The long-term goal of our laboratory is the development of analog resistive network-based VLSI implementations of early and intermediate vision algorithms. We demonstrate an experimental circuit for smoothing and segmenting noisy and sparse depth data using the resistive fuse and a 1-D edge-detection circuit for computing zero-crossings using two resistive grids with different spaceconstants. To demonstrate the robustness of our algorithms and of the fabricated analog CMOS VLSI chips, we are mounting these circuits onto small mobile vehicles operating in a real-time, laboratory environment.

The vestibulo-ocular reflex (VOR) is the primary mechanism that controls the compensatory eye movements that stabilize retinal images during rapid head motion. The primary pathways of this system are feed-forward, with inputs from the semicircular canals and outputs to the oculomotor system. Since visual feedback is not used directly in the VOR computation, the system must exploit motor learning to perform correctly. Lisberger(1988) has proposed a model for adapting the VOR gain using image-slip information from the retina. We have designed and tested analog very largescale integrated (VLSI) circuitry that implements a simplified version of Lisberger's adaptive VOR model.

The paper suggests a statistical framework for the parameter estimation problem associated with unsupervised learning in a neural network, leading to an exploratory projection pursuit network that performs feature extraction, or dimensionality reduction.

We have used information-theoretic ideas to derive a class of practical and nearly optimal schemes for adapting the size of a neural network. By removing unimportant weights from a network, several improvements can be expected: better generalization, fewer training examples required, and improved speed of learning and/or classification. The basic idea is to use second-derivative information to make a tradeoff between network complexity and training set error. Experiments confirm the usefulness of the methods on a real-world application. 1 INTRODUCTION Most successful applications of neural network learning to real-world problems have been achieved using highly structured networks of rather large size [for example (Waibel, 1989; Le Cun et al., 1990a)]. As applications become more complex, the networks will presumably become even larger and more structured.

In this paper we compare regression and classification systems. A regression system can generate an output f for an input X, where both X and f are continuous and, perhaps, multidimensional. A classification system can generate an output class, C, for an input X, where X is continuous and multidimensional and C is a member of a finite alphabet. The statistical technique of Classification And Regression Trees (CART) was developed during the years 1973 (Meisel and Michalpoulos) through 1984 (Breiman el al).

A new concept for unsupervised learning based upon examples introduced to the neural network is proposed. Each example is considered as an interpolation node of the velocity field in the phase space. The velocities at these nodes are selected such that all the streamlines converge to an attracting set imbedded in the subspace occupied by the cluster of examples. The synaptic interconnections are found from learning procedure providing selected field. The theory is illustrated by examples. This paper is devoted to development of a new concept for unsupervised learning based upon examples introduced to an artificial neural network.

A methodology for faster supervised learning in dynamical nonlinear neural networks is presented. It exploits the concept of adjoint operntors to enable computation of changes in the network's response due to perturbations in all system parameters, using the solution of a single set of appropriately constructed linear equations. The lower bound on speedup per learning iteration over conventional methods for calculating the neuromorphic energy gradient is O(N2), where N is the number of neurons in the network. 1 INTRODUCTION The biggest promise of artifcial neural networks as computational tools lies in the hope that they will enable fast processing and synthesis of complex information patterns. In particular, considerable efforts have recently been devoted to the formulation of efficent methodologies for learning (e.g., Rumelhart et al., 1986; Pineda, 1988; Pearlmutter, 1989; Williams and Zipser, 1989; Barhen, Gulati and Zak, 1989). The development of learning algorithms is generally based upon the minimization of a neuromorphic energy function. The fundamental requirement of such an approach is the computation of the gradient of this objective function with respect to the various parameters of the neural architecture, e.g., synaptic weights, neural Adjoint Operator Algorithms 499

The computational territory between the linearly summing McCulloch-Pitts neuron and the nonlinear differential equations of Hodgkin & Huxley is relatively sparsely populated. Connectionists use variants of the former and computational neuroscientists struggle with the exploding parameter spaces provided by the latter. However, evidence from biophysical simulations suggests that the voltage transfer properties of synapses, spines and dendritic membranes involve many detailed nonlinear interactions, not just a squashing function at the cell body. Real neurons may indeed be higher-order nets. For the computationally-minded, higher order interactions means, first of all, quadratic terms. This contribution presents a simple learning principle for a binary tree with a logistic/quadratic transfer function at each node. These functions, though highly nested, are shown to be capable of changing their shape in concert. The resulting tree structure receives inputs at its leaves, and outputs an estimate of the probability that the input pattern is a member of one of two classes at the top.

The goal in this work has been to identify the neuronal elements of the cortical column that are most likely to support the learning of nonlinear associative maps. We show that a particular style of network learning algorithm based on locally-tuned receptive fields maps naturally onto cortical hardware, and gives coherence to a variety of features of cortical anatomy, physiology, and biophysics whose relations to learning remain poorly understood.

Kanerva's sparse distributed memory (SDM) is an associative-memory model based on the mathematical properties of high-dimensional binary address spaces. Holland's genetic algorithms are a search technique for high-dimensional spaces inspired by evolutionary processes of DNA. "Genetic Memory" is a hybrid of the above two systems, in which the memory uses a genetic algorithm to dynamically reconfigure its physical storage locations to reflect correlations between the stored addresses and data. For example, when presented with raw weather station data, the Genetic Memory discovers specific features in the weather data which correlate well with upcoming rain, and reconfigures the memory to utilize this information effectively. This architecture is designed to maximize the ability of the system to scale-up to handle real-world problems.