This phenomenon is observed in various areas of the brain both in animal studies and human studies.

I present a theory of mean field approximation based on information geometry. This theory includes in a consistent way the naive mean field approximation, as well as the TAP approach and the linear response theorem in statistical physics, giving clear information-theoretic interpretations to them. 1 INTRODUCTION Many problems of neural networks, such as learning and pattern recognition, can be cast into a framework of statistical estimation problem. How difficult it is to solve a particular problem depends on a statistical model one employs in solving the problem. For Boltzmann machines[ 1] for example, it is computationally very hard to evaluate expectations of state variables from the model parameters. Mean field approximation[2], which is originated in statistical physics, has been frequently used in practical situations in order to circumvent this difficulty.

The W-S (Wake-Sleep) algorithm is a simple learning rule for the models with hidden variables. It is shown that this algorithm can be applied to a factor analysis model which is a linear version of the Helmholtz machine. But even for a factor analysis model, the general convergence is not proved theoretically. In this article, we describe the geometrical understanding of the W-S algorithm in contrast with the EM (Expectation Maximization) algorithm and the em algorithm. As the result, we prove the convergence of the W-S algorithm for the factor analysis model. We also show the condition for the convergence in general models.

We present a method for learning complex appearance mappings.

Determining the relationship between the activity of a single nerve cell to that of an entire population is a fundamental question that bears on the basic neural computation paradigms. In this paper we apply an information theoretic approach to quantify the level of cooperative activity among cells in a behavioral context. It is possible to discriminate between synergetic activity of the cells vs. redundant activity, depending on the difference between the information they provide when measured jointly and the information they provide independently. We define a synergy value that is positive in the first case and negative in the second and show that the synergy value can be measured by detecting the behavioral mode of the animal from simultaneously recorded activity of the cells. We observe that among cortical cells positive synergy can be found, while cells from the basal ganglia, active during the same task, do not exhibit similar synergetic activity.

Classifier systems are now viewed disappointing because of their problems such as the rule strength vs rule set performance problem and the credit assignment problem. In order to solve the problems, we have developed a hybrid classifier system: GLS (Generalization Learning System). In designing GLS, we view CSs as model free learning in POMDPs and take a hybrid approach to finding the best generalization, given the total number of rules. GLS uses the policy improvement procedure by Jaakkola et al. for an locally optimal stochastic policy when a set of rule conditions is given. GLS uses GA to search for the best set of rule conditions. 1 INTRODUCTION Classifier systems (CSs) (Holland 1986) have been among the most used in reinforcement learning.

Since every electrode is in a different position it will measure a different contribution from each of the different neurons. Simply stated, the problem is this: how can these complex signals be untangled to determine when each individual cell fired? This problem is difficult because, a) the objects being classified are very similar and often noisy, b) spikes coming from the same cell can ·Permanent address: Institute of Computer Science and Center for Neural Computation, The Hebrew University, Jerusalem, Israel.

Humans demonstrate a remarkable ability to generate accurate and appropriate motor behavior under many different and oftpn uncprtain environmental conditions. This paper describes a new modular approach to human motor learning and control, baspd on multiple pairs of inverse (controller) and forward (prpdictor) models. This architecture simultaneously learns the multiple inverse models necessary for control as well as how to select the inverse models appropriate for a given em'ironm0nt. Simulations of object manipulation demonstrates the ability to learn mUltiple objects, appropriate generalization to novel objects and the inappropriate activation of motor programs based on visual cues, followed by online correction, seen in the "size-weight illusion".

Humans demonstrate a remarkable ability to generate accurate and appropriate motor behavior under many different and oftpn uncprtain environmental conditions. This paper describes a new modular approach tohuman motor learning and control, baspd on multiple pairs of inverse (controller) and forward (prpdictor) models. This architecture simultaneously learns the multiple inverse models necessary for control as well as how to select the inverse models appropriate for a given em'ironm0nt. Simulationsof object manipulation demonstrates the ability to learn mUltiple objects, appropriate generalization to novel objects and the inappropriate activation of motor programs based on visual cues, followed by online correction, seen in the "size-weight illusion".

The actor and the critic are approximated by Normalized Gaussian Networks (NGnet), which are networks of local linear regression units. The NGnet is trained by the online EM algorithm proposed in our previous paper.We apply our RL method to the task of swinging-up and stabilizing a single pendulum and the task of balancing a double pendulumnear the upright position.