However, learning simple behavior can be quite "Also with NEC Research Institute.

Several regions of the rat brain contain neurons known as head-direction celis,which encode the animal's directional heading during spatial navigation. This paper presents a biophysical model of head-direction cell acti vity, which suggests that a thalamocortical circuit might compute therat's head direction by integrating the angular velocity of the head over time. The model was implemented using the neural simulator NEURON, and makes testable predictions about the structure and function ofthe rat head-direction circuit.

A neural network model of 3-D lightness perception is presented which builds upon the FACADE Theory Boundary Contour System/Feature ContourSystem of Grossberg and colleagues. Early ratio encoding by retinal ganglion neurons as well as psychophysical resultson constancy across different backgrounds (background constancy) are used to provide functional constraints to the theory and suggest a contrast negation hypothesis which states that ratio measures between coplanar regions are given more weight in the determination of lightness of the respective regions.

Ralph Neuneier* Siemens AG, Corporate Research and Development Otto-Hahn-Ring 6, D-81730 Munchen, Germany Abstract In recent years, the interest of investors has shifted to computerized assetallocation (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 byapplying dynamic programming or reinforcement learning based algorithms. Using an artificial exchange rate, the asset allocation strategyoptimized with reinforcement learning (Q-Learning) is shown to be equivalent to a policy computed by dynamic programming. Theapproach is then tested on the task to invest liquid capital in the German stock market. Here, neural networks are used as value function approximators.

We introduce a constructive, incremental learning system for regression problems that models data by means of locally linear experts. In contrast to other approaches, the experts are trained independently and do not compete for data during learning. Only when a prediction for a query is required do the experts cooperate by blending their individual predictions. Eachexpert is trained by minimizing a penalized local cross validation errorusing second order methods. In this way, an expert is able to find a local distance metric by adjusting the size and shape of the receptive fieldin which its predictions are valid, and also to detect relevant input features by adjusting its bias on the importance of individual input dimensions. We derive asymptotic results for our method. In a variety of simulations the properties of the algorithm are demonstrated with respect to interference, learning speed, prediction accuracy, feature detection, and task oriented incremental learning.

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.

In the past years the unsupervised learning schemes arose strong interest among researchers but for the time being a little is known about underlying learning mechanisms, aswell as still less rigorous results like convergence theorems were obtained in this field. One of promising concepts along this line is so called "unlearning" for the Hopfield-type neural networks (Hopfield et ai, 1983, van Hemmen & Klemmer, 1992,Wimbauer et ai, 1994). Elaborating that elegant ideas the convergent unlearning algorithm has recently been proposed (Plakhov & Semenov, 1994), executing withoutpatterns presentation. It is aimed at to correct initial Hebbian connectivity in order to provide extensive storage of arbitrary correlated data. This algorithm is stated as follows. Pick up at iteration step m, m 0,1,2, ... a random network state s(m)

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 data. Such a predictingas a good scientific theory predicts future to comparemodel would require copious top-down connections the input. That feedback could improve thethe predictions with 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.

A linear threshold element computes a function that is a sign of a weighted sum of the input variables. The weights are arbitrary integers; actually, they can be very big integers-exponential in the number of the input variables. However, in practice, it is difficult to implement big weights. In the present literature a distinction is made between the two extreme cases: linear threshold functions with polynomial-size weights as opposed to those with exponential-size weights. The main contribution of this paper is to fill up the gap by further refining that separation.

This paper presents two methods that can improve generalization on a broad class of problems. This class includes identifying low risk pneumonia patients. The first method, rankprop, tries to learn simple models that support ranking future cases while simultaneously learning to rank the training set. The second, multitask learning, uses lab tests available only during training, as additional target values to bias learning towards a more predictive hidden layer. Experiments using a database of pneumonia patients indicate that together these methods outperform standard backpropagation by 10-50%. Rankprop and MTL are applicable to a large class of problems in which the goal is to learn a relative ranking over the instance space, and where the training data includes features that will not be available at run time. Such problems include identifying higher-risk medical patients as early as possible, identifying lower-risk financial investments, and visual analysis of scenes that become easier to analyze as they are approached in the future. Acknowledgements We thank Greg Cooper, Michael Fine, and other members of the Pitt/CMU Cost-Effective Health Care group for help with the Medis Database. This work was supported by ARPA grant F33615-93-1-1330, NSF grant BES-9315428, Agency for Health Care Policy and Research grant HS06468, and an NSF Graduate Student Fellowship (Baluja).