For any research field to have a lasting impact, there must be a firm theoretical foundation. Neural networks research is no exception. Some of the founda tional concepts, established several decades ago, led to the early promise of developing machines exhibiting intelligence. The motivation for studying such machines comes from the fact that the brain is far more efficient in visual processing and speech recognition than existing computers. Undoubtedly, neu robiological systems employ very different computational principles. The study of artificial neural networks aims at understanding these computational prin ciples and applying them in the solutions of engineering problems. Due to the recent advances in both device technology and computational science, we are currently witnessing an explosive growth in the studies of neural networks and their applications. It may take many years before we have a complete understanding about the mechanisms of neural systems. Before this ultimate goal can be achieved, an swers are needed to important fundamental questions such as (a) what can neu ral networks do that traditional computing techniques cannot, (b) how does the complexity of the network for an application relate to the complexity of that problem, and (c) how much training data are required for the resulting network to learn properly? Everyone working in the field has attempted to answer these questions, but general solutions remain elusive. However, encouraging progress in studying specific neural models has been made by researchers from various disciplines.
This text brings together in one volume some of the recent advances in the development of a theoretical framework for studying neural networks. A variety of novel techniques from disciplines such as computer science, electrical engineering, statistics, and mathematics have been integrated and applied to develop ground-breaking analytical tools for such studies. This volume emphasizes the computational issues in artificial neural networks and compiles a set of pioneering research works, which together establish a general framework for studying the complexity of neural networks and their learning capabilities. This volume represents one of the first efforts to highlight these fundamental results, and provides a unified platform for a theoretical exploration of neural computation. Each chapter is authored by a leading researcher and/or scholar who has made significant contributions in this area. Part 1 provides a complexity theoretic study of different models of neural computation.
Complexity measures for neural models are introduced, and techniques for the efficient design of networks for performing basic computations, as well as analytical tools for understanding the capabilities and limitations of neural computation are discussed. The results describe how the computational cost of a neural network increases with the problem size. Equally important, these results go beyond the study of single neural elements, and establish to computational power of multilayer networks. Part 2 discusses concepts and results concerning learning using models of neural computation. Basic concepts such as VC-dimension and PAC-learning are introduced, and recent results relating neural networks to learning theory are derived. In addition, a number of the chapters address fundamental issues concerning learning algorithms, such as accuracy and rate of convergence, selection of training data, and efficient algorithms for learning useful classes of mappings.
