The occurence of chaos in recurrent neural networks is supposed to depend on the architecture and on the synaptic coupling strength. It is studied here for a randomly diluted architecture. By normalizing the variance of synaptic weights, we produce a bifurcation parameter, dependent on this variance and on the slope of the transfer function but independent of the connectivity, that allows a sustained activity and the occurence of chaos when reaching a critical value. Even for weak connectivity and small size, we find numerical results in accordance with the theoretical ones previously established for fully connected infinite sized networks. Moreover the route towards chaos is numerically checked to be a quasi-periodic one, whatever the type of the first bifurcation is (Hopf bifurcation, pitchfork or flip).

These results show how combinatorial structure can be based on the spatial nature of networks, and not just on their emulation of logical structure.

We propose a model of the development of geometric reasoning in children that explicitly involves learning. The model uses a neural network that is initialized with an understanding of geometry similar to that of second-grade children. Through the presentation of a series of examples, the model is shown to develop an understanding of geometry similar to that of fifth-grade children who were trained using similar materials.

We describe two successfully working, analog VLSI vision circuits that move beyond pixel-based early vision algorithms. One circuit, implementing the dynamic wires model, provides for dedicated lines of communication among groups of pixels that share a common property. The chip uses the dynamic wires model to compute the arclength of visual contours. Another circuit labels all points inside a given contour with one voltage and all other with another voltage. Itsbehavior is very robust, since small breaks in contours are automatically sealed, providing for Figure-Ground segregation in a noisy environment. Both chips are implemented using networks of resistors and switches and represent a step towards object level processing since a single voltage value encodes the property of an ensemble of pixels.

Isaac Meilijson EytanRuppin Moshe Sipper School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences Tel Aviv University, 69978 Tel Aviv, Israel Abstract We analyze in detail the performance of a Hamming network classifying inputsthat are distorted versions of one of its m stored memory patterns. The activation function of the memory neurons in the original Hamming network is replaced by a simple threshold function. The THN drastically reduces the time and space complexity of Hamming Network classifiers. 1 Introduction Originally presented in (Steinbuch 1961, Taylor 1964) the Hamming network (HN) has received renewed attention in recent years (Lippmann et. The HN calculates the Hamming distance between the input pattern and each memory pattern, and selects the memory with the smallest distance. It is composed of two subnets: The similarity subnet, consisting of an n-neuron input layer connected with an m-neuron memory layer, calculates the number of equal bits between the input and each memory pattern.

We present the information-theoretic derivation of a learning algorithm that clusters unlabelled data with linear discriminants. In contrast to methods that try to preserve information about the input patterns, we maximize the information gained from observing the output of robust binary discriminators implemented with sigmoid nodes. We deri ve a local weight adaptation rule via gradient ascent in this objective, demonstrate its dynamics on some simple data sets, relate our approach to previous work and suggest directions in which it may be extended.

Vector Quantization is useful for data compression. Competitive Learning whichminimizes reconstruction error is an appropriate algorithm for vector quantization of unlabelled data. Vector quantization of labelled data for classification has a different objective, to minimize the number of misclassifications, and a different algorithm is appropriate. We show that a variant of Kohonen's LVQ2.1 algorithm can be seen as a multiclass extensionof an algorithm which in a restricted 2 class case can be proven to converge to the Bayes optimal classification boundary. We compare the performance of the LVQ2.1 algorithm to that of a modified version having a decreasing window and normalized step size, on a ten class vowel classification problem.

University of Colorado Boulder, CO 80309-0430 Abstract We present a general formulation for a network of stochastic directional units.This formulation is an extension of the Boltzmann machine in which the units are not binary, but take on values in a cyclic range, between 0 and 271' radians. The conditional distribution of a unit's stochastic state is a circular version of the Gaussian probability distribution, known as the von Mises distribution. This combination of a value and a certainty provides additional representational powerin a unit. Many kinds of information can naturally be represented in terms of angular, or directional, variables. A circular range forms a suitable representation for explicitly directional information, such as wind direction, as well as for information where the underlying range is periodic, such as days of the week or months of the year.

Genevieve B. Orr and Todd K. Leen Department of Computer Science and Engineering Oregon Graduate Institute of Science & Technology 19600 N.W. von Neumann Drive Beaverton, OR 97006-1999 Abstract In stochastic learning, weights are random variables whose time evolution is governed by a Markov process. We summarize the theory of the time evolution of P, and give graphical examples of the time evolution that contrast the behavior of stochastic learning with true gradient descent (batch learning). Finally, we use the formalism to obtain predictions of the time required for noise-induced hopping between basins of different optima. We compare the theoretical predictions with simulations of large ensembles of networks for simple problems in supervised and unsupervised learning. Despite the recent application of convergence theorems from stochastic approximation theoryto neural network learning (Oja 1982, White 1989) there remain outstanding questionsabout the search dynamics in stochastic learning.

When m n, we say that the manipulator has redundant degrees--of-freedom (dot). The inverse kinematics problem is the following: given a desired workspace location x, find joint variables 0 such that f(O) x. Even when the forward kinematics is known, 255 256 DeMers and Kreutz-Delgado the inverse kinematics for a manipulator is not generically solvable in closed form (Craig. 1986).