In recent years many researchers have investigated the use of Markov Random Fields (MRFs) for computer vision. They can be applied for example to reconstruct surfaces from sparse and noisy depth data coming from the output of a visual process, or to integrate early vision processes to label physical discontinuities. In this paper we show that by applying mean field theory to those MRFs models a class of neural networks is obtained. Those networks can speed up the solution for the MRFs models. The method is not restricted to computer vision. 1 Introduction

Decision making tasks that involve delayed consequences are very common yet difficult to address with supervised learning methods. If there is an accurate model of the underlying dynamical system, then these tasks can be formulated as sequential decision problems and solved by Dynamic Programming. This paper discusses reinforcement learning in terms of the sequential decision framework and shows how a learning algorithm similar to the one implemented by the Adaptive Critic Element used in the pole-balancer of Barto, Sutton, and Anderson (1983), and further developed by Sutton (1984), fits into this framework. Adaptive neural networks can play significant roles as modules for approximating the functions required for solving sequential decision problems.

The firing patterns of populations of cells in the cat visual cortex can exhibit oscillatory responses in the range of 35 - 85 Hz. Furthermore, groups of neurons many mm's apart can be highly synchronized as long as the cells have similar orientation tuning. We investigate two basic network architectures that incorporate either nearest-neighbor or global feedback interactions and conclude that non-local feedback plays a fundamental role in the initial synchronization and dynamic stability of the oscillations.

In this paper we describe the VLSI design and testing of a high capacity associative memory which we call the exponential correlation associative memory (ECAM). The prototype 3J.'-CMOS programmable chip is capable of storing 32 memory patterns of 24 bits each. The high capacity of the ECAM is partly due to the use of special exponentiation neurons, which are implemented via sub-threshold MOS transistors in this design. The prototype chip is capable of performing one associative recall in 3 J.'S.

Traditional methods of studying neural coding characterize the encoding of known stimuli in average neural responses. Organisms face nearly the opposite task - decoding short segments of a spike train to extract information about an unknown, time-varying stimulus. Here we present strategies for characterizing the neural code from the point of view of the organism, culminating in algorithms for real-time stimulus reconstruction based on a single sample of the spike train. These methods are applied to the design and analysis of experiments on an identified movement-sensitive neuron in the fly visual system. As far as we know this is the first instance in which a direct "reading" of the neural code has been accomplished.

In this paper, we present a novel implementation of the widely used Back-propagation neural net learning algorithm on the Connection Machine CM-2 - a general purpose, massively parallel computer with a hypercube topology. This implementation runs at about 180 million interconnections per second (IPS) on a 64K processor CM-2. The main interprocessor communication operation used is 2D nearest neighbor communication. The techniques developed here can be easily extended to implement other algorithms for layered neural nets on the CM-2, or on other massively parallel computers which have 2D or higher degree connections among their processors. 1 Introduction High-speed simulation of large artificial neural nets has become an important tool for solving real world problems and for studying the dynamic behavior of large populations of interconnected processing elements [3, 2]. This work is intended to provide such a simulation tool for a widely used neural net learning algorithm - the Back-propagation (BP) algorithm.[7] The hardware we have used is the Connection Machine CM-2.2

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.

We introduce a cost function for learning in feed-forward neural networks which is an explicit function of the internal representation in addition to the weights. The learning problem can then be formulated as two simple perceptrons and a search for internal representations. Back-propagation is recovered as a limit. The frequency of successful solutions is better for this algorithm than for back-propagation when weights and hidden units are updated on the same timescale i.e. once every learning step. 1 INTRODUCTION In their review of back-propagation in layered networks, Rumelhart et al. (1986) describe the learning process in terms of finding good "internal representations" of the input patterns on the hidden units. However, the search for these representations is an indirect one, since the variables which are adjusted in its course are the connection weights, not the activations of the hidden units themselves when specific input patterns are fed into the input layer. Rather, the internal representations are represented implicitly in the connection weight values. More recently, Grossman et al. (1988 and 1989)1 suggested a way in which the search for internal representations could be made much more explicit.

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 midbrain of the barn owl contains a map-like representation of sound source direction which is used to precisely orient the head toward targets of interest. Elevation is computed from the interaural difference in sound level. We present models and computer simulations of two stages of level difference processing which qualitatively agree with known anatomy and physiology, and make several striking predictions. 1 INTRODUCTION