Parallelizable optimization techniques are applied to the problem of learning in feedforward neural networks. In addition to having superior convergence properties, optimization techniques such as the Polak Ribiere method are also significantly more efficient than the Backpropagation algorithm. These results are based on experiments performed on small boolean learning problems and the noisy real-valued learning problem of handwritten character recognition. 1 INTRODUCTION The problem of learning in feedforward neural networks has received a great deal of attention recently because of the ability of these networks to represent seemingly complex mappings in an efficient parallel architecture. This learning problem can be characterized as an optimization problem, but it is unique in several respects. Function evaluation is very expensive. However, because the underlying network is parallel in nature, this evaluation is easily parallelizable.

ABSTRACT We describe pulse - stream firing integrated circuits that implement asynchronous analog neural networks. Synaptic weights are stored dynamically, and weighting uses time-division of the neural pulses from a signalling neuron to a receiving neuron. MOS transistors in their "ON" state act as variable resistors to control a capacitive discharge, and time-division is thus achieved by a small synapse circuit cell. The VLSI chip set design uses 2.5J.1.m INTRODUCTION Neural network implementations fall into two broad classes - digital [1,2] and analog (e.g. The strengths of a digital approach include the ability to use well-proven design techniques, high noise immunity, and the ability to implement programmable networks.

The performance of these networks has been better than that of conventional methods.

Popular neuron models are based upon some statistical measure of known natural behavior. Whether that measure is expressed in terms of average firing rate or a firing probability, the instantaneous neuron activation is only represented in an abstract sense. Artificial electronic neurons derived from these models represent this excitation level as a binary code or a continuous voltage at the output of a summing amplifier. While such models have been shown to perform well for many applications, and form an integral part of much current work, they only partially emulate the manner in which natural neural networks operate. They ignore, for example, differences in relative arrival times of neighboring action potentials -- an important characteristic known to exist in natural auditory and visual networks {Sejnowski, 1986}. They are also less adaptable to fme-grained, neuron-centered learning, like the post-tetanic facilitation observed in natural neurons. We are investigating the implementation and application of neuron circuits which better approximate natural neuron function.

This paper describes an ongoing effort which approaches neural net research in a program of close collaboration of neurosc i ent i sts and eng i neers. The effort is des i gned to elucidate associative learning in the marine snail Hermissenda crassicornist in which Pavlovian conditioning has been observed. Learning has been isolated in the four neuron network at the convergence of the v i sua 1 and vestibular pathways in this animal t and biophysical changes t specific to learning t have been observed in the membrane of the photoreceptor B cell. A basic charging capacitance model of a neuron is used and enhanced with biologically plausible mechanisms that are necessary to replicate the effect of learning at the cellular level. These mechanisms are nonlinear and are t primarilYt instances of second order control systems (e.g.

We have used analog VLSI technology to model a class of small oscillating biological neural circuits known as central pattern generators (CPG). These circuits generate rhythmic patterns of activity which drive locomotor behaviour in the animal. We have designed, fabricated, and tested a model neuron circuit which relies on many of the same mechanisms as a biological central pattern generator neuron, such as delays and internal feedback. We show that this neuron can be used to build several small circuits based on known biological CPG circuits, and that these circuits produce patterns of output which are very similar to the observed biological patterns. To date, researchers in applied neural networks have tended to focus on mammalian systems as the primary source of potentially useful biological information. However, invertebrate systems may represent a source of ideas in many ways more appropriate, given current levels of engineering sophistication in building neural-like systems, and given the state of biological understanding of mammalian circuits.

A great deal of interest has recently been focused on theories concerning parallel distributed processing in central nervous systems. In particular, many researchers have become very interested in the structure and function of "computational maps" in sensory systems. As defined in a recent review (Knudsen et al, 1987), a "map" is an array of nerve cells, within which there is a systematic variation in the "tuning" of neighboring cells for a particular parameter. For example, the projection from retina to visual cortex is a relatively simple topographic map; each cortical hypercolumn itself contains a more complex "computational" map of preferred line orientation representing the angle of tilt of a simple line stimulus. The overall goal of the research in my lab is to determine how a relatively complex mapped sensory system extracts and encodes information from external stimuli.

While we are waiting for the ultimate biophysics of cell membranes and synapses to be completed, we may speculate on the shapes of neurons and on the patterns of their connections. Much of this will be significant whatever the outcome of future physiology. Take as an example the isotropy, anisotropy and periodicity of different kinds of neural networks. The very existence of these different types in different parts of the brain (or in different brains) defeats explanation in terms of embryology; the mechanisms of development are able to make one kind of network or another. The reasons for the difference must be in the functions they perform.

A mathematical model based on the bulbar anatomy and electrophysiology is described. Simulations produce a 35-60 Hz modulated activity coherent across the bulb, mimicing the observed field potentials. The decision states (for the odor information) here can be thought of as stable cycles, rather than point stable states typical of simpler neuro-computing models. Analysis and simulations show that a group of coupled nonlinear oscillators are responsible for the oscillatory activities determined by the odor input, and that the bulb, with appropriate inputs from higher centers, can enhance or suppress the sensitivity to partiCUlar odors. The model provides a framework in which to understand the transform between odor input and the bulbar output to olfactory cortex.

We have fabricated a test chip in 2 micron CMOS technology that embodies these ideas and we report our evaluation of the microchip and our plans for improvements. Knowledge is encoded in the test chip by presenting digital patterns to it that are examples of a desired input-output Boolean mapping. This knowledge is learned and stored entirely on chip in a digitally controlled synapse-like element in the form of connection strengths between neuron-like elements. The only portion of this learning system which is off chip is the VLSI test equipment used to present the patterns. This learning system uses a modified Boltzmann machine algorithm[3] which, if simulated on a serial digital computer, takes enormous amounts of computer time. Our physical implementation is about 100,000 times faster. The test chip, if expanded to a board-level system of thousands of neurons, would be an appropriate architecture for solving artificial intelligence problems whose solutions are hard to specify using a conventional rule-based approach. Examples include speech and pattern recognition and encoding some types of expert knowledge.