A gradient descent algorithm for parameter estimation which is similar to those used for continuous-time recurrent neural networks was derived for Hodgkin-Huxley type neuron models. Using membrane potentialtrajectories as targets, the parameters (maximal conductances, thresholds and slopes of activation curves, time constants) weresuccessfully estimated. The algorithm was applied to modeling slow non-spike oscillation of an identified neuron in the lobster stomatogastric ganglion. A model with three ionic currents was trained with experimental data. It revealed a novel role of A-current for slow oscillation below -50 mY. 1 INTRODUCTION Conductance-based neuron models, first formulated by Hodgkin and Huxley [10], are commonly used for describing biophysical mechanisms underlying neuronal behavior.

The recurrent network,containing six continuous-time analog neurons and 42 free parameters (connection strengths and thresholds), is trained to generate time-varying outputs approximating given periodic signals presented to the network. The chip implements a stochastic perturbative algorithm,which observes the error gradient along random directions in the parameter space for error-descent learning. In addition tothe integrated learning functions and the generation of pseudo-random perturbations, the chip provides for teacher forcing andlong-term storage of the volatile parameters. The network learns a 1 kHz circular trajectory in 100 sec. The chip occupies 2mm x 2mm in a 2JLm CMOS process, and dissipates 1.2 mW. 1 Introduction Exact gradient-descent algorithms for supervised learning in dynamic recurrent networks [1-3]are fairly complex and do not provide for a scalable implementation in a standard 2-D VLSI process. We have implemented a fairly simple and scalable ·Present address: Johns Hopkins University, ECE Dept., Baltimore MD 21218-2686.

Computational models of the hippocampal-region provide an important method for understanding the functional role of this brain system in learning and memory. The presentations in this workshop focused on how modeling can lead to a unified understanding of the interplay among hippocampal physiology, anatomy, and behavior. One approach can be characterized as "top-down" analyses of the neuropsychology of memory, drawing upon brain-lesion studies in animals and humans. Other models take a "bottom-up" approach, seeking to infer emergent computational and functional properties from detailed analyses of circuit connectivity and physiology (see Gluck & Granger, 1993, for a review). Among the issues discussed were: (1) integration of physiological and behavioral theories of hippocampal function, (2) similarities and differences between animal and human studies, (3) representational vs. temporal properties of hippocampaldependent behaviors,(4) rapid vs. incremental learning, (5) mUltiple vs. unitary memory systems, (5) spatial navigation and memory, and (6) hippocampal interaction with other brain systems.

We show how an "Elman" network architecture, constructed from recurrently connected oscillatory associative memory network modules, canemploy selective "attentional" control of synchronization to direct the flow of communication and computation within the architecture to solve a grammatical inference problem. Previously we have shown how the discrete time "Elman" network algorithm can be implemented in a network completely described by continuous ordinary differential equations. The time steps (machine cycles)of the system are implemented by rhythmic variation (clocking) of a bifurcation parameter. In this architecture, oscillation amplitudecodes the information content or activity of a module (unit), whereas phase and frequency are used to "softwire" the network. Only synchronized modules communicate by exchanging amplitudeinformation; the activity of non-resonating modules contributes incoherent crosstalk noise. Attentional control is modeled as a special subset of the hidden modules with ouputs which affect the resonant frequencies of other hidden modules. They control synchrony among the other modules anddirect the flow of computation (attention) to effect transitions betweentwo subgraphs of a thirteen state automaton which the system emulates to generate a Reber grammar. The internal crosstalk noise is used to drive the required random transitions of the automaton.

In this paper, we will consider the problem of classifying electroencephalogram (EEG)signals of normal subjects, and subjects suffering from psychiatric disorder, e.g., obsessive compulsive disorder, schizophrenia, using a class of artificial neural networks, viz., multi-layer perceptron. It is shown that the multilayer perceptron is capable of classifying unseen test EEG signals to a high degree of accuracy.

We describe the use of smoothing spline analysis of variance (SS ANOVA) in the penalized log likelihood context, for learning (estimating) the probability p of a '1' outcome, given a training setwith attribute vectors and outcomes.

We built a high-speed, digital mean-field Boltzmann chip and SBus board for general problems in constraint satjsfaction and learning. Each chip has 32 neural processors and 4 weight update processors, supporting an arbitrary topology of up to 160 functional neurons. On-chip learning is at a theoretical maximum rate of 3.5 x 108 connection updates/sec;recall is 12000 patterns/sec for typical conditions. The chip's high speed is due to parallel computation of inner products, limited (but adequate) precision for weights and activations (5bits), fast clock (125 MHz), and several design insights.

We consider the problem of how the CNS learns to control dynamics ofa mechanical system. By using a paradigm where a subject's hand interacts with a virtual mechanical environment, we show that learning control is via composition of a model of the imposed dynamics. Some properties of the computational elements with which the CNS composes this model are inferred through the generalization capabilitiesof the subject outside the training data. 1 Introduction At about the age of three months, children become interested in tactile exploration of objects around them. They attempt to reach for an object, but often fail to properly control their arm and end up missing their target. In the ensuing weeks, they rapidly improve and soon they can not only reach accurately, they can also pick up the object and place it.

We study feed-forward nets with arbitrarily many layers, using the standard sigmoid,tanh x. Aside from technicalities, our theorems are: 1. Complete knowledge of the output of a neural net for arbitrary inputs uniquely specifies the architecture, weights and thresholds; and 2. There are only finitely many critical points on the error surface for a generic training problem. Neural nets were originally introduced as highly simplified models of the nervous system. Today they are widely used in technology and studied theoretically by scientists from several disciplines. However, they remain little understood.

Department of Electrical Engineering The University of Maryland College Park, MD 20722 Abstract Recent physiological research has shown that synchronization of oscillatory responses in striate cortex may code for relationships between visual features of objects. A VLSI circuit has been designed toprovide rapid phase-locking synchronization of multiple oscillators to allow for further exploration of this neural mechanism. By exploiting the intrinsic random transistor mismatch of devices operated in subthreshold, large groups of phase-locked oscillators can be readily partitioned into smaller phase-locked groups. A mUltiple target tracker for binary images is described utilizing this phase-locking architecture. A VLSI chip has been fabricated and tested to verify the architecture.