An incremental network model is introduced which is able to learn the important topological relations in a given set of input vectors by means of a simple Hebb-like learning rule. In contrast to previous approaches like the "neural gas" method of Martinetz and Schulten (1991, 1994), this model has no parameters which change over time and is able to continue learning, adding units and connections, until a performance criterion has been met. Applications of the model include vector quantization, clustering, and interpolation.

For unbiased models the regulatizer reducesto the intuitive form that penalizes the mean squared difference between the network output for transformed and untransformed inputs - i.e. the error in satisfying the desired invariance. In general the regularizer includes a term that measures correlations between the error in fitting the data, and the error in satisfying the desired inva.riance. For infinitesimal transformations, the regularizer is equivalent (up to terms linear in the variance of the transformation parameters) to the tangent prop form given by Simard et a1.

A neural network learning paradigm based on information theory is proposed asa way to perform in an unsupervised fashion, redundancy reduction among the elements of the output layer without loss of information fromthe sensory input. The model developed performs nonlinear decorrelation up to higher orders of the cumulant tensors and results in probabilistically independent components of the output layer. This means that we don't need to assume Gaussian distribution neither at the input nor at the output. The theory presented is related to the unsupervised-learning theoryof Barlow, which proposes redundancy reduction as the goal of cognition. When nonlinear units are used nonlinear principal componentanalysis is obtained.

The past few years have produced a number of efforts to design VLSI chips which "learn from experience." The first step toward this goal is developing a silicon analog for a synapse. We have successfully developed such a synapse using only 818 PaulHasler, Chris Diorio, Bradley A. Minch, Carver Mead Drain Gate

Such sensors realize the simultaneous needfor wide field-of-view and good visual acuity. One popular class of space-variant sensors is formed by log-polar sensors which have a small area near the optical axis of greatly increased resolution (the fovea) coupled with a peripheral region that witnesses a gradual logarithmic falloff in resolution as one moves radially outward. These sensors are inspired by similar structures found in the primate retina where one finds both a peripheral region of gradually decreasing acuity and a circularly symmetric area centmlis characterized by a greater density of receptors and a disproportionate representation in the optic nerve [3]. The peripheral region, though of low visual acuity, is more sensitive to light intensity and movement. The existence of a region optimized for discrimination and recognition surrounded by a region geared towards detection thus allows the image of an object of interest detected in the outer region to be placed on the more analytic center for closer scrutiny. Such a strategy however necessitates the existence of (a) methods to determine which location in the periphery to foveate next, and (b) fast gaze-shifting mechanisms to achieve this 894 RajeshP.

A suggestive computational model for how such separate modules can be learned and combined is the mixture-of-experts neural network architecture (Jacobs et al., 1991).

Several investigations have shed light on the effects of vestibular input and visual input on the head direction representation. In this paper, a model is formulated of the neural mechanisms underlying the head direction system. The model is built out of simple ingredients, depending on nothing more complicated than connectional specificity, attractor dynamics, Hebbian learning, and sigmoidal nonlinearities, but it behaves in a sophisticated way and is consistent with most of the observed properties ofreal head direction cells. In addition it makes a number of predictions that ought to be testable by reasonably straightforward experiments.

Networks of this type have a single layer of units with a selective response for some range of the input variables.

Second order properties of cost functions for recurrent networks are investigated. We analyze a layered fully recurrent architecture, the virtue of this architecture is that it features the conventional feedforward architecture as a special case. A detailed description of recursive computation of the full Hessian of the network cost function isprovided. We discuss the possibility of invoking simplifying approximations of the Hessian and show how weight decays iron the cost function and thereby greatly assist training. We present tentative pruningresults, using Hassibi et al.'s Optimal Brain Surgeon, demonstrating that recurrent networks can construct an efficient internal memory. 1 LEARNING IN RECURRENT NETWORKS Time series processing is an important application area for neural networks and numerous architectures have been suggested, see e.g.

We construct a mixture of locally linear generative models of a collection ofpixel-based images of digits, and use them for recognition. Different models of a given digit are used to capture different styles of writing, and new images are classified by evaluating their log-likelihoods under each model. We use an EMbased algorithm in which the M-step is computationally straightforward principal components analysis (PCA). Incorporating tangent-plane information [12]about expected local deformations only requires adding tangent vectors into the sample covariance matrices for the PCA, and it demonstrably improves performance.