The architecture of the network is feedforward, with one hidden layer and several outputs. Starting from a fixed training set, we consider the network as a function of its weights. We derive, for a wide family of transfer functions, a lower and an upper bound on the number of hidden units for exact learning, given the size of the dataset and the dimensions of the input and output spaces. 1 RELATED WORKS The context of our work is rather similar to the well-known results of Baum et al. [1, 2,3,5, 10], but we consider both real inputs and outputs, instead ofthe dichotomies usually addressed. We are interested in learning exactly all the examples of a fixed database, hence our work is different from stating that multilayer networks are universal approximators [6, 8, 9]. Since we consider real outputs and not only dichotomies, it is not straightforward to compare our results to the recent works about the VC-dimension of multilayer networks [11, 12, 13]. Our study is more closely related to several works of Sontag [14, 15], but with different hypotheses on the transfer functions of the units. Finally, our approach is based on geometrical considerations and is close to the model of Coetzee and Stonick [4]. First we define the model of network and the notations and second we develop our analytic approach and prove the fundamental theorem. In the last section, we discuss our point of view and propose some practical consequences of the result.

Recently, there has been a vigorous debate concerning the nature of neural coding (Rieke et al. 1996; Stevens and Zador 1995; Shadlen and Newsome 1994). The prevailing viewhas been that the mean firing rate conveys all information about the sensory stimulus in a spike train and the precise timing of the individual spikes is noise. This belief is, in part, based on a lack of correlation between the precise timing ofthe spikes and the sensory qualities of the stimulus under study, particularly, on a lack of spike timing repeatability when identical stimulation is delivered. This view has been challenged by a number of recent studies, in which highly repeatable temporal patterns of spikes can be observed both in vivo (Bair and Koch 1996; Abeles et al. 1993) and in vitro (Mainen and Sejnowski 1994). Furthermore, application ofinformation theory to the coding problem in the frog and house fly (Bialek et al. 1991; Bialek and Rieke 1992) suggested that additional information could be extracted from spike timing. In the absence of direct evidence for a timing code in the cerebral cortex, the role of spike timing in neural coding remains controversial.

The weakly electric fish, Eigenmannia, generates a quasi sinusoidal, dipole-like electric fieldat individually fixed frequencies (250 - 600 Hz) by discharging an electric organ located in its tail (see Bullock and Heilgenberg, 1986 for reviews).

Automatic speech recognition is one of the fastest growing and commercially most promising applications of natural language technology. The technology has achieved a point where carefully designed systems for suitably constrained applications are a reality. Commercial systems are available today for such tasks as large-vocabulary dictation and voice control of medical equipment. This article reviews how state-of-the-art speech-recognition systems combine statistical modeling, linguistic knowledge, and machine learning to achieve their performance and points out some of the research issues in the field.

In recent years, there has been a resurgence in research on empirical methods in natural language processing. These methods employ learning techniques to automatically extract linguistic knowledge from natural language corpora rather than require the system developer to manually encode the requisite knowledge. This article presents an introduction to the series of specialized articles on these topics and attempts to describe and explain the growing interest in using learning methods to aid the development of natural language processing systems.

This article surveys the use of empirical, machine-learning methods for a particular natural language-understanding task-information extraction. The author presents a generic architecture for information-extraction systems and then surveys the learning algorithms that have been developed to address the problems of accuracy, portability, and knowledge acquisition for each component of the architecture.

Gary Kasparov in the final game of of Technology Computer Science Computer Chess, created in a tied, six-game match last May 11. Soon thereafter, the team moved to IBM, where they have been ever since, working under wraps on Deep Blue. The $100,000 third tier of the prize was awarded at AAAI-97 to this IBM team, who built the first computer chess machine that beat a world chess champion. The members of the Deep Blue team were also honored for their achievement with the Allen Newell Research Excellence Medal, sponsored by Carnegie Mellon University. Allen Newell Medals were presented to each of the major researchers in the field whose earlier contributions ultimately led to the success of Deep Blue.

This article posits the idea of robot learning as a new subfield. The results of the Robolearn-96 Workshop provide evidence that learning in modern robotics is distinct from traditional machine learning. The article examines the role of robotics in the social and natural sciences and the potential impact of learning on robotics, generating both a continuum of research issues and a description of the divergent terminology, target domains, and standards of proof associated with robot learning. The article argues that although robot learning is a new subfield, there is significant potential for synergy with traditional machine learning if the differences in research cultures can be overcome.

Machine-learning research has been making great progress in many directions. This article summarizes four of these directions and discusses some current open problems. The four directions are (1) the improvement of classification accuracy by learning ensembles of classifiers, (2) methods for scaling up supervised learning algorithms, (3) reinforcement learning, and (4) the learning of complex stochastic models.

This article surveys the use of empirical, machine-learning methods for a particular natural language-understanding task-information extraction. The author presents a generic architecture for information-extraction systems and then surveys the learning algorithms that have been developed to address the problems of accuracy, portability, and knowledge acquisition for each component of the architecture.