(June 1987).

INTRODUCTION TO A SYSTEM FOR IMPLEMENTING NEURAL NET CONNECTIONS ON SIMD ARCHITECTURES Sherryl Tomboulian Institute for Computer Applications in Science and Engineering NASA Langley Research Center, Hampton VA 23665 ABSTRACT Neural networks have attracted much interest recently, and using parallel architectures to simulate neural networks is a natural and necessary application. The SIMD model of parallel computation is chosen, because systems of this type can be built with large numbers of processing elements. However, such systems are not naturally suited to generalized communication. A method is proposed that allows an implementation of neural network connections on massively parallel SIMD architectures. The key to this system is an algorithm that allows the formation of arbitrary connections between the "neurons". A feature is the ability to add new connections quickly. It also has error recovery ability and is robust over a variety of network topologies. Simulations of the general connection system, and its implementation on the Connection Machine, indicate that the time and space requirements are proportional to the product of the average number of connections per neuron and the diameter of the interconnection network.

QUALITATIVE RESULTS Analysis of the weights produced by training a network is an exceedingly difficult problem, which we have only been able to approach qualitatively. In Figure 1 we present a diagram showing the connection strengths in a network with 651 input units and no hidden units.

LEARNING IN NETWORKS OF NONDETERMINISTIC ADAPTIVE LOGIC ELEMENTS Richard C. Windecker* AT&T Bell Laboratories, Middletown, NJ 07748 ABSTRACT This paper presents a model of nondeterministic adaptive automata that are constructed from simpler nondeterministic adaptive information processing elements. The first half of the paper describes the model. Chief among these properties is that network aggregates of the model elements can adapt appropriately when a single reinforcement channel provides the same positive or negative reinforcement signal to all adaptive elements of the network at the same time. This holds for multiple-input, multiple-output, multiple-layered, combinational and sequential networks. It also holds when some network elements are "hidden" in that their outputs are not directly seen by the external environment. INTRODUCTION There are two primary motivations for studying models of adaptive automata constructed from simple parts. First, they let us learn things about real biological systems whose properties are difficult to study directly: We form a hypothesis about such systems, embody it in a model, and then see if the model has reasonable learning and behavioral properties. In the present work, the hypothesis being tested is: that much of an animal's behavior as determined by its nervous system is intrinsically nondeterministic; that learning consists of incremental changes in the probabilities governing the animal's behavior; and that this is a consequence of the animal's nervous system consisting of an aggregate of information processing elements some of which are individually nondeterministic and adaptive. The second motivation for studying models of this type is to find ways of building machines that can learn to do (artificially) intelligent and practical things.

A NEURAL-NETWORK SOLUTION TO THE CONCENTRATOR ASSIGNNlENT PROBLEM Gene A. Tagliarini Edward W. Page Department of Computer Science, Clemson University, Clemson, SC 29634-1906 ABSTRACT Networks of simple analog processors having neuron-like properties have been employed to compute good solutions to a variety of optimization problems. This paper presents a neural-net solution to a resource allocation problem that arises in providing local access to the backbone of a wide-area communication network. The problem is described in terms of an energy function that can be mapped onto an analog computational network. Simulation results characterizing the performance of the neural computation are also presented. INTRODUCTION This paper presents a neural-network solution to a resource allocation problem that arises in providing access to the backbone of a communication network. 1 In the field of operations research, this problem was first known as the warehouse location problem and heuristics for finding feasible, suboptimal solutions have been developed previously.2.

Here, X is a finite or infinite set, and Y is another finite or infinite set. A learning machine observes any set of pairs (x, y) sampled randomly from X x Y. (X x Y means the Cartesian product of X and Y.) And, it computes some estimate j:

A general method, the tensor product representation, is described for the distributed representation of value/variable bindings. The method allows the fully distributed representation of symbolic structures: the roles in the structures, as well as the fillers for those roles, can be arbitrarily non-local. Fully and partially localized special cases reduce to existing cases of connectionist representations of structured data; the tensor product representation generalizes these and the few existing examples of fuUy distributed representations of structures. The representation saturates gracefully as larger structures are represented; it penn its recursive construction of complex representations from simpler ones; it respects the independence of the capacities to generate and maintain multiple bindings in parallel; it extends naturally to continuous structures and continuous representational patterns; it pennits values to also serve as variables; it enables analysis of the interference of symbolic structures stored in associative memories; and it leads to characterization of optimal distributed representations of roles and a recirculation algorithm for learning them. Introduction Any model of complex infonnation processing in networks of simple processors must solve the problem of representing complex structures over network elements. Connectionist models of realistic natural language processing, for example, must employ computationally adequate representations of complex sentences. Many connectionists feel that to develop connectionist systems with the computational power required by complex tasks, distributed representations must be used: an individual processing unit must participate in the representation of multiple items, and each item must be represented as a pattern of activity of multiple processors. Connectionist models have used more or less distributed representations of more or less complex structures, but little if any general analysis of the problem of distributed representation of complex infonnation has been carried out This paper reports results of an analysis of a general method called the tensor product representation.

ABSTRACT A computer model of the hippocampal pyramidal cell (HPC) is described which integrates data from a variety of sources in order to develop a consistent description for this cell type. The model presently includes descriptions of eleven nonlinear somatic currents of the HPC, and the electrotonic structure of the neuron is modelled with a soma/short-cable approximation. Model simulations qualitatively or quantitatively reproduce a wide range of somatic electrical behavior i HPCs, and demonstrate possible roles for the various currents in information processing. There are several substrates for neuronal computation, including connectivity, synapses, morphometries of dendritic trees, linear parameters of cell membrane, as well as nonlinear, time-varying membrane conductances, also referred to as currents or channels. In the classical description of neuronal function, the contribution of membrane channels is constrained to that of generating the action potential, setting firing threshold, and establishing the relationship between (steady-state) stimulus intensity and firing frequency.

We show how to estimate (1) the number of functions that can be implemented by a particular network architecture, (2) how much analog precision is needed in the connections in the network, and (3) the number of training examples the network must see before it can be expected to form reliable generalizations.

The network model considered consists of interconnected groups of neurons, where each group could be fully interconnected (it could have feedback connections, with possibly asymmetric weights), but no loops between the groups are allowed. A stochastic descent algorithm is applied, under a certain inequality constraint on each intragroup weight matrix which ensures for the network to possess a unique equilibrium state for every input. Introduction It has been shown in the last few years that large networks of interconnected "neuron" -like elemp.nts