No finite sample is sufficient to determine the density, and therefore the entropy, of a signal directly. Some assumption about either the functional form of the density or about its smoothness is necessary.

We show that for a single neuron with the logistic function as the transfer function the number of local minima of the error function based on the square loss can grow exponentially in the dimension.

In recent years, the interest of investors has shifted to computerized asset allocation (portfolio management) to exploit the growing dynamics of the capital markets. In this paper, asset allocation is formalized as a Markovian Decision Problem which can be optimized by applying dynamic programming or reinforcement learning based algorithms. Using an artificial exchange rate, the asset allocation strategy optimized with reinforcement learning (Q-Learning) is shown to be equivalent to a policy computed by dynamic programming. The approach is then tested on the task to invest liquid capital in the German stock market. Here, neural networks are used as value function approximators. The resulting asset allocation strategy is superior to a heuristic benchmark policy. This is a further example which demonstrates the applicability of neural network based reinforcement learning to a problem setting with a high dimensional state space.

This paper describes a policy iteration algorithm for optimizing the performance of a harmonic function-based controller with respect to a user-defined index. Value functions are represented as potential distributions over the problem domain, being control policies represented as gradient fields over the same domain. All intermediate policies are intrinsically safe, i.e. collisions are not promoted during the adaptation process. The algorithm has efficient implementation in parallel SIMD architectures. One potential application - travel distance minimization - illustrates its usefulness.

A statistical theory for overtraining is proposed. The analysis treats realizable stochastic neural networks, trained with Kullback Leibler loss in the asymptotic case. It is shown that the asymptotic gain in the generalization error is small if we perform early stopping, even if we have access to the optimal stopping time. Considering cross-validation stopping we answer the question: In what ratio the examples should be divided into training and testing sets in order to obtain the optimum performance. In the non-asymptotic region cross-validated early stopping always decreases the generalization error. Our large scale simulations done on a CM5 are in nice agreement with our analytical findings.

When a sensory system constructs a model of the environment from its input, it might need to verify the model's accuracy. One method of verification is multivariate time-series prediction: a good model could predict the near-future activity of its inputs, much as a good scientific theory predicts future data. Such a predicting model would require copious top-down connections to compare the predictions with the input. That feedback could improve the model's performance in two ways: by biasing internal activity toward expected patterns, and by generating specific error signals if the predictions fail. A proof-of-concept model-an event-driven, computationally efficient layered network, incorporating "cortical" features like all-excitatory synapses and local inhibition-was constructed to make near-future predictions of a simple, moving stimulus. After unsupervised learning, the network contained units not only tuned to obvious features of the stimulus like contour orientation and motion, but also to contour discontinuity ("end-stopping") and illusory contours.

A technique for segmenting sounds using processing based on mammalian early auditory processing is presented. The technique is based on features in sound which neuron spike recording suggests are detected in the cochlear nucleus. The sound signal is bandpassed and each signal processed to enhance onsets and offsets. The onset and offset signals are compressed, then clustered both in time and across frequency channels using a network of integrateand-fire neurons. Onsets and offsets are signalled by spikes, and the timing of these spikes used to segment the sound. 1 Background Traditional speech interpretation techniques based on Fourier transforms, spectrum recoding, and a hidden Markov model or neural network interpretation stage have limitations both in continuous speech and in interpreting speech in the presence of noise, and this has led to interest in front ends modelling biological auditory systems for speech interpretation systems (Ainsworth and Meyer 92; Cosi 93; Cole et al 95).

In natural contexts, visual object recognition in humans is remarkably fast, reliable, and viewpoint invariant. The present approach to object recognition is "view-based" (e.g.

Most studies of attention have focused on the selection process of incoming sensory cues (Posner et al., 1980; Koch et al., 1985; Desimone et al., 1995). Emphasis was placed on the phenomena of causing different percepts for the same sensory stimuli. However, the selection of sensory input itself is not the final goal of attention. We consider attention as a means for goal-directed behavior and survival of the animal. In this view, dynamical properties of attention are crucial. While attention has to be maintained long enough to enable robust response to sensory input, it also has to be shifted quickly to a novel cue that is potentially important. Long-term maintenance and quick transition are critical requirements for attention dynamics.

Learning long-term dependencies is not as difficult with NARX recurrent neural networks.