We implement a model of obstacle avoidance in flying insects on a small, monocular robot. The result is a system that is capable of rapid navigation through a dense obstacle field. The key to the system is the use of zigzag behavior to articulate the body during movement. It is shown that this behavior compensates for a parallax blind spot surrounding the focus of expansion normally found in systems without parallax behavior.

Active data clustering is a novel technique for clustering of proximity data which utilizes principles from sequential experiment design in order to interleave data generation and data analysis. The proposed active data sampling strategy is based on the expected value of information, a concept rooting in statistical decision theory. This is considered to be an important step towards the analysis of largescale data sets, because it offers a way to overcome the inherent data sparseness of proximity data.

A simple linear averaging of the outputs of several networks as e.g. in bagging [3], seems to follow naturally from a bias/variance decomposition of the sum-squared error. The sum-squared error of the average model is a quadratic function of the weighting factors assigned to the networks in the ensemble [7], suggesting a quadratic programming algorithm for finding the "optimal" weighting factors. If we interpret the output of a network as a probability statement, the sum-squared error corresponds to minus the loglikelihood or the Kullback-Leibler divergence, and linear averaging of the outputs to logarithmic averaging of the probability statements: the logarithmic opinion pool. The crux of this paper is that this whole story about model averaging, bias/variance decompositions, and quadratic programming to find the optimal weighting factors, is not specific for the sumsquared error, but applies to the combination of probability statements of any kind in a logarithmic opinion pool, as long as the Kullback-Leibler divergence plays the role of the error measure. As examples we treat model averaging for classification models under a cross-entropy error measure and models for estimating variances.

A model of motion detection is presented. The model contains three stages. The first stage is unoriented and is selective for contrast polarities. The next two stages work in parallel. A phase insensitive stage pools across different contrast polarities through a spatiotemporal filter and thus can detect first and second order motion.

A new algorithm is presented which approximates the perceived visual similarity between images. The images are initially transformed into a feature space which captures visual structure, texture and color using a tree of filters. Similarity is the inverse of the distance in this perceptual feature space. Using this algorithm we have constructed an image database system which can perform example based retrieval on large image databases. Using carefully constructed target sets, which limit variation to only a single visual characteristic, retrieval rates are quantitatively compared to those of standard methods. 1 Introduction Without supplementary information, there exists no way to directly measure the similarity between the content of images.

While the understanding of the functional role of different classes of neurons in the awake primary visual cortex has been extensively studied since the time of Hubel and Wiesel (Hubel and Wiesel, 1962), our understanding of the feature selectivity and functional role of neurons in the primary auditory cortex is much farther from complete. Moving bars have long been recognized as an optimal stimulus for many visual cortical neurons, and this finding has recently been confirmed and extended in detail using reverse correlation methods (Jones and Palmer, 1987; Reid and Alonso, 1995; Reid et al., 1991; llingach et al., 1997). In this study, we recorded from neurons in the primary auditory cortex of the awake primate, and used a novel reverse correlation technique to compute receptive fields (or preferred stimuli), encompassing both multiple frequency components and ongoing time. These spectrotemporal receptive fields make clear that neurons in the primary auditory cortex, as in the primary visual cortex, typically show considerable structure in their feature processing properties, often including multiple excitatory and inhibitory regions in their receptive fields. These neurons can be sensitive to stimulus edges in frequency composition or in time, and sensitive to stimulus transitions such as changes in frequency. These neurons also show strong responses and selectivity to continuous frequency modulated stimuli analogous to visual drifting gratings.

Recently researchers have derived formal complexity analysis of analog computation in the setting of discrete-time dynamical systems. As an empirical constrast, training recurrent neural networks (RNNs) produces self -organized systems that are realizations of analog mechanisms. Previous work showed that a RNN can learn to process a simple context-free language (CFL) by counting. Herein, we extend that work to show that a RNN can learn a harder CFL, a simple palindrome, by organizing its resources into a symbol-sensitive counting solution, and we provide a dynamical systems analysis which demonstrates how the network: can not only count, but also copy and store counting infonnation. 1 INTRODUCTION Several researchers have recently derived results in analog computation theory in the setting of discrete-time dynamical systems(Siegelmann, 1994; Maass & Opren, 1997; Moore, 1996; Casey, 1996). For example, a dynamical recognizer (DR) is a discrete-time continuous dynamical system with a given initial starting point and a finite set of Boolean output decision functions(pollack.

Department of Mathematics University of California, San Diego La Jolla, CA 92093-0112 Abstract We propose diffusion networks, a type of recurrent neural network with probabilistic dynamics, as models for learning natural signals that are continuous in time and space. We give a formula for the gradient of the log-likelihood of a path with respect to the drift parameters for a diffusion network. This gradient can be used to optimize diffusion networks in the nonequilibrium regime for a wide variety of problems paralleling techniques which have succeeded in engineering fields such as system identification, state estimation and signal filtering. An aspect of this work which is of particular interest to computational neuroscience and hardware design is that with a suitable choice of activation function, e.g., quasi-linear sigmoidal, the gradient formula is local in space and time. 1 Introduction Many natural signals, like pixel gray-levels, line orientations, object position, velocity and shape parameters, are well described as continuous-time continuous-valued stochastic processes; however, the neural network literature has seldom explored the continuous stochastic case. Since the solutions to many decision theoretic problems of interest are naturally formulated using probability distributions, it is desirable to have a flexible framework for approximating probability distributions on continuous path spaces.

Consistency problems arise if the discretization needs to be refined, e.g. for more accuracy, application of multi-grid iteration or better starting values for the iteration of the approximate optimal value function. In [7] it was shown, that for diffusion dominated problems, a state to time discretization ratio k/ h of Ch'r, I

We derive a first-order approximation of the density of maximum entropy for a continuous 1-D random variable, given a number of simple constraints. This results in a density expansion which is somewhat similar to the classical polynomial density expansions by Gram-Charlier and Edgeworth. Using this approximation of density, an approximation of 1-D differential entropy is derived. The approximation of entropy is both more exact and more robust against outliers than the classical approximation based on the polynomial density expansions, without being computationally more expensive. The approximation has applications, for example, in independent component analysis and projection pursuit. 1 Introduction The basic information-theoretic quantity for continuous one-dimensional random variables is differential entropy. The differential entropy H of a scalar random variable X with density f(x) is defined as H(X) - / f(x) log f(x)dx.