We consider a 2-layer, 3-node, n-input neural network whose nodes compute linear threshold functions of their inputs. We show that it is NPcomplete to decide whether there exist weights and thresholds for the three nodes of this network so that it will produce output consistent with a given set of training examples. We extend the result to other simple networks. This result suggests that those looking for perfect training algorithms cannot escape inherent computational difficulties just by considering only simple or very regular networks. It also suggests the importance, given a training problem, of finding an appropriate network and input encoding for that problem. It is left as an open problem to extend our result to nodes with nonlinear functions such as sigmoids.

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.

Hardware implementation of neuromorphic algorithms is hampered by high degrees of connectivity. Functionally equivalent feedforward networks may be formed by using limited fan-in nodes and additional layers.

We discuss in this paper architectures for executing probabilistic rule-bases in a parallel manner, using as a theoretical basis recently introduced information-theoretic models. We will begin by describing our (non-neural) learning algorithm and theory of quantitative rule modelling, followed by a discussion on the exact nature of two particular models. Finally we work through an example of our approach, going from database to rules to inference network, and compare the network's performance with the theoretical limits for specific problems.

We propose an optimality principle for training an unsupervised feedforwardneural network based upon maximal ability to reconstruct the input data from the network outputs. Wedescribe an algorithm which can be used to train either linear or nonlinear networks with certain types of nonlinearity. Examples of applications to the problems of image coding, feature detection, and analysis of randomdot stereogramsare presented.

The first case shows recurrent activity, while the second case is non-recurrent or feed forward. The polarity of these terms signify excitatory or inhibitory interactions. Shunting network equations can be derived from various sources such as the passive membrane equation with synaptic interaction (Grossberg 1973, Pinter 1983), models of dendritic interaction (RaIl 1977), or experiments on motoneurons (Ellias and Grossberg 1975). While the exact mechanisms of synaptic interactions are not known in every individual case,neurobiological evidence of shunting interactions appear in several 696 Nabet, Darling and Pinter areas such as sensory systems, cerebellum, neocortex, and hippocampus (Grossberg 1973, Pinter 1987). In addition to neurobiology, these networks have been used to successfully explain data from disciplines ranging from population biology (Lotka 1956) to psychophysics and behavioral psychology (Grossberg 1983). Shunting nets have important advantages over additive models which lack the extra nonlinearityintroduced by the multiplicative terms.

ABSTRACT We describe pulse - stream firing integrated circuits that implement asynchronousanalog 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.

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, andform 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.

ABSTRACT The Parsing and Learning System(PALS) is a massively parallel self-tuning context-free parser. It is capable of parsing sentences of unbounded length mainly due to its parse-tree representation scheme. The system is capable of improving its parsing performance through the presentation of training examples. INTRODUCTION Recent PDP research[Rumelhart et al.- 1986; Feldman and Ballard, 1982; Lippmann, 1987] involving natural language processtng[Fanty, 1988; Selman, 1985; Waltz and Pollack, 1985] have unrealistically restricted sentences to a fixed length. A solution to this problem was presented in the system CONPARSE[Charniak and Santos.

In particular we examine what happens when the ntunber of layers is large or when the connectivity between layers is local and investigate some of the properties of an autoassociative algorithm. Notation will be as in [1] where additional motivations and references can be found. It is usual to criticize linear networks because "linear functions do not compute" and because several layers can always be reduced to one by the proper multiplication of matrices. However this is not the point of view adopted here. It is assumed that the architecture of the network is given (and could perhaps depend on external constraints) and the purpose is to understand what happens during the learning phase, what strategies are adopted by a synaptic weights modifying algorithm, ... [see also Cottrell et al. (1988) for an example of an application andthe work of Linsker (1988) on the emergence of feature detecting units in linear networks}.