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 to the integrated learning functions and the generation of pseudo-random perturbations, the chip provides for teacher forcing and long-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 m W. 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.

The assumption is that there exists an underlying (possibly noisy) functional relationship relating the outputs to the inputs y /(u,e) where e denotes the noise. The aim of the learning process is to approximate this relationship based on the the training set.

The task of drug activity prediction is to predict the activity of proposed drug compounds by learning from the observed activity of previously-synthesized drug compounds. Accurate drug activity prediction can save substantial time and money by focusing the efforts of chemists and biologists on the synthesis and testing of compounds whose predicted activity is high. If the requirements for highly active binding can be displayed in three dimensions, chemists can work from such displays to design new compounds having high predicted activity. Drug molecules usually act by binding to localized sites on large receptor molecules or large enyzme molecules. One reasonable way to represent drug molecules is to capture the location of their surface in the (fixed) frame of reference of the (hypothesized) binding site.

Data clustering amounts to a combinatorial optimization problem to reduce the complexity of a data representation and to increase its precision. Central and pairwise data clustering are studied in the maximum entropy framework. For central clustering we derive a set of reestimation equations and a minimization procedure which yields an optimal number of clusters, their centers and their cluster probabilities. A meanfield approximation for pairwise clustering is used to estimate assignment probabilities. A se1fconsistent solution to multidimensional scaling and pairwise clustering is derived which yields an optimal embedding and clustering of data points in a d-dimensional Euclidian space. 1 Introduction A central problem in information processing is the reduction of the data complexity with minimal loss in precision to discard noise and to reveal basic structure of data sets. Data clustering addresses this tradeoff by optimizing a cost function which preserves the original data as complete as possible and which simultaneously favors prototypes with minimal complexity (Linde et aI., 1980; Gray, 1984; Chou et aI., 1989; Rose et ai., 1990). We discuss an objective function for the joint optimization of distortion errors and the complexity of a reduced data representation. A maximum entropy estimation of the cluster assignments yields a unifying framework for clustering algorithms with a number of different distortion and complexity measures. The close analogy of complexity optimized clustering with winner-take-all neural networks suggests a neural-like implementation resembling topological feature maps (see Figure 1).

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 potential trajectories as targets, the parameters (maximal conductances, thresholds and slopes of activation curves, time constants) were successfully 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.

Feed-forward networks of localized (e.g., Gaussian) units are an interesting alternative to the more frequently used networks of global (e.g., sigmoidal) units. It has been shown that with localized units one hidden layer suffices in principle to approximate any continuous function, whereas with sigmoidal units two layers are necessary. In the following we are considering radial basis function networks similar to those proposed by Moody & Darken (1989) or Poggio & Girosi (1990). Such networks consist of one layer L of Gaussian units.

Most connectionist research has focused on learning mappings from one space to another (eg.

This paper presents a formulation for unsupervised learning of clusters reflecting multiple causal structure in binary data. Unlike the standard mixture model, a multiple cause model accounts for observed data by combining assertions from many hidden causes, each of which can pertain to varying degree to any subset of the observable dimensions. A crucial issue is the mixing-function for combining beliefs from different cluster-centers in order to generate data reconstructions whose errors are minimized both during recognition and learning. We demonstrate a weakness inherent to the popular weighted sum followed by sigmoid squashing, and offer an alternative form of the nonlinearity. Results are presented demonstrating the algorithm's ability successfully to discover coherent multiple causal representat.ions of noisy test data and in images of printed characters. 1 Introduction The objective of unsupervised learning is to identify patterns or features reflecting underlying regularities in data. Single-cause techniques, including the k-means algorithm and the standard mixture-model (Duda and Hart, 1973), represent clusters of data points sharing similar patterns of Is and Os under the assumption that each data point belongs to, or was generated by, one and only one cluster-center; output activity is constrained to sum to 1. In contrast, a multiple-cause model permits more than one cluster-center to become fully active in accounting for an observed data vector.

Several recurrent networks have been proposed as representations for the task of formal language learning. After training a recurrent network recognize a formal language or predict the next symbol of a sequence, the next logical step is to understand the information processing carried out by the network. Some researchers have begun to extracting finite state machines from the internal state trajectories of their recurrent networks. This paper describes how sensitivity to initial conditions and discrete measurements can trick these extraction methods to return illusory finite state descriptions.

We show how an "Elman" network architecture, constructed from recurrently connected oscillatory associative memory network modules, can employ 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 amplitude codes 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 amplitude information; 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 and direct the flow of computation (attention) to effect transitions between two 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.