The mapping of the back-propagation and mean field theory learning algorithms onto a generic 2-D SIMD computer is described. This architecture proves to be very adequate for these applications since efficiencies close to the optimum can be attained. Expressions to find the learning rates are given and then particularized to the DAP array procesor.

In fact, performance was often improved over the original learning rule.

In this paper, several techniques for addressing this problem are discussed in the context of an isolated word recognition task.

The distributed-neuron synapses are arranged inblocks of 16, which we call '4 x 4 tiles'. Switch matrices are interleaved between each of these tiles to provide programmability ofinterconnections. With a small area overhead (15 %), the 1024 units of the network can be rearranged in various configurations. Someof the possible configurations are, a 12-32-12 network, a 16-12-12-16 network, two 12-32 networks etc. (the numbers separated bydashes indicate the number of units per layer, including the input layer). Weights are stored in analog form on MaS capacitors.

We have calculated, both analytically and in simulations, the rate of convergence at long times in the backpropagation learning algorithm fornetworks with and without hidden units. Our basic finding for units using the standard sigmoid transfer function is lit convergence of the error for large t, with at most logarithmic corrections fornetworks with hidden units. Other transfer functions may lead to a 8lower polynomial rate of convergence. Our analytic calculations were presented in (Tesauro, He & Ahamd, 1989). Here we focus in more detail on our empirical measurements of the convergence ratein numerical simulations, which confirm our analytic results.

ABSTRACT The CHAC storage scheme has been used as a basis for a software implementation of an associative .emory A major disadvantage of this CHAC-concept is that the degree of local generalization (area of interpolation) isfixed. This paper deals with an algorithm for self-organizing variable generalization for the AKS, based on ideas of T. Kohonen. 1 INTRODUCTION For several years research at the Department of Control Theory andRobotics at the Technical University of Darmstadt has been concerned with the design of a learning real-time control loop with neuron-like associative memories (LERNAS) A Self-organizing Associative Memory System for Control Applications 333 for the control of unknown, nonlinear processes (Ersue, Tolle, 1988). This control concept uses an associative memory systemAHS, based on the cerebellar cortex model CHAC by Albus (Albus, 1972), for the storage of a predictive nonlinear processmodel and an appropriate nonlinear control strategy (Fig.1). Figure 1: The learning control loop LERNAS One problem for adjusting the control loop to a process is, however, to find a suitable set of parameters for the associative memory.The parameters in question determine the degree of generalization within the memory and therefore have a direct influence on the number of training steps required tolearn the process behaviour. For a good performance of the control loop it· is desirable to have a very small generalization around a given setpoint but to have a large generalization elsewhere.

How good are the reconstructions?

Pentti Kanerva Research Institute for Advanced Computer Science Mail Stop 230-5, NASA Ames Research Center Moffett Field, California 94035 ABSTRACT Contour maps provide a general method for recognizing two-dimensional shapes. All but blank images give rise to such maps, and people are good at recognizing objects and shapes from them. The maps are encoded easily in long feature vectors that are suitable for recognition by an associative memory. These properties of contour maps suggest a role for them in early visual perception. The prevalence of direction-sensitive neurons in the visual cortex of mammals supports this view.

Given a set of input-output training samples, we describe a procedure fordetermining the time sequence of weights for a dynamic neural network to model an arbitrary input-output process. We formulate the input-output mapping problem as an optimal control problem,defining a performance index to be minimized as a function of time-varying weights.

One popular class of unsupervised algorithms are competitive algorithms. In the traditional view of competition, only one competitor, the winner, adapts for any given case. I propose to view competitive adaptation as attempting to fit a blend of simple probability generators (such as gaussians) to a set of data-points. The maximum likelihood fit of a model of this type suggests a "softer" form of competition, in which all competitors adapt in proportion to the relative probability that the input came from each competitor. I investigate one application of the soft competitive model, placement of radial basis function centers for function interpolation, and show that the soft model can give better performance with little additional computational cost. 1 INTRODUCTION Interest in unsupervised learning has increased recently due to the application of more sophisticated mathematical tools (Linsker, 1988; Plumbley and Fallside, 1988; Sanger, 1989) and the success of several elegant simulations of large scale selforganization (Linsker, 1986; Kohonen, 1982). One popular class of unsupervised algorithms are competitive algorithms, which have appeared as components in a variety of systems (Von der Malsburg, 1973; Fukushima, 1975; Grossberg, 1978). Generalizing the definition of Rumelhart and Zipser (1986), a competitive adaptive system consists of a collection of modules which are structurally identical except, possibly, for random initial parameter variation.