Instead, a signal space approach is used to gain new insights via ease of analysis and geometrical interpretation.

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. INTRODUCTION Highly interconnected simple analog processors which mmnc a biological neural network are known to excel at certain collective computational tasks.

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.

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].

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.

Paolo Gaudiano Dept. of Aerospace Engineering Sciences, University of Colorado, Boulder CO 80309, USA January 5, 1988 Abstract Patterns of activity over real neural structures are known to exhibit timedependent behavior.It would seem that the brain may be capable of utilizing temporal behavior of activity in neural networks as a way of performing functions which cannot otherwise be easily implemented. These might include the origination of sequential behavior and the recognition of time-dependent stimuli. A model is presented here which uses neuronal populations with recurrent feedback connections inan attempt to observe and describe the resulting time-dependent behavior. Shortcomings and problems inherent to this model are discussed. Current models by other researchers are reviewed and their similarities and differences discussed. METHODS / PRELIMINARY RESULTS In previous papers,[2,3] computer models were presented that simulate a net consisting oftwo spatially organized populations of realistic neurons.

In this paper research of the second line is described: Starting from a neurophysiologically inspired model of stimulusresponse (SR)and/or associative memorization and a psychologically motivated ministructure for basic control tasks, preconditions and conditions are studied for cooperation of such units in a hierarchical organisation, as can be assumed to be the general layout of macrostructures in the brain. I. INTRODUCTION Theoretic modelling in brain theory is a highly speculative subject. However, it is necessary since it seems very unlikely to get a clear picture of this very complicated device by just analyzing theavailable measurements on sound and/or damaged brain parts only. As in general physics, one has to realize, that there are different levels of modelling: in physics stretching from the atomary levelover atom assemblies till up to general behavioural models like kinematics and mechanics, in brain theory stretching from chemical reactions over electrical spikes and neuronal cell assembly cooperation till general human behaviour. The research discussed in this paper is located just above the direct study of synaptic cooperation of neuronal cell assemblies as studied e. g. in /Amari 1988/. It takes into account the changes of synaptic weighting, without simulating the physical details of such changes, and makes use of a general imitation of learning situation (stimuli) - response connections for building up trainable basic control loops, which allow dynamic SR memorization and which are themsel ves elements of some more complex behavioural loops.

Using a parallel processing model,the current work explores how the biological visual system might solve this problem and how the neurophysiologist might go about understanding the solution.

Correlational Strength and Computational Algebra of Synaptic Connections Between Neurons Eberhard E. Fetz Department of Physiology & Biophysics, University of Washington, Seattle, WA 98195 ABSTRACT Intracellular recordings in spinal cord motoneurons and cerebral cortex neurons have provided new evidence on the correlational strength of monosynaptic connections, and the relation between the shapes of postsynaptic potentials and the associated increased firing probability. In these cells, excitatory postsynaptic potentials (EPSPs) produce crosscorrelogram peakswhich resemble in large part the derivative of the EPSP. Additional synaptic noise broadens the peak, but the peak area -- i.e., the number of above-chance firings triggered per EPSP -- remains proportional to the EPSP amplitude. The consequences of these data for information processing by polysynaptic connections is discussed. The effects of sequential polysynaptic links can be calculated by convolving the effects of the underlying monosynaptic connections.