A new model for chemosensory reception is presented.

Although artificial neural networks have been applied in a variety of real-world scenarios with remarkable success, they have often been criticized for exhibiting a low degree of human comprehensibility. Techniques that compile compact sets of symbolic rules out of artificial neural networks offer a promising perspective to overcome this obvious deficiency of neural network representations. This paper presents an approach to the extraction of if-then rules from artificial neural networks. Its key mechanism is validity interval analysis, which is a generic tool for extracting symbolic knowledge by propagating rule-like knowledge through Backpropagation-style neural networks. Empirical studies in a robot arm domain illustrate the appropriateness of the proposed method for extracting rules from networks with real-valued and distributed representations.

Using a statistical mechanical formalism we calculate the evidence, generalisation error and consistency measure for a linear perceptron trained and tested on a set of examples generated by a non linear teacher. The teacher is said to be unrealisable because the student can never model it without error. Our model allows us to interpolate between the known case of a linear teacher, and an unrealisable, nonlinear teacher. A comparison of the hyperparameters which maximise the evidence with those that optimise the performance measures reveals that, in the nonlinear case, the evidence procedure is a misleading guide to optimising performance. Finally, we explore the extent to which the evidence procedure is unreliable and find that, despite being sub-optimal, in some circumstances it might be a useful method for fixing the hyperparameters. 1 INTRODUCTION The analysis of supervised learning or learning from examples is a major field of research within neural networks.

We present a new algorithm for finding low complexity networks with high generalization capability. The algorithm searches for large connected regions of so-called ''fiat'' minima of the error function. In the weight-space environment of a "flat" minimum, the error remains approximately constant. Using an MDL-based argument, flat minima can be shown to correspond to low expected overfitting. Although our algorithm requires the computation of second order derivatives, it has backprop's order of complexity. Experiments with feedforward and recurrent nets are described. In an application to stock market prediction, the method outperforms conventional backprop, weight decay, and "optimal brain surgeon".

A neural network learning paradigm based on information theory is proposed as a way to perform in an unsupervised fashion, redundancy reduction among the elements of the output layer without loss of information from the sensory input. The model developed performs nonlinear decorrelation up to higher orders of the cumulant tensors and results in probabilistic ally independent components of the output layer. This means that we don't need to assume Gaussian distribution neither at the input nor at the output. The theory presented is related to the unsupervised-learning theory of Barlow, which proposes redundancy reduction as the goal of cognition. When nonlinear units are used nonlinear principal component analysis is obtained.

Multi-class classification problems can be efficiently solved by partitioning the original problem into sub-problems involving only two classes: for each pair of classes, a (potentially small) neural network is trained using only the data of these two classes. We show how to combine the outputs of the two-class neural networks in order to obtain posterior probabilities for the class decisions. The resulting probabilistic pairwise classifier is part of a handwriting recognition system which is currently applied to check reading. We present results on real world data bases and show that, from a practical point of view, these results compare favorably to other neural network approaches.

Dynamic Cell Structures (DCS) represent a family of artificial neural architectures suited both for unsupervised and supervised learning. They belong to the recently [Martinetz94] introduced class of Topology Representing Networks (TRN) which build perlectly topology preserving feature maps. DCS empI'oy a modified Kohonen learning rule in conjunction with competitive Hebbian learning. The Kohonen type learning rule serves to adjust the synaptic weight vectors while Hebbian learning establishes a dynamic lateral connection structure between the units reflecting the topology of the feature manifold. In case of supervised learning, i.e. function approximation, each neural unit implements a Radial Basis Function, and an additional layer of linear output units adjusts according to a delta-rule. DCS is the first RBF-based approximation scheme attempting to concurrently learn and utilize a perfectly topology preserving map for improved performance. Simulations on a selection of CMU-Benchmarks indicate that the DCS idea applied to the Growing Cell Structure algorithm [Fritzke93] leads to an efficient and elegant algorithm that can beat conventional models on similar tasks.

We investigate the computational power of a formal model for networks ofspiking neurons, both for the assumption of an unlimited timing precision, and for the case of a limited timing precision. We also prove upper and lower bounds for the number of examples that are needed to train such networks.

Volker Tresp*and Michiaki Taniguchi Siemens AG, Central Research Otto-Hahn-Ring 6 81730 Miinchen, Germany Abstract This paper discusses the linearly weighted combination of estimators inwhich the weighting functions are dependent on the input. We show that the weighting functions can be derived either by evaluating the input dependent variance of each estimator or by estimating how likely it is that a given estimator has seen data in the region of the input space close to the input pattern. The latter solutionis closely related to the mixture of experts approach and we show how learning rules for the mixture of experts can be derived from the theory about learning with missing features. The presented approaches are modular since the weighting functions can easily be modified (no retraining) if more estimators are added. Furthermore,it is easy to incorporate estimators which were not derived from data such as expert systems or algorithms. 1 Introduction Instead of modeling the global dependency between input x E D and output y E using a single estimator, it is often very useful to decompose a complex mapping -'\.t the time of the research for this paper, a visiting researcher at the Center for Biological and Computational Learning, MIT.

The paper presents a rapid speaker-normalization technique based on neural network spectral mapping. The neural network is used as a front-end of a continuous speech recognition system (speakerdependent, HMM-based)to normalize the input acoustic data from a new speaker. The spectral difference between speakers can be reduced using a limited amount of new acoustic data (40 phonetically richsentences). Recognition error of phone units from the acoustic-phonetic continuous speech corpus APASCI is decreased with an adaptability ratio of 25%. We used local basis networks of elliptical Gaussian kernels, with recursive allocation of units and online optimization of parameters (GRAN model). For this application, themodel included a linear term. The results compare favorably with multivariate linear mapping based on constrained orthonormal transformations.