We present a tree-structured architecture for supervised learning. The statistical model underlying the architecture is a hi-erarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models (GLIM’s). Learning is treated as a max-imum likelihood problem; in particular, we present an Expectation-Maximization (EM) algorithm for adjusting the parame-ters of the architecture. We also develop an on-line learning algorithm in which the pa-rameters are updated incrementally. Com-parative simulation results are presented in the robot dynamics domain. 1

This paper examines whether temporal difference methods for training connectionist networks, such as Suttons's TD(lambda) algorithm can be successfully applied to complex real-world problems. A number of important practical issues are identified and discussed from a general theoretical perspective. These practical issues are then examined in the context of a case study in which TD(lambda) is applied to learning the game of backgammon from the outcome of self-play. This is apparently the first application of this algorithm to a complex nontrivial task. It is found that, with zero knowledge built in, the network is able to learn from scratch to play the entire game at a fairly strong intermediate level of performance which is clearly better than conventional commercial programs and which in fact surpasses comparable networks trained on a massive human expert data set. This indicates that TD learning may work better in practice than one would expect based on current theory, and it suggests that further analysis of TD methods, as well as applications in other complex domains may be worth investigating.

A long-standing difficulty for connectionist modeling has been how to represent variable-sized recursive data structures, such as trees and lists, in fixed-width patterns. This paper presents a connectionist architecture which automatically develops compact distributed representations for such compositional structures, as well as efficient accessing mechanisms for them. Patterns which stand for the internal nodes of fixed-valence trees are devised through the recursive use of back-propagation on three-layer autoassociative encoder networks. The resulting representations are novel, in that they combine apparently immiscible aspects of features, pointers, and symbol structures. They form a bridge between the data structures necessary for high-level cognitive tasks and the associative, pattern recognition machinery provided by neural networks. 2 J. B. Pollack 1. Introduction One of the major stumbling blocks in the application of Connectionism to higherlevel cognitive tasks, such as Na...

We had previously shown that regularization principles lead to approximation schemes which are equivalent to networks with one layer of hidden units, called Regularization Networks. In particular, standard smoothness functionals lead to a subclass of regularization networks, the well known Radial Basis Functions approximation schemes. This paper shows that regularization networks encompass a much broader range of approximation schemes, including many of the popular general additive models and some of the neural networks. In particular, we introduce new classes of smoothness functionals that lead to different classes of basis functions. Additive splines as well as some tensor product splines can be obtained from appropriate classes of smoothness functionals. Furthermore, the same generalization that extends Radial Basis Functions (RBF) to Hyper Basis Functions (HBF) also leads from additive models to ridge approximation models, containing as special cases Breiman's hinge functions, som...

A higher order recurrent neural network architecture learns to recognize and generate languages after being "trained " on categorized exemplars. Studying these networks from the perspective of dynamical systems yields two interesting discoveries: First, a longitudinal examination of the learning process illustrates a new form of mechanical inference: Induction by phase transition. A small weight adjustment causes a "bifurcation" in the limit behavior of the network. This phase transition corresponds to the onset of the network’s capacity for generalizing to arbitrary-length strings. Second, a study of the automata resulting from the acquisition of previously published training sets indicates that while the architecture is not guaranteed to find a minimal finite automaton consistent with the given exemplars, which is an NP-Hard problem, the architecture does appear capable of generating non-regular languages by exploiting fractal and chaotic dynamics. I end the paper with a hypothesis relating linguistic generative capacity to the behavioral regimes of non-linear dynamical systems.

A novel modular connectionist architecture is presented in which the networks composing the architecture compete to learn the training patterns. As a result of the competition, different networks learn different training patterns and, thus, learn to compute different functions. The architecture performs task decomposition in the sense that it learns to partition a task into two or more functionally independent vii tasks and allocates distinct networks to learn each task. In addition, the architecture tends to allocate to each task the network whose topology is most appropriate to that task, and tends to allocate the same network to similar tasks and distinct networks to dissimilar tasks. Furthermore, it can be easily modified so as to...

A direct adaptive tracking control architecture is proposed and evaluated for a class of continuous -time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible. The architecture employs a network of gaussian radial basis functions to adaptively compensate for the plant nonlinearities. Under mild assumptions about the degree of smoothness exhibited by the nonlinear functions, the algorithm is proven to be globally stable, with tracking errors converging to a neighborhood of zero. A constructive procedure is detailed, which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy. A stable weight adjustment mechanism is then determined using Lyapunov theory. The network construction and performance of the resulting controller are illustrated through simulations with example syst...

. To operate successfully in indoor environments, mobile robots must be able to localize themselves. Most current localization algorithms lack flexibility, autonomy, and often optimality, since they rely on a human to determine what aspects of the sensor data to use in localization (e.g., what landmarks to use). This paper describes a learning algorithm, called BaLL, that enables mobile robots to learn what features/landmarks are best suited for localization, and also to train artificial neural networks for extracting them from the sensor data. A rigorous Bayesian analysis of probabilistic localization is presented, which produces a rational argument for evaluating features, for selecting them optimally, and for training the networks that approximate the optimal solution. In a systematic experimental study, BaLL outperforms two other recent approaches to mobile robot localization. Keywords: artificial neural networks, Bayesian analysis, feature extraction, landmarks, localization, mobi...

Quartz, S. & Sejnowski, T.J. (1997). The neural basis of cognitive development: A constructivist manifesto.

Several researchers characterized the activation fimction under which multilayer feedforward networks can act as universal approximators. We show that most of all the characterizations that were reported thus far in the literature are special cases of the following general result: A standard multilayer feedforward network with a locally bounded piecewise continuous activation fimction can approximate an3, continuous function to any degree of accuracy if and only if the network's activation function is not a polynomial. We also emphasize the important role of the threshold, asserting that without it the last theorem does not hold.