Bell-shaped response curves are commonly found in biological neurons whenever a natural metric exist on the corresponding relevant stimulus variable (orientation, position in space, frequency, time delay,...). As a result, they are often used in neural models in different context ranging from resolution enhancement and interpolation to learning (see, for instance, Baldi et al. (1988), Moody et al. (1989) *and Division of Biology, California Institute of Technology. The complete title of this paper should read: "Computing with arrays of bell-shaped and sigmoid functions.

We describe a CMOS neural net chip with a reconfigurable network architecture. It contains 32,768 binary, programmable connections arranged in 256 'building block' neurons. Several'building blocks' can be connected to form long neurons with up to 1024 binary connections or to form neurons with analog connections. Single-or multi-layer networks can be implemented with this chip. We have integrated this chip into a board system together with a digital signal processor and fast memory.

The learning time of a simple neural network model is obtained through an analytic computation of the eigenvalue spectrum for the Hessian matrix, which describes the second order properties of the cost function in the space of coupling coefficients. The form of the eigenvalue distribution suggests new techniques for accelerating the learning process, and provides a theoretical justification for the choice of centered versus biased state variables.

A neural network model of motion segmentation by visual cortex is described. The model clarifies how preprocessing of motion signals by a Motion Oriented Contrast Filter (MOC Filter) is joined to long-range cooperative motion mechanisms in a motion Cooperative Competitive Loop (CC Loop) to control phenomena such as as induced motion, motion capture, and motion aftereffects. The total model system is a motion Boundary Contour System (BCS) that is computed in parallel with a static BCS before both systems cooperate to generate a boundary representation for three dimensional visual form perception. The present investigations clarify how the static BCS can be modified for use in motion segmentation problems, notably for analyzing how ambiguous local movements (the aperture problem) on a complex moving shape are suppressed and actively reorganized into a coherent global motion signal. 1 INTRODUCTION: WHY ARE STATIC AND MOTION BOUNDARY CONTOUR SYSTEMS NEEDED? Some regions, notably MT, of visual cortex are specialized for motion processing. However, even the earliest stages of visual cortex processing, such as simple cells in VI, require stimuli that change through time for their maximal activation and are direction-sensitive. Why has evolution generated regions such as MT, when even VI is change-sensitive and direction-sensitive? What computational properties are achieved by MT that are not already available in VI?

Learning an input-output mapping from a set of examples can be regarded as synthesizing an approximation of a multidimensional function.

Simple classical spin models well-known to physicists as the ANNNI and Heisenberg XY Models. in which long-range interactions occur in a pattern given by the Mexican Hat operator.

Robustness is a commonly bruited property of neural networks; in particular, a folk theorem in neural computation asserts that neural networks-in contexts with large interconnectivity-continue to function efficiently, albeit with some degradation, in the presence of component damage or loss. A second folk theorem in such contexts asserts that dense interconnectivity between neural elements is a sine qua non for the efficient usage of resources. These premises are formally examined in this communication in a setting that invokes the notion of the "devil"

In response to a puff of wind, the American cockroach turns away and runs. The circuit underlying the initial turn of this escape response consists of three populations of individually identifiable nerve cells and appears to employ distributed representations in its operation. We have reconstructed several neuronal and behavioral properties of this system using simplified neural network models and the backpropagation learning algorithm constrained by known structural characteristics of the circuitry. In order to test and refine the model, we have also compared the model's responses to various lesions with the insect's responses to similar lesions.

A massively parallel, all-digital, stochastic architecture - TlnMAN N - is described which performs competitive and Kohonen types of learning. A VLSI design is shown for a TlnMANN neuron which fits within a small, inexpensive MOSIS TinyChip frame, yet which can be used to build larger networks of several hundred neurons. The neuron operates at a speed of 15 MHz which allows the network to process 290,000 training examples per second. Use of level sensitive scan logic provides the chip with 100% fault coverage, permitting very reliable neural systems to be built.

The Neural Prediction Model is the speech recognition model based on pattern prediction by multilayer perceptrons. Its effectiveness was confirmed by the speaker-independent digit recognition experiments. This paper presents an improvement in the model and its application to large vocabulary speech recognition, based on subword units. The improvement involves an introduction of "backward prediction," which further improves the prediction accuracy of the original model with only "forward prediction". In application of the model to speaker-dependent large vocabulary speech recognition, the demi-syllable unit is used as a subword recognition unit.