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Statistical Mechanics of Learning

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The effort to build machines that are able to learn and undertake tasks such as datamining, image processing and pattern recognition has led to the development of artificial neural networks in which learning from examples may be described and understood. The contribution to this subject made over the past decade by researchers applying the techniques of statistical mechanics is the subject of this book. The authors provide a coherent account of various important concepts and techniques that are currently only found scattered in papers, supplement this with background material in mathematics and physics, and include many examples and exercises.

Understanding intelligent behaviour has always been fascinating to both laymen and scientists. The question has become very topical through the concurrence of a number of different issues. First, there is a growing awareness of the computational limits of serial computers, while parallel computation is gaining ground, both technically and conceptually. Second, several new non-invasive scanning techniques allow the human brain to be studied from its collective behaviour down to the activity of single neurons. Third, the increased automatization of our society leads to an increased need for algorithms that control complex machines performing complex tasks. Finally, conceptual advances in physics, such as scaling, fractals, bifurcation theory and chaos, have widened its horizon and stimulate the modelling and study of complex non-linear systems. At the crossroads of these developments, artificial neural networks have something to offer to each of them.

The observation that these networks can learn from examples and are able to discern an underlying rule has spurred a decade of intense theoretical activity in the statistical mechanics community on the subject. Indeed, the ability to infer a rule from a set of examples is widely regarded as a sign of intelligence. Without embarking on a thorny discussion about the nature or definition of intelligence, we just note that quite a few of the problems posed in standard IQ tests are exactly of this nature: given a sequence of objects (letters, pictures, . . .) one is asked to continue the sequence “meaningfully”, which requires one to decipher the underlying rule. We can thus hope that a theoretical study of learning from examples in simple, well understood scenarios will shed some light on how intelligent behaviour emerges or operates.
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