We demonstrate that the problem of training neural networks with small (average) squared error is computationally intractable.

Q-Iearning is a popular reinforcement learning (RL) algorithm whose convergence is well demonstrated in the literature (Jaakkola et al., 1994; Tsitsiklis, 1994; Littman and Szepesvari, 1996; Szepesvari and Littman, 1996). Our aim in this paper is to provide an upper bound for the convergence rate of (lookup-table based) Q-Iearning algorithms. Although, this upper bound is not strict, computer experiments (to be presented elsewhere) and the form of the lemma underlying the proof indicate that the obtained upper bound can be made strict by a slightly more complicated definition for R. Our results extend to learning on aggregated states (see (Singh et al., 1995» and other related algorithms which admit a certain form of asynchronous stochastic approximation (see (Szepesv iri and Littman, 1996». Present address: Associative Computing, Inc., Budapest, Konkoly Thege M. u. 29-33, HUNGARY-1121 The Asymptotic Convergence-Rate of Q-leaming

We consider the general problem of learning multi-category classification from labeled examples. We present experimental results for a nearest neighbor algorithm which actively selects samples from different pattern classes according to a querying rule instead of the a priori class probabilities. The amount of improvement of this query-based approach over the passive batch approach depends on the complexity of the Bayes rule. The principle on which this algorithm is based is general enough to be used in any learning algorithm which permits a model-selection criterion and for which the error rate of the classifier is calculable in terms of the complexity of the model. 1 INTRODUCTION We consider the general problem of learning multi-category classification from labeled examples. In many practical learning settings the time or sample size available for training are limited. This may have adverse effects on the accuracy of the resulting classifier. For instance, in learning to recognize handwritten characters typical time limitation confines the training sample size to be of the order of a few hundred examples. It is important to make learning more efficient by obtaining only training data which contains significant information about the separability of the pattern classes thereby letting the learning algorithm participate actively in the sampling process. Querying for the class labels of specificly selected examples in the input space may lead to significant improvements in the generalization error (cf.

An asynchronous PDM (Pulse-Density-Modulating) digital neural network system has been developed in our laboratory. It consists of one thousand neurons that are physically interconnected via one million 7-bit synapses. It can solve one thousand simultaneous nonlinear first-order differential equations in a fully parallel and continuous fashion. The performance of this system was measured by a winner-take-all network with one thousand neurons. Although the magnitude of the input and network parameters were identical for each competing neuron, one of them won in 6 milliseconds.

This paper describes some of the interactions of model learning algorithms and planning algorithms we have found in exploring model-based reinforcement learning. The paper focuses on how local trajectory optimizers can be used effectively with learned nonparametric models. We find that trajectory planners that are fully consistent with the learned model often have difficulty finding reasonable plans in the early stages of learning. Trajectory planners that balance obeying the learned model with minimizing cost (or maximizing reward) often do better, even if the plan is not fully consistent with the learned model.

Similarity based fault tolerant retrieval in neural associative memories (N AM) has not lead to wiedespread applications. A drawback of the efficient Willshaw model for sparse patterns [Ste61, WBLH69], is that the high asymptotic information capacity is of little practical use because of high cross talk noise arising in the retrieval for finite sizes. Here a new bidirectional iterative retrieval method for the Willshaw model is presented, called crosswise bidirectional (CB) retrieval, providing enhanced performance. We discuss its asymptotic capacity limit, analyze the first step, and compare it in experiments with the Willshaw model. Applying the very efficient CB memory model either in information retrieval systems or as a functional model for reciprocal cortico-cortical pathways requires more than robustness against random noise in the input: Our experiments show also the segmentation ability of CB-retrieval with addresses containing the superposition of pattens, provided even at high memory load.

We present a novel generic approach to the problem of Event Related Potential identification and classification, based on a competitive N eural Net architecture. The network weights converge to the embedded signal patterns, resulting in the formation of a matched filter bank. The network performance is analyzed via a simulation study, exploring identification robustness under low SNR conditions and compared to the expected performance from an information theoretic perspective. The classifier is applied to real event-related potential data recorded during a classic oddball type paradigm; for the first time, withinsession variable signal patterns are automatically identified, dismissing the strong and limiting requirement of a-priori stimulus-related selective grouping of the recorded data.

The challenge of this problem is to decide which models to rely on for prediction and how much weight to give each. The goal of combining learned models is to obtain a more accurate prediction than can be obtained from any single source alone.

We present a computationally efficient algorithm for function approximation with piecewise linear sigmoidal nodes. A one hidden layer network is constructed one node at a time using the method of fitting the residual. The task of fitting individual nodes is accomplished using a new algorithm that searchs for the best fit by solving a sequence of Quadratic Programming problems. This approach offers significant advantages over derivative-based search algorithms (e.g.

A model of motion detection is presented. The model contains three stages. The first stage is unoriented and is selective for contrast polarities. The next two stages work in parallel. A phase insensitive stage pools across different contrast polarities through a spatiotemporal filter and thus can detect first and second order motion.