Mathematical Aspects of Spin Glasses and Neural Networks, Vol. 41 Book

This book grew out of a set of course notes for a neural networks module given as part of a Masters degree in "Intelligent Systems". The people on this course came from a wide variety of intellectual backgrounds (from philosophy, through psychology to computer science and engineering) and the author knew that he could not count on their being able to come to grips with the largely technical and mathematical approach which is often used (and in some ways easier to do). As a result he was forced to look carefully at the basic conceptual principles at work in the subject and try to recast these using ordinary language, drawing on the use of physical metaphors or analogies, and pictorial or graphical representations. I was pleasantly surprised to find that, as a result of this process, my own understanding was considerably deepened; I had now to unravel, as it were, condensed formal descriptions and say exactly how these were related to the "physical" world of artificial neurons, signals, computational processes, etc. However, the author was acutely aware that, while a litany of equations does not constitute a full description of fundamental principles, without some mathematics, a purely descriptive account runs the risk of dealing only with approximations and cannot be sharpened up to give any formulaic prescriptions. Therefore, the book introduced what author believed was just sufficient mathematics to bring the basic ideas into sharp focus.