Neural Networks - Notes
Dr I F Wilde
These notes are based on lectures given some years ago in the Mathematics Department at King's College London (as part of the MSc programme in Information Processing and Neural Networks). An attempt has been made to present a reasonably logical (mathematical) account of some of the basic ideas of the "artificial intelligence" aspects of the subject. Thanks to John Chiasson (Boise State University, Idaho) for reporting a number of typographical errors.
Brains have been around for quite a time now, so it would be
nice to know how they work and very nice to be able to build machines which
mimic their function (or even some aspects of their function).
An interesting point of view of the application of neural networks to statistical problems has been offered by D. Ripley in the collection "Networks and Chaos - Statistical and Probabilistic Aspects", edited by O,E. Barndorff-Nielsen, J.L. Jensen and W.S. Kendall, Chapman and Hall, London, 1993.
An overview of some rigorous mathematical results (as well as some remarks on lesser-mathematical methods) has been given by D. Petritis (in Ann. Inst. Henri Poincare, 64, 255-288, 1996.) This article contains many references including some to further rigorous work - a selection being that of: M. Aizenman, J. Lebowitz and D. Ruelle, A. Bovier, J. Bricmont, A. van Enter, J. Frohlich, C. Newman, M. Talagrand, B. Zegarlinski.
Ivan F Wilde
e-mail: iwilde (dot) mth (at) ntlworld (dot) com
<Updated 19 March 2015>