to be maintained long enough to enable robust response to sensory input, it also has to be shifted quickly to a novel cue that is potentially important. Long-term maintenance and quick transition are critical requirements for attention dynamics.

A new online learning algorithm which minimizes a statistical dependency among outputs is derived for blind separation of mixed signals. The dependency is measured by the average mutual information (MI) of the outputs. The source signals and the mixing matrix are unknown except for the number of the sources. The Gram-Charlier expansion instead of the Edgeworth expansion is used in evaluating the MI. The natural gradient approach is used to minimize the MI. A novel activation function is proposed for the online learning algorithm which has an equivariant property and is easily implemented on a neural network like model. The validity of the new learning algorithm are verified by computer simulations.

The center-surround opponent receptive field (CSRF) mechanism represents one such example. Here, analogous CSRFs are shown to be formed in an artificial neural network which learns to localize contours (edges) of the luminance difference. Furthermore, when the input pattern is corrupted by a background noise, the CSRFs of the hidden units becomes shallower and broader with decrease of the signal-to-noise ratio (SNR). The same kind of SNR-dependent plasticity is present in the CSRF of real visual neurons; in bipolar cells of the carp retina as is shown here experimentally, as well as in large monopolar cells of the fly compound eye as was described by others. Also, analogous SNRdependent plasticity is shown to be present in the biphasic flash responses (BPFR) of these artificial and biological visual systems. Thus, the spatial (CSRF) and temporal (BPFR) filtering properties with which a wide variety of creatures see the world appear to be optimized for detectability of changes in space and time. 1 INTRODUCTION A number of learning algorithms have been developed to make synthetic neural machines be trainable to function in certain optimal ways. If the brain and nervous systems that we see in nature are best answers of the evolutionary process, then one might be able to find some common'softwares' in real and artificial neural systems. This possibility is examined in this paper, with respect to a basic visual 160 S. Y ASUI, T. FURUKAWA, M. YAMADA, T. SAITO