We present a computationally efficient algorithm for function approximation with piecewise linear sigmoidal nodes. A one hidden layer network is constructed one node at a time using the method of fitting the residual. The task of fitting individual nodes is accomplished using a new algorithm that searchs for the best fit by solving a sequence of Quadratic Programming problems. This approach offers significant advantages over derivative-based search algorithms (e.g.

We first describe a hierarchical, generative model that can be viewed as a nonlinear generalisation of factor analysis and can be implemented in a neural network. The model performs perceptual inference in a probabilistically consistent manner by using top-down, bottom-up and lateral connections. These connections can be learned using simple rules that require only locally available information. We then show how to incorporate lateral connections into the generative model. The model extracts a sparse, distributed, hierarchical representation of depth from simplified random-dot stereograms and the localised disparity detectors in the first hidden layer form a topographic map. When presented with image patches from natural scenes, the model develops topographically organised local feature detectors.

The investigation of neural information structures in music is a rather new, exciting research area bringing together different disciplines such as computer science, mathematics, musicology and cognitive science. One of its aims is to find out what determines the personal style of a composer. It has been shown that neural network models - better than other AI approaches - are able to learn and reproduce styledependent features from given examples, e.g., chorale harmonizations in the style of Johann Sebastian Bach (Hild et al., 1992). However when dealing with melodic sequences, e.g., folksong style melodies, all of these models have considerable difficulties to learn even simple structures. The reason is that they are unable to capture high-order structure such as harmonies, motifs and phrases simultaneously occurring at multiple time scales.

The idea is to calculate differentials by using a relative increment instead of an absolute increment in the parameter space. This idea has been extended to compute the relative Hessian by (Pham, 1996).

In most neural network models, synapses are treated as static weights that change only on the slow time scales of learning. In fact, however, synapses are highly dynamic, and show use-dependent plasticity over a wide range of time scales. Moreover, synaptic transmission is an inherently stochastic process: a spike arriving at a presynaptic terminal triggers release of a vesicle of neurotransmitter from a release site with a probability that can be much less than one. Changes in release probability represent one of the main mechanisms by which synaptic efficacy is modulated in neural circuits. We propose and investigate a simple model for dynamic stochastic synapses that can easily be integrated into common models for neural computation. We show through computer simulations and rigorous theoretical analysis that this model for a dynamic stochastic synapse increases computational power in a nontrivial way. Our results may have implications for the processing of time-varying signals by both biological and artificial neural networks. A synapse 8 carries out computations on spike trains, more precisely on trains of spikes from the presynaptic neuron. Each spike from the presynaptic neuron mayor may not trigger the release of a neurotransmitter-filled vesicle at the synapse.

Severe contamination of electroencephalographic (EEG) activity by eye movements, blinks, muscle, heart and line noise is a serious problem for EEG interpretation and analysis. Rejecting contaminated EEG segments results in a considerable loss of information and may be impractical for clinical data. Many methods have been proposed to remove eye movement and blink artifacts from EEG recordings. Often regression in the time or frequency domain is performed on simultaneous EEG and electrooculographic (EOG) recordings to derive parameters characterizing the appearance and spread of EOG artifacts in the EEG channels. However, EOG records also contain brain signals [1, 2], so regressing out EOG activity inevitably involves subtracting a portion of the relevant EEG signal from each recording as well. Regression cannot be used to remove muscle noise or line noise, since these have no reference channels. Here, we propose a new and generally applicable method for removing a wide variety of artifacts from EEG records. The method is based on an extended version of a previous Independent Component Analysis (lCA) algorithm [3, 4] for performing blind source separation on linear mixtures of independent source signals with either sub-Gaussian or super-Gaussian distributions. Our results show that ICA can effectively detect, separate and remove activity in EEG records from a wide variety of artifactual sources, with results comparing favorably to those obtained using regression-based methods.

The ability to rely on similarity metrics invariant to image transformations is an important issue for image classification tasks such as face or character recognition. We analyze an invariant metric that has performed well for the latter - the tangent distance - and study its limitations when applied to regular images, showing that the most significant among these (convergence to local minima) can be drastically reduced by computing the distance in a multiresolution setting. This leads to the multi resolution tangent distance, which exhibits significantly higher invariance to image transformations, and can be easily combined with robust estimation procedures.

Image intensity variations can result from several different object surface effects, including shading from 3-dimensional relief of the object, or paint on the surface itself. An essential problem in vision, which people solve naturally, is to attribute the proper physical cause, e.g.

Until recently, artificial intelligence researchers have frowned upon the application of probability propagation in Bayesian belief networks that have cycles. The probability propagation algorithm is only exact in networks that are cycle-free. However, it has recently been discovered that the two best error-correcting decoding algorithms are actually performing probability propagation in belief networks with cycles. 1 Communicating over a noisy channel Our increasingly wired world demands efficient methods for communicating bits of information over physical channels that introduce errors. Examples of real-world channels include twisted-pair telephone wires, shielded cable-TV wire, fiberoptic cable, deep-space radio, terrestrial radio, and indoor radio. Engineers attempt to correct the errors introduced by the noise in these channels through the use of channel coding which adds protection to the information source, so that some channel errors can be corrected.

We have studied the application of an independent component analysis (ICA) approach to the identification and possible removal of artifacts from a magnetoencephalographic (MEG) recording.