The Self-Organizing Map (SOM) algorithm has been extensively studied and has been applied with considerable success to a wide variety of problems. However, the algorithm is derived from heuristic ideasand this leads to a number of significant limitations. In this paper, we consider the problem of modelling the probability densityof data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. We introduce a novel form of latent variable model, which we call the GTM algorithm (forGenerative Topographic Mapping), which allows general nonlinear transformations from latent space to data space, and which is trained using the EM (expectation-maximization) algorithm. Ourapproach overcomes the limitations of the SOM, while introducing no significant disadvantages. We demonstrate the performance ofthe GTM algorithm on simulated data from flow diagnostics for a multiphase oil pipeline.

In this paper we apply the method of complexity regularization to derive estimationbounds for nonlinear function estimation using a single hidden layer radial basis function network.

Standard recurrent nets cannot deal with long minimal time lags between relevant signals. Several recent NIPS papers propose alternative methods.We first show: problems used to promote various previous algorithms can be solved more quickly by random weight guessing than by the proposed algorithms. We then use LSTM, our own recent algorithm, to solve a hard problem that can neither be quickly solved by random search nor by any other recurrent net algorithm we are aware of. 1 TRIVIAL PREVIOUS LONG TIME LAG PROBLEMS Traditional recurrent nets fail in case'of long minimal time lags between input signals andcorresponding error signals [7, 3]. Many recent papers propose alternative methods, e.g., [16, 12, 1,5,9]. For instance, Bengio et ale investigate methods such as simulated annealing, multi-grid random search, time-weighted pseudo-Newton optimization, and discrete error propagation [3].

Neural Computing Research Group Aston University, Birmingham, B4 7ET, U.K. http://www.ncrg.aston.ac.uk/ Abstract The techniques of Bayesian inference have been applied with great success to many problems in neural computing including evaluation of regression functions, determination of error bars on predictions, and the treatment of hyper-parameters. However, the problem of model comparison is a much more challenging one for which current techniques have significant limitations. In this paper we show how an extended form of Markov chain Monte Carlo, called chaining, is able to provide effective estimates of the relative probabilities of different models. We present results from the robot arm problem and compare them with the corresponding results obtained using the standard Gaussian approximation framework. Initially this is chosen to be some prior distribution p(wIM), which can be combined with a likelihood function p( Dlw, M) using Bayes' theorem to give a posterior distribution p(wID, M) in the form ( ID M) p(Dlw,M)p(wIM) p w, p(DIM) (1) where D is the data set. Predictions of the model are obtained by performing integrations weighted by the posterior distribution.

The optimal control problem reduces to a boundary value problem for a fully nonlinear second-order elliptic differential equation of Hamilton Jacobi-Bellman (HJB-) type. Numerical analysis provides multigrid methodsfor this kind of equation. In the case of Learning Control, however,the systems of equations on the various grid-levels are obtained using observed information (transitions and local cost). To ensure consistency, special attention needs to be directed toward thetype of time and space discretization during the observation. Analgorithm for multi-grid observation is proposed.

Support Vector Learning Machines (SVM) are finding application in pattern recognition, regression estimation, and operator inversion forill-posed problems. Against this very general backdrop, any methods for improving the generalization performance, or for improving the speed in test phase, of SVMs are of increasing interest. Inthis paper we combine two such techniques on a pattern recognition problem. The method for improving generalization performance (the"virtual support vector" method) does so by incorporating known invariances of the problem. This method achieves a drop in the error rate on 10,000 NIST test digit images of 1.4% to 1.0%.

The classes in classification tasks often have a natural ordering, and the training and testing examples are often incomplete. We propose a nonlinear ordinalmodel for classification into ordered classes. Predictive, simulation-based approaches are used to learn from past and classify future incompleteexamples. These techniques are illustrated by making prognoses for patients who have suffered severe head injuries.

We study the effect of noise and regularization in an online gradient-descent learning scenario for a general two-layer student network with an arbitrary number of hidden units. Training examples arerandomly drawn input vectors labeled by a two-layer teacher network with an arbitrary number of hidden units; the examples arecorrupted by Gaussian noise affecting either the output or the model itself. We examine the effect of both types of noise and that of weight-decay regularization on the dynamical evolution ofthe order parameters and the generalization error in various phases of the learning process. 1 Introduction One of the most powerful and commonly used methods for training large layered neural networks is that of online learning, whereby the internal network parameters {J} are modified after the presentation of each training example so as to minimize the corresponding error.

"Emperor AI, Where Is Your New Mind?" The "emperor's new mind" is not here yet, but it is The first two tiers are necessary for developing s AI dead as a science for investigating the Penrose (1989), is the emperor's mind actually an AI theory of the mind simply because without hollow? Should AI be used simply to superficially the right technology, one just could not describe those studies that produce implement such a theory. However, as demonstrated intelligent programs? Several indicators suggest in past AI research and as I argue later, that the answer to these questions might they alone are not sufficient; the machines created be yes.

In adjacent agents from dropping their commitments; (held in Kyoto, Japan, on 10-13 December domains (logical philosophy, social or better, how to regulate 1996). Both the program committee philosophy, decision theory), both legal agents dropping their commitments and the contributors included and social norms have received to a joint action to not disrupt the scientists from different backgrounds considerable, if not satisfactory, attention. The discussion addressed on, has contributed dramatically to These tasks have now entered the several issues: (1) What is the the attention given by the scientific MAS field's common knowledge. Often action is reduced to decision authorization, access regulation, For example, the existence of so-called (that is, a choice among one's privacy maintenance, respect of decency, Georgeff 1991) have shown that we and Tennenholtz 1992). Why? Don't we need a reciprocity.