Using a statistical mechanical formalism we calculate the evidence, generalisation error and consistency measure for a linear perceptron trainedand 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, nonlinearteacher. A comparison of the hyperparameters which maximise the evidence with those that optimise the performance measuresreveals 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.

This paper studies the problem of diffusion in Markovian models, such as hidden Markov models (HMMs) and how it makes very difficult the task of learning of long-term dependencies in sequences. Using results from Markov chain theory, we show that the problem of diffusion is reduced if the transition probabilities approach 0 or 1. Under this condition, standard HMMs have very limited modeling capabilities, but input/output HMMs can still perform interesting computations.

The parietal cortex is thought to represent the egocentric positions ofobjects in particular coordinate systems. We propose an alternative approach to spatial perception of objects in the parietal cortexfrom the perspective of sensorimotor transformations. The responses of single parietal neurons can be modeled as a gaussian functionof retinal position multiplied by a sigmoid function of eye position, which form a set of basis functions. We show here how these basis functions can be used to generate receptive fields in either retinotopic or head-centered coordinates by simple linear transformations. This raises the possibility that the parietal cortex does not attempt to compute the positions of objects in a particular frameof reference but instead computes a general purpose representation of the retinal location and eye position from which any transformation can be synthesized by direct projection. This representation predicts that hemineglect, a neurological syndrome produced by parietal lesions, should not be confined to egocentric coordinates, but should be observed in multiple frames of reference in single patients, a prediction supported by several experiments.

We present a new method for obtaining local error bars for nonlinear regression, i.e., estimates of the confidence in predicted values that depend onthe input. We approach this problem by applying a maximumlikelihood frameworkto an assumed distribution of errors. We demonstrate our method first on computer-generated data with locally varying, normally distributed target noise. We then apply it to laser data from the Santa Fe Time Series Competition where the underlying system noise is known quantization error and the error bars give local estimates of model misspecification. In both cases, the method also provides a weightedregression effectthat improves generalization performance.

Songbirds learn to imitate a tutor song through auditory and motor learning. Wehave developed a theoretical framework for song learning that accounts for response properties of neurons that have been observed in many of the nuclei that are involved in song learning. Specifically, we suggest that the anteriorforebrain pathway, which is not needed for song production in the adult but is essential for song acquisition, provides synaptic perturbations and adaptive evaluations for syllable vocalization learning. A computer model based on reinforcement learning was constructed thatcould replicate a real zebra finch song with 90% accuracy based on a spectrographic measure.

Increasing attention has been paid to reinforcement learning algorithms inrecent years, partly due to successes in the theoretical analysis of their behavior in Markov environments. If the Markov assumption is removed, however, neither generally the algorithms nor the analyses continue to be usable. We propose and analyze a new learning algorithm to solve a certain class of non-Markov decision problems. Our algorithm applies to problems in which the environment is Markov, but the learner has restricted access to state information. The algorithm involves a Monte-Carlo policy evaluationcombined with a policy improvement method that is similar to that of Markov decision problems and is guaranteed to converge to a local maximum. The algorithm operates in the space of stochastic policies, a space which can yield a policy that performs considerablybetter than any deterministic policy. Although the space of stochastic policies is continuous-even for a discrete action space-our algorithm is computationally tractable.

This system combines a robust input representation, which preserves the dynamic writing information, with a neural network architecture, a so called Multi-State Time Delay Neural Network (MS-TDNN), which integrates rec.ognition and segmentation ina single framework. Our preprocessing transforms the original coordinate sequence into a (still temporal) sequence offeature vectors,which combine strictly local features, like curvature or writing direction, with a bitmap-like representation of the coordinate's proximity.The MS-TDNN architecture is well suited for handling temporal sequences as provided by this input representation. Oursystem is tested both on writer dependent and writer independent tasks with vocabulary sizes ranging from 400 up to 20,000 words. For example, on a 20,000 word vocabulary we achieve word recognition rates up to 88.9% (writer dependent) and 84.1 % (writer independent) without using any language models.

Hinton Dept. of Computer Science University of Toronto Toronto, M5S lA4, Canada Abstract We propose an alternative model for mixtures of experts which uses a different parametric form for the gating network. The modified model is trained by the EM algorithm. In comparison with earlier models-trained by either EM or gradient ascent-there is no need to select a learning stepsize. We report simulation experiments which show that the new architecture yields faster convergence. We also apply the new model to two problem domains: piecewise nonlinear function approximation and the combination of multiple previously trained classifiers. 1 INTRODUCTION For the mixtures of experts architecture (Jacobs, Jordan, Nowlan & Hinton, 1991), the EM algorithm decouples the learning process in a manner that fits well with the modular structure and yields a considerably improved rate of convergence (Jordan & Jacobs, 1994).

Semi-Markov Decision Problems are continuous time generalizations ofdiscrete time Markov Decision Problems. A number of reinforcement learning algorithms have been developed recently for the solution of Markov Decision Problems, based on the ideas of asynchronous dynamic programming and stochastic approximation. Amongthese are TD(,x), Q-Iearning, and Real-time Dynamic Programming. After reviewing semi-Markov Decision Problems and Bellman's optimality equation in that context, we propose algorithms similarto those named above, adapted to the solution of semi-Markov Decision Problems. We demonstrate these algorithms by applying them to the problem of determining the optimal control fora simple queueing system. We conclude with a discussion of circumstances under which these algorithms may be usefully applied. 1 Introduction A number of reinforcement learning algorithms based on the ideas of asynchronous dynamic programming and stochastic approximation have been developed recently for the solution of Markov Decision Problems.

This paper outlines a dynamic theory of development and adaptation inneural networks with feedback connections. Given input ensemble, the connections change in strength according to an associative learning rule and approach a stable state where the neuronal outputs are decorrelated. We apply this theory to primary visualcortex and examine the implications of the dynamical decorrelation of the activities of orientation selective cells by the intracortical connections. The theory gives a unified and quantitative explanationof the psychophysical experiments on orientation contrast and orientation adaptation. Using only one parameter, we achieve good agreements between the theoretical predictions and the experimental data. 1 Introduction The mammalian visual system is very effective in detecting the orientations of lines and most neurons in primary visual cortex selectively respond to oriented lines and form orientation columns [1) . Why is the visual system organized as such? We *Present address: Rockefeller University, B272, 1230 York Avenue, NY, NY 10021-6399.