The support-vector network is a new learning machine for two-group classification problems. The machine conceptually implements the following idea: input vectors are non-linearly mapped to a very high-dimension feature space. In this feature space a linear decision surface is constructed. Special properties of the decision surface ensures high generalization ability of the learning machine. The idea behind the supportvector network was previously implemented for the restricted case where the training data can be separated without errors. We here extend this result to non-separable training data.

Abstract. This article presents a general class of associative reinforcement learning algorithms for connectionist networks containing stochastic units. These algorithms, called REINFORCE algorithms, are shown to make weight adjustments in a direction that lies along the gradient of expected reinforcement in both immediate-reinforcement tasks and certain limited forms of delayed-reinforcement tasks, and they do this without explicitly computing gradient estimates or even storing information from which such estimates could be computed. Specific examples of such algorithms are presented, some of which bear a close relationship to certain existing algorithms while others are novel but potentially interesting in their own right. Also given are results that show how such algorithms can be naturally integrated with backpropagation. We close with a brief discussion of a number of additional issues surrounding the use of such algorithms, including what is known about their limiting behaviors as well as further considerations that might be used to help develop similar but potentially more powerful reinforcement learning algorithms.

Most connectionist or "neural network" learning systems use some form of the back-propagation algorithm. However, back-propagation learning is too slow for many applications, and it scales up poorly as tasks become larger and more complex. The factors governing learning speed are poorly understood. I have begun a systematic, empirical study of learning speed in backprop-like algorithms, measured against a variety of benchmark problems. The goal is twofold: to develop faster learning algorithms and to contribute to the development of a methodology that will be of value in future studies of this kind. This paper is a progress report describing the results obtained during the first six months of this study. To date I have looked only at a limited set of benchmark problems, but the results on these are encouraging: I have developed a new learning algorithm that is faster than standard backprop by an order of magnitude or more and that appears to scale up very well as the problem size increases.

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...

Abstract | We survey learning algorithms for recurrent neural networks with hidden units, and put the various techniques into a common framework. We discuss xedpoint learning algorithms, namely recurrent backpropagation and deterministic Boltzmann Machines, and non- xedpoint algorithms, namely backpropagation through time, Elman's history cuto, and Jordan's output feedback architecture. Forward propagation, an online technique that uses adjoint equations, and variations thereof, are also discussed. In many cases, the uni ed presentation leads to generalizations of various sorts. We discuss advantages and disadvantages of temporally continuous neural networks in contrast to clocked ones, continue with some \tricks of the trade" for training, using, and simulating continuous time and recurrent neural networks. We present somesimulations, and at the end, address issues of computational complexity and learning speed.

Learning control involves modifying a controller's behavior to improve its performance as measured by some predefined index of performance (IP). If control actions that improve performance as measured by the IP are known, supervised learning methods, or methods for learning from examples, can be used to train the controller. But when such control actions are not known a priori, appropriate control behavior has to be inferred from observations of the IP. One can distinguish between two classes of methods for training controllers under such circumstances. Indirect methods involve constructing a model of the problem's IP and using the model to obtain training information for the controller. On the other hand, direct, or model-free,...

Many neural net learning algorithms aim at finding "simple" nets to explain training data. The expectation is: the "simpler" the networks, the better the generalization on test data (! Occam's razor). Previous implementations, however, use measures for "simplicity" that lack the power, universality and elegance of those based on Kolmogorov complexity and Solomonoff's algorithmic probability. Likewise, most previous approaches (especially those of the "Bayesian" kind) suffer from the problem of choosing appropriate priors. This paper addresses both issues. It first reviews some basic concepts of algorithmic complexity theory relevant to machine learning, and how the Solomonoff-Levin distribution (or universal prior) deals with the prior problem. The universal prior leads to a probabilistic method for finding "algorithmically simple" problem solutions with high generalization capability. The method is based on Levin complexity (a time-bounded generalization of Kolmogorov comple...

Developmental psychology and developmental neuropsychology have traditionally focused on the study of children. But these two fields are also supposed to be about the study of change, i.e. changes in behavior, changes in the neural structures that underlie behavior, and changes in the relationship between mind and brain across the course of development. Ironically, there has been relatively little interest in the mechanisms responsible for change in the last 15–20 years of developmental research. The reasons for this de-emphasis on change have a great deal to do with a metaphor for mind and brain that has influenced most of experimental psychology, cognitive science and neuropsychology for the last few decades, i.e. the metaphor of the serial digital computer. We will refer to this particu-

Many machine learning algorithms aim at finding "simple" rules to explain training data. The expectation is: the "simpler" the rules, the better the generalization on test data (! Occam's razor). Most practical implementations, however, use measures for "simplicity" that lack the power, universality and elegance of those based on Kolmogorov complexity and Solomonoff's algorithmic probability. Likewise, most previous approaches (especially those of the "Bayesian" kind) suffer from the problem of choosing appropriate priors. This paper addresses both issues. It first reviews some basic concepts of algorithmic complexity theory relevant to machine learning, and how the Solomonoff-Levin distribution (or universal prior) deals with the prior problem. The universal prior leads to a probabilistic method for finding "algorithmically simple" problem solutions with high generalization capability. The method is based on Levin complexity (a time-bounded generalization of Kolmogorov complexity) and...

. We consider an incremental gradient method with momentum term for minimizing the sum of continuously di#erentiable functions. This method uses a new adaptive stepsize rule that decreases the stepsize whenever su#cient progress is not made. We show that if the gradients of the functions are bounded and Lipschitz continuous over a certain level set, then every cluster point of the iterates generated by the method is a stationary point. In addition, if the gradient of the functions have a certain growth property, then the method is either linearly convergent in some sense or the stepsizes are bounded away from zero. The new stepsize rule is much in the spirit of heuristic learning rules used in practice for training neural networks via backpropagation. As such, the new stepsize rule may suggest improvements on existing learning rules. Finally, extension of the method and the convergence results to constrained minimization is discussed, as are some implementation issues and numerical exp...