It is widely accepted that the use of more compact representations than lookup tables is crucial to scaling reinforcement learning (RL) algorithms to real-world problems. Unfortunately almost all of the theory of reinforcement learning assumes lookup table representations. In this paper we address the pressing issue of combining function approximation and RL, and present 1) a function approximator based on a simple extension to state aggregation (a commonly used form of compact representation), namely soft state aggregation, 2) a theory of convergence for RL with arbitrary, but fixed, soft state aggregation, 3) a novel intuitive understanding of the effect of state aggregation on online RL, and 4) a new heuristic adaptive state aggregation algorithm that finds improved compact representations by exploiting the non-discrete nature of soft state aggregation. Preliminary empirical results are also presented.

Our results show that maximal diversity of neuronal response properties is attained when the ratio of dendritic and axonal arbor sizes is equal to 1, a value found in many cortical areas and across species (Lund et al., 1993; Malach, 1994). Maximization of diversity also leads to better performance in systems of receptive fields implementing steerablejshiftable filters, which may be necessary for generating the seemingly continuous range of orientation selectivity found in VI, and in ma.tching spatially distributed signals. This cortical organization principle may, therefore, have the double advantage of accounting for the formation of the cortical columns and the associated patchy projection patterns, and of explaining how systems of receptive fields can support functions such as the generation of precise response tuning from imprecise distributed inputs, and the matching of distributed signals, a problem that arises in visual tasks such as stereopsis, motion processing, and recognition.

We prove the convergence of an actor/critic algorithm that is equivalent to Q-Iearning by construction. Its equivalence is achieved by encoding Q-values within the policy and value function of the actor and critic. The resultant actor/critic algorithm is novel in two ways: it updates the critic only when the most probable action is executed from any given state, and it rewards the actor using criteria that depend on the relative probability of the action that was executed.

We investigate the computational power of a formal model for networks of spiking neurons, both for the assumption of an unlimited timing precision, and for the case of a limited timing precision. We also prove upper and lower bounds for the number of examples that are needed to train such networks.

Understanding knowledge representations in neural nets has been a difficult problem. Principal components analysis (PCA) of contributions (products of sending activations and connection weights) has yielded valuable insights into knowledge representations, but much of this work has focused on the correlation matrix of contributions. The present work shows that analyzing the variance-covariance matrix of contributions yields more valid insights by taking account of weights.

K-Means is a popular clustering algorithm used in many applications, including the initialization of more computationally expensive algorithms (Gaussian mixtures, Radial Basis Functions, Learning Vector Quantization and some Hidden Markov Models). The practice of this initialization procedure often gives the frustrating feeling that K-Means performs most of the task in a small fraction of the overall time. This motivated us to better understand this convergence speed. A second reason lies in the traditional debate between hard threshold (e.g.

We introduce and study methods of inserting synaptic noise into dynamically-driven recurrent neural networks and show that applying a controlled amount of noise during training may improve convergence and generalization. In addition, we analyze the effects of each noise parameter (additive vs. multiplicative, cumulative vs. non-cumulative, per time step vs. per string) and predict that best overall performance can be achieved by injecting additive noise at each time step. Extensive simulations on learning the dual parity grammar from temporal strings substantiate these predictions.

Such sensors realize the simultaneous need for wide field-of-view and good visual acuity. One popular class of space-variant sensors is formed by log-polar sensors which have a small area near the optical axis of greatly increased resolution (the fovea) coupled with a peripheral region that witnesses a gradual logarithmic falloff in resolution as one moves radially outward. These sensors are inspired by similar structures found in the primate retina where one finds both a peripheral region of gradually decreasing acuity and a circularly symmetric area centmlis characterized by a greater density of receptors and a disproportionate representation in the optic nerve [3]. The peripheral region, though of low visual acuity, is more sensitive to light intensity and movement. The existence of a region optimized for discrimination and recognition surrounded by a region geared towards detection thus allows the image of an object of interest detected in the outer region to be placed on the more analytic center for closer scrutiny. Such a strategy however necessitates the existence of (a) methods to determine which location in the periphery to foveate next, and (b) fast gaze-shifting mechanisms to achieve this 894 Rajesh P. N. Rao, Dana H. Ballard

In supervised learning, learning from queries rather than from random examples can improve generalization performance significantly. We study the performance of query learning for problems where the student cannot learn the teacher perfectly, which occur frequently in practice. As a prototypical scenario of this kind, we consider a linear perceptron student learning a binary perceptron teacher. Two kinds of queries for maximum information gain, i.e., minimum entropy, are investigated: Minimum student space entropy (MSSE) queries, which are appropriate if the teacher space is unknown, and minimum teacher space entropy (MTSE) queries, which can be used if the teacher space is assumed to be known, but a student of a simpler form has deliberately been chosen. We find that for MSSE queries, the structure of the student space determines the efficacy of query learning, whereas MTSE queries lead to a higher generalization error than random examples, due to a lack of feedback about the progress of the student in the way queries are selected.

We study the asymptotic properties of the sequence of iterates of weight-vector estimates obtained by training a multilayer feed forward neural network with a basic gradient-descent method using a fixed learning constant and no batch-processing. In the onedimensional case, an exact analysis establishes the existence of a limiting distribution that is not Gaussian in general. For the general case and small learning constant, a linearization approximation permits the application of results from the theory of random matrices to again establish the existence of a limiting distribution. We study the first few moments of this distribution to compare and contrast the results of our analysis with those of techniques of stochastic approximation. 1 INTRODUCTION The wide applicability of neural networks to problems in pattern classification and signal processing has been due to the development of efficient gradient-descent algorithms for the supervised training of multilayer feedforward neural networks with differentiable node functions. A basic version uses a fixed learning constant and updates all weights after each training input is presented (online mode) rather than after the entire training set has been presented (batch mode). The properties of this algorithm as exhibited by the sequence of iterates are not yet well-understood. There are at present two major approaches.