We define the concept of polynomial uniform convergence of relative frequencies to probabilities in the distribution-dependent context.

Several parallel analogue algorithms, based upon mean field theory (MFT) approximations to an underlying statistical mechanics formulation, and requiring an externally prescribed annealing schedule, now exist for finding approximate solutions to difficult combinatorial optimisation problems. They have been applied to the Travelling Salesman Problem (TSP), as well as to various issues in computational vision and cluster analysis. I show here that any given MFT algorithm can be combined in a natural way with notions from the areas of constrained optimisation and adaptive simulated annealing to yield a single homogenous and efficient parallel relaxation technique, for which an externally prescribed annealing schedule is no longer required. The results of numerical simulations on 50-city and 100-city TSP problems are presented, which show that the ensuing algorithms are typically an order of magnitude faster than the MFT algorithms alone, and which also show, on occasion, superior solutions as well. 1 INTRODUCTION Several promising parallel analogue algorithms, which can be loosely described by the term "deterministic annealing", or "mean field theory (MFT) annealing", have *also at Theoretical Division and Center for Nonlinear Studies, MSB213, Los Alamos National Laboratory, Los Alamos, NM 87545.

PA 15261 Abstract Five experiments were performed using several neural network architectures to identify the location of a wave in the time ordered graphical results from a medical test. Baseline results from the first experiment found correct identification of the target wave in 85% of cases (n 20). Other experiments investigated the effect of different architectures and preprocessing the raw data on the results. The methods used seem most appropriate for time oriented graphical data which has a clear starting point such as electrophoresis Or spectrometry rather than continuous teSts such as ECGs and EEGs. I INTRODUCTION Complex wave form recognition is generally considered to be a difficult task for machines. Analytical approaches to this problem have been described and they work with reasonable accuracy (Gabriel et al. 1980.

Although the detection of invariant structure in a given set of input patterns is vital to many recognition tasks, connectionist learning rules tend to focus on directions of high variance (principal components). The prediction paradigm is often used to reconcile this dichotomy; here we suggest a more direct approach to invariant learning based on an anti-Hebbian learning rule. An unsupervised tWO-layer network implementing this method in a competitive setting learns to extract coherent depth information from random-dot stereograms. 1 INTRODUCTION: LEARNING INVARIANT STRUCTURE Many connectionist learning algorithms share with principal component analysis (Jolliffe, 1986) the strategy of extracting the directions of highest variance from the input. A single Hebbian neuron, for instance, will come to encode the input's first principal component (Oja and Karhunen, 1985); various forms of lateral interaction can be used to force a layer of such nodes to differentiate and span the principal component subspace - cf. (Sanger, 1989; Kung, 1990; Leen, 1991), and others. The same type of representation also develops in the hidden layer of backpropagation autoassociator networks (Baldi and Hornik, 1989).

Animal locomotion patterns are controlled by recurrent neural networks called central pattern generators (CPGs). Although a CPG can oscillate autonomously, its rhythm and phase must be well coordinated with the state of the physical system using sensory inputs. In this paper we propose a learning algorithm for synchronizing neural and physical oscillators with specific phase relationships. Sensory input connections are modified by the correlation between cellular activities and input signals. Simulations show that the learning rule can be used for setting sensory feedback connections to a CPG as well as coupling connections between CPGs. 1 CENTRAL AND SENSORY MECHANISMS IN LOCOMOTION CONTROL Patterns of animal locomotion, such as walking, swimming, and fiying, are generated by recurrent neural networks that are located in segmental ganglia of invertebrates and spinal cords of vertebrates (Barnes and Gladden, 1985).

We apply this method to the task of controlling the outflow and temperature of a water tank, producing statistically-significant gains in accuracy over both a standard neural network approach and a non-learning PID controller. Furthermore, using the PID knowledge to initialize the weights of the network produces statistically less variation in testset accuracy when compared to networks initialized with small random numbers.

The English alphabet is difficult to recognize automatically because many letters sound alike; e.g., BID, PIT, VIZ and F IS. When spoken over the telephone, the information needed to discriminate among several of these pairs, such as F IS, PIT, BID and VIZ, is further reduced due to the limited bandwidth of the channel Speaker-independent recognition of spelled names over the telephone is difficult due to variability caused by channel distortions, different handsets, and a variety of background noises. Finally, when dealing with a large population of speakers, dialect and foreign accents alter letter pronunciations. An R from a Boston speaker may not contain an [r]. Human classification performance on telephone speech underscores the difficulty of the problem.

We designed and trained a connectionist network to generate letterfonns in a new font given just a few exemplars from that font.

Analog hardware has obvious advantages in terms of its size, speed, cost, and power consumption. Analog chip designers, however, should not feel constrained to mapping existing digital algorithms to silicon. Many times, new algorithms must be adapted or invented to ensure efficient implementation in analog hardware. Novel analog algorithms embedded in the hardware must be simple and obey the natural constraints of physics. Much algorithm intuition can be gained from experimenting with these continuous-time nonlinear systems. For example, the algorithm described in this paper arose from experimentation with existing analog segmentation hardware. Surprisingly, many of these "analog" algorithms may prove useful even if a computer vision researcher is limited to simulating the analog hardware on a digital computer [7].

G/SPLINES is an algorithm for building functional models of data. It uses genetic search to discover combinations of basis functions which are then used to build a least-squares regression model. Because it produces a population of models which evolve over time rather than a single model, it allows analysis not possible with other regression-based approaches. 1 INTRODUCTION G/SPLINES is a hybrid of Friedman's Multivariable Adaptive Regression Splines (MARS) algorithm (Friedman, 1990) with Holland's Genetic Algorithm (Holland, 1975). G/SPLINES has advantages over MARS in that it requires fewer least-squares computations, is easily extendable to non-spline basis functions, may discover models inaccessible to local-variable selection algorithms, and allows significantly larger problems to be considered. These issues are discussed in (Rogers, 1991). This paper begins with a discussion of linear regression models, followed by a description of the G/SPLINES algorithm, and finishes with a series of experiments illustrating its performance, robustness, and analysis capabilities.