The complexity of cortical circuits may be characterized by the number of synapses per neuron. We study the dependence of complexity on the fraction of the cortical volume that is made up of "wire" (that is, ofaxons and dendrites), and find that complexity is maximized when wire takes up about 60% of the cortical volume. This prediction is in good agreement with experimental observations. A consequence of our arguments is that any rearrangement of neurons that takes more wire would sacrifice computational power.

Function approximation is essential to reinforcement learning, but the standard approach of approximating a value function and determining a policy from it has so far proven theoretically intractable. In this paper we explore an alternative approach in which the policy is explicitly represented by its own function approximator, independent of the value function, and is updated according to the gradient of expected reward with respect to the policy parameters. Williams's REINFORCE method and actor-critic methods are examples of this approach. Our main new result is to show that the gradient can be written in a form suitable for estimation from experience aided by an approximate action-value or advantage function. Using this result, we prove for the first time that a version of policy iteration with arbitrary differentiable function approximation is convergent to a locally optimal policy.

I present a simple variation of importance sampling that explicitly searches for important regions in the target distribution. I prove that the technique yields unbiased estimates, and show empirically it can reduce the variance of standard Monte Carlo estimators. This is achieved by concentrating samples in more significant regions of the sample space. 1 Introduction It is well known that general inference and learning with graphical models is computationally hard [1] and it is therefore necessary to consider restricted architectures [13], or approximate algorithms to perform these tasks [3, 7]. Among the most convenient and successful techniques are stochastic methods which are guaranteed to converge to a correct solution in the limit oflarge samples [10, 11, 12, 15]. These methods can be easily applied to complex inference problems that overwhelm deterministic approaches.

We discuss an information theoretic approach for categorizing and modeling dynamic processes. The approach can learn a compact and informative statistic which summarizes past states to predict future observations. Furthermore, the uncertainty of the prediction is characterized nonparametrically by a joint density over the learned statistic and present observation. We discuss the application of the technique to both noise driven dynamical systems and random processes sampled from a density which is conditioned on the past. In the first case we show results in which both the dynamics of random walk and the statistics of the driving noise are captured. In the second case we present results in which a summarizing statistic is learned on noisy random telegraph waves with differing dependencies on past states. In both cases the algorithm yields a principled approach for discriminating processes with differing dynamics and/or dependencies. The method is grounded in ideas from information theory and nonparametric statistics.

We provide an analysis of the turbo decoding algorithm (TDA) in a setting involving Gaussian densities. In this context, we are able to show that the algorithm converges and that - somewhat surprisingly - though the density generated by the TDA may differ significantly from the desired posterior density, the means of these two densities coincide.

I describe a silicon network consisting of a group of excitatory neurons and a global inhibitory neuron. The output of the inhibitory neuron is normalized with respect to the input strengths.

Visualization of input data and feature selection are intimately related. A good feature selection algorithm can identify meaningful coordinate projections for low dimensional data visualization. Conversely, a good visualization technique can suggest meaningful features to include in a model. Input variable selection is the most important step in the model selection process. Given a target variable, a set of input variables can be selected as explanatory variables by some prior knowledge.

We propose a new approach to the problem of searching a space of stochastic controllers for a Markov decision process (MDP) or a partially observable Markov decision process (POMDP). Following several other authors, our approach is based on searching in parameterized families of policies (for example, via gradient descent) to optimize solution quality. However, rather than trying to estimate the values and derivatives of a policy directly, we do so indirectly using estimates for the probability densities that the policy induces on states at the different points in time. This enables our algorithms to exploit the many techniques for efficient and robust approximate density propagation in stochastic systems. We show how our techniques can be applied both to deterministic propagation schemes (where the MDP's dynamics are given explicitly in compact form,) and to stochastic propagation schemes (where we have access only to a generative model, or simulator, of the MDP).

A system emulating the functionality of a moving eye-hence the name oculomotor system-has been built and successfully tested.

A figure-ground segregation network is proposed based on a novel boundary pair representation. Nodes in the network are boundary segments obtained through local grouping. Each node is excitatorily coupled with the neighboring nodes that belong to the same region, and inhibitorily coupled with the corresponding paired node. Gestalt grouping rules are incorporated by modulating connections. The status of a node represents its probability being figural and is updated according to a differential equation.