Current Focus Of Learning Research Most connectionist learning algorithms may be grouped into three general catagories, commonly referred to as supenJised, unsupenJised, and reinforcement learning. Supervised learning requires the explicit participation of an intelligent teacher, usually to provide the learning system with task-relevant input-output pairs (for two recent examples, see [1,2]). Unsupervised learning, exemplified by "clustering" algorithms, are generally concerned with detecting structure in a stream of input patterns [3,4,5,6,7]. In its final state, an unsupervised learning system will typically represent the discovered structure as a set of categories representing regions of the input space, or, more generally, as a mapping from the input space into a space of lower dimension that is somehow better suited to the task at hand. In reinforcement learning, a "critic" rewards or penalizes the learning system, until the system ultimately produces the correct output in response to a given input pattern [8].

Two approaches are described which allow parallel computation of a model's nonlinear functions, parallel modification of a model's weights, and parallel propagation of a model's activation and error. Each approach also allows a model's interconnect structure to be physically dynamic. A Hopfield model is implemented with each approach at six sizes over the same number of CM processors to provide a performance comparison. INTRODUCflON Simulations of neural network models on digital computers perform various computations by applying linear or nonlinear functions, defined in a program, to weighted sums of integer or real numbers retrieved and stored by array reference. The numerical values are model dependent parameters like time averaged spiking frequency (activation), synaptic efficacy (weight), the error in error back propagation models, and computational temperature in thermodynamic models. The interconnect structure of a particular model is implied by indexing relationships between arrays defined in a program. On the Connection Machine (CM), these relationships are expressed in hardware processors interconnected by a 16-dimensional hypercube communication network. Mappings are constructed to defme higher dimensional interconnectivity between processors on top of the fundamental geometry of the communication network.

Many optimization models of neural networks need constraints to restrict the space of outputs to a subspace which satisfies external criteria. Optimizations using energy methods yield "forces" which act upon the state of the neural network. The penalty method, in which quadratic energy constraints are added to an existing optimization energy, has become popular recently, but is not guaranteed to satisfy the constraint conditions when there are other forces on the neural model or when there are multiple constraints. In this paper, we present the basic differential multiplier method (BDMM), which satisfies constraints exactly; we create forces which gradually apply the constraints over time, using "neurons" that estimate Lagrange multipliers. The basic differential multiplier method is a differential version of the method of multipliers from Numerical Analysis.

We propose a new scheme to construct neural networks to classify patterns. Thenew scheme has several novel features: 1. We focus attention on the important attributes of patterns in ranking order.

Asa means of probing these cerebellar mechanisms, my colleagues and I have been conducting microelectrode studies of the neural messages that flow through the intermediate divisionof the cerebellum and onward to limb muscles via the rubrospinal tract. We regard this cerebellorubrospinal pathwayas a useful model system for studying general problems of sensorimotor integration and adaptive brain function.

ABSTRACT The information capacity of Kanerva's Sparse, Distributed Memory (SDM) and Hopfield-type neural networks is investigated. Under the approximations used here, it is shown that the total informationstored in these systems is proportional to the number connections in the network. Theproportionality constant is the same for the SDM and HopJreld-type models independent ofthe particular model, or the order of the model. The approximations are checked numerically. This same analysis can be used to show that the SDM can store sequences ofspatiotemporal patterns, and the addition of time-delayed connections allows the retrieval of context dependent temporal patterns. A minor modification of the SDM can be used to store correlated patterns. INTRODUCTION Many different models of memory and thought have been proposed by scientists over the years.

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.

Much experimental study of real neural networks relies on the proper classification of extracellulary sampled neural signals (i.e.

For related finite array models classical phase transi t.ions (which describe steady-state behavior) may not.

Box 150, Cheongryang, Seoul, Korea ABSTRACT Inverse matrix calculation can be considered as an optimization. We have demonstrated that this problem can be rapidly solved by highly interconnected simple neuron-like analog processors. A network for matrix inversion based on the concept of Hopfield's neural network was designed, and implemented with electronic hardware. With slight modifications, the network is readily applicable to solving a linear simultaneous equation efficiently. Notable features of this circuit are potential speed due to parallel processing, and robustness against variations of device parameters.