Linsker has reported the development of centre---surround receptive fields and oriented receptive fields in simulations of a Hebb-type equation in a linear network. The dynamics of the learning rule are analysed in terms of the eigenvectors of the covariance matrix of cell activities. Analytic and computational results for Linsker's covariance matrices, and some general theorems, lead to an explanation ofthe emergence of centre---surround and certain oriented structures. Linsker [Linsker, 1986, Linsker, 1988] has studied by simulation the evolution of weight vectors under a Hebb-type teacherless learning rule in a feed-forward linear network. The equation for the evolution of the weight vector w of a single neuron, derived by ensemble averaging the Hebbian rule over the statistics of the input patterns, is:!

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

Data is usually available in the form of a set S consisting of {x,y} pairs, where x is a input vector and y is the corresponding output vector.

Interest in this algorithm waned in the 1970's after it was emphasized[Minsky andPapert, 1969] (1) that the class of problems solvable by a single half space was limited, and (2) that the Perceptron algorithm, although converging infinite time, did not converge in polynomial time. In the 1980's, however, it has become evident that there is no hope of providing a learning algorithm which can learn arbitrary functions in polynomial time and much research has thus been restricted to algorithms which learn a function drawn from a particular class of functions. Moreover, learning theory has focused on protocols like that of [Valiant, 1984] where we seek to classify, not a fixed set of examples, but examples drawn from a probability distribution. This allows a natural notion of "generalization" . There are very few classes which have yet been proven learnable in polynomial time, and one of these is the class of half spaces. Thus there is considerable theoretical interest now in studying the problem of learning a single half space, and so it is natural to reexamine the Percept ron algorithm within the formalism of Valiant. The Perceptron Algorithm Is Fast for Non-Malicious Distributions 677 In Valiant's protocol, a class of functions is called learnable if there is a learning algorithm which works in polynomial time independent of the distribution D generating the examples. Under this definition the Perceptron learning algorithm is not a polynomial time learning algorithm. However we will argue in section 2 that this definition is too restrictive.

In this paper, we discuss a current attempt at applying the organizational principleEdelman calls Neuronal Group Selection to the control of a real, two-link robotic manipulator. We begin by motivating theneed for an alternative to the position-control paradigm of classical robotics, and suggest that a possible avenue is to look at the primitive animal limb'neurologically ballistic' control mode. We have been considering a selectionist approach to coordinating a simple perception-action task. 1 MOTIVATION The majority of industrial robots in the world are mechanical manipUlators - often armlike devices consisting of some number of rigid links with actuators mounted where the links join that move adjacent links relative to each other, rotationally or translation ally. At the joints there are typically also sensors measuring the relative position of adjacent links, and it is in terms of position that manipulators are generally controlled (a desired motion is specified as a desired position of the end effector, from which can be derived the necessary positions of the links comprising the manipulator). Position control dominates largely for historical reasons, rooted in bang-bang control: manipulators bumped between mechanical stops placed so as to enforce a desired trajectory for the end effector.

We present a number of Time-Delay Neural Network (TDNN) based architectures for multi-speaker phoneme recognition (/b,d,g/ task). We use speech of two females and four males to compare the performance of the various architectures against a baseline recognition rate of 95.9% for a single IDNN on the six-speaker /b,d,g/ task.

We outline a computational model of the development and regeneration ofspecific eye-brain circuits. The model comprises a self-organizing map-forming network which uses local Hebb rules.

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 weshow 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

Analog neurons with limited precision essentially compute k-ary weighted multilinear threshold functions.

A central problem in connectionist modelling is the control of network and architectural resources during learning. In the present approach, weights reflect a coarse prediction history as coded by a distribution of values and parameterized in the mean and standard deviation of these weight distributions. Weight updates are a function of both the mean and standard deviation of each connection in the network and vary as a function of the error signal ("stochastic delta rule"; Hanson, 1990). Consequently, the weights maintain information on their central tendency and their "uncertainty" in prediction. Such information is useful in establishing a policy concerning the size of the nodal complexity of the network and growth of new nodes. For example, during problem solving the present network can undergo "meiosis", producing two nodes where there was one "overtaxed" node as measured by its coefficient of variation. It is shown in a number of benchmark problems that meiosis networks can find minimal architectures, reduce computational complexity, and overall increase the efficiency of the representation learning interaction.