Trajectory generation finds interesting applications in the field of robotics, automation, filtering, or time series prediction. Neural networks, with their ability to learn from examples, have been proposed very early on for solving nonlinear control problems adaptively. Several neural net architectures have been proposed for trajectory generation, most notably recurrent networks, either with discrete time and externalloops (Jordan, 1986), or with continuous time (Pearlmutter, 1988). Aside from being recurrent, these networks are not specifically tailored for trajectory generation. It has been shown that specific architectures, such as the Time Delay Neural Networks (Lang and Hinton, 1988), or convolutional networks in general, are better than fully connected networks at recognizing time sequences such as speech (Waibel et al., 1989), or pen trajectories (Guyon et al., 1991). We show that special architectures can also be devised for trajectory generation, with dramatic performance improvement.

A constructive algorithm is proposed for feed-forward neural networks, which uses node-splitting in the hidden layers to build large networks from smaller ones. The small network forms an approximate model of a set of training data, and the split creates a larger more powerful network which is initialised with the approximate solution already found. The insufficiency of the smaller network in modelling the system which generated the data leads to oscillation in those hidden nodes whose weight vectors cover regions in the input space where more detail is required in the model. These nodes are identified and split in two using principal component analysis, allowing the new nodes t.o cover the two main modes of each oscillating vector. Nodes are selected for splitting using principal component analysis on the oscillating weight vectors, or by examining the Hessian matrix of second derivatives of the network error with respect to the weight.s.

Automated monitoring of vigilance in attention intensive tasks such as air traffic control or sonar operation is highly desirable. As the operator monitors the instrument, the instrument would monitor the operator, insuring against lapses. We have taken a first step toward this goal by using feedforward neural networks trained with backpropagation to interpret event related potentials (ERPs) and electroencephalogram (EEG) associated with periods of high and low vigilance. The accuracy of our system on an ERP data set averaged over 28 minutes was 96%, better than the 83% accuracy obtained using linear discriminant analysis. Practical vigilance monitoring will require prediction over shorter time periods. We were able to average the ERP over as little as 2 minutes and still get 90% correct prediction of a vigilance measure. Additionally, we achieved similarly good performance using segments of EEG power spectrum as short as 56 sec.

To test whether the known connectivies of neurons in the lamprey spinal cord are sufficient to account for locomotor rhythmogenesis, a CCconnectionist" neural network simulation was done using identical cells connected according to experimentally established patterns. It was demonstrated that the network oscillates in a stable manner with the same phase relationships among the neurons as observed in the lamprey. The model was then used to explore coupling between identical?scillators. It was concluded that the neurons can have a dual role as rhythm generators and as coordinators between oscillators to produce the phase relations observed among segmental oscillators during swimming.

We present a feed-forward network architecture for recognizing an unconstrained handwritten multi-digit string. This is an extension of previous work on recognizing isolated digits. In this architecture a single digit recognizer is replicated over the input. The output layer of the network is coupled to a Viterbi alignment module that chooses the best interpretation of the input. Training errors are propagated through the Viterbi module.

Recently, high resolution images of the simultaneous representation of orientation preference, orientation selectivity and ocular dominance have been obtained for large areas in monkey striate cortex by optical imaging [1-3]. These data allow for the first time a "local" as well as "global" description of the spatial patterns and provide strong evidence for correlations between orientation selectivity and ocular dominance. A quantitative analysis reveals that these correlations arise when a fivedimensional feature space (two dimensions for retinotopic space, one each for orientation preference, orientation specificity, and ocular dominance) is mapped into the two available dimensions of cortex while locally preserving topology. These results provide strong evidence for the concept of topology preserving maps which have been suggested as a basic design principle of striate cortex [4-7]. Monkey striate cortex contains a retinotopic map in which are embedded the highly repetitive patterns of orientation selectivity and ocular dominance. The retinotopic projection establishes a "global" order, while maps of variables describing other stimulus features, in particular line orientation and ocularity, dominate cortical organization locally. A large number of pattern models [8-12] as well as models of development [6,7,13-21] have been proposed to describe the spatial structure of these patterns and their development during ontogenesis. However, most models have not been compared with experimental data in detail. There are two reasons for this: (i) many model-studies were not elaborated enough to be experimentally testable and (ii) a sufficient amount of experimental data obtained from large areas of striate cortex was not available.

Because eye muscles never cocontract and do not deal with external loads, one can write an equation that relates motoneuron firing rate to eye position and velocity - a very uncommon situation in the CNS. The semicircular canals transduce head velocity in a linear manner by using a high background discharge rate, imparting linearity to the premotor circuits that generate eye movements. This has allowed deducing some of the signal processing involved, including a neural network that integrates. These ideas are often summarized by block diagrams. Unfortunately, they are of little value in describing the behavior of single neurons - a fmding supported by neural network models.

This paper briefly describes an artificial neural network for preattentive visual processing. The network is capable of determiuing image motioll in a type of stimulus which defeats most popular methods of motion detect.ion

In many machine learning applications, one has access, not only to training data, but also to some high-level a priori knowledge about the desired behavior of the system. For example, it is known in advance that the output of a character recognizer should be invariant with respect to small spatial distortions of the input images (translations, rotations, scale changes, etcetera). We have implemented a scheme that allows a network to learn the derivative of its outputs with respect to distortion operators of our choosing. This not only reduces the learning time and the amount of training data, but also provides a powerful language for specifying what generalizations we wish the network to perform. 1 INTRODUCTION In machine learning, one very often knows more about the function to be learned than just the training data. An interesting case is when certain directional derivatives of the desired function are known at certain points.

One method proposed for improving the generalization capability of a feedforward network trained with the backpropagation algorithm is to use artificial training vectors which are obtained by adding noise to the original training vectors. We discuss the connection of such backpropagation training with noise to kernel density and kernel regression estimation. We compare by simulated examples (1) backpropagation, (2) backpropagation with noise, and (3) kernel regression in mapping estimation and pattern classification contexts.