Abstract
A description is given of the role of mathematics in shaping our understanding of how neural networks operate, and the curious new mathematical concepts generated by our attempts to capture neural networks in equations. A selection of relatively simple examples of neural network tasks, models and calculations, is presented.
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Bibliography
D. Amit, Modeling Brain Function, Cambridge U.P., 1989
B. Müller and J. Reinhardt, Neural Networks, an Introduction, Springer (Berlin), 1990
J. Hertz, A. Krogh and R.G. Palmer, Introduction to the Theory of Neural Computation, Addison-Wesley (Redwood City), 1991
P. Peretto, An Introduction to the Modeling of Neural Networks, Cambridge U.P. 1992
S. Haykin, Neural Networks, A Comprehensive Foundation, Macmillan (New York), 1994
J.A. Anderson and E. Rosenfeld (eds.), Neurocomputing, Foundations of Research, MIT Press (Cambridge Mass.), 1988
M.L. Minsky and S.A. Papert, Perceptrons, MIT Press (Cambridge Mass.), 1969
T. Kohonen, Self-organization and Associative Memory, Springer (Berlin), 1984
Y. Kamp and M. Hasler, Recursive Neural Networks for Associative Memory, Wiley (Chichester), 1990
H. Ritter, T. Martinetz and К. Schulten, Neural Computation and Self-organizing Maps, Addison-Wesley (Reading Mass.), 1992
T. Kohonen, Self-organizing Maps, Springer (Berlin), 1995
E. Domany, J.L. van Hemmen and K. Schulten (eds.), Models of Neural Networks I, Springer (Berlin), 1991
E. Domany, J.L. van Hemmen and K. Schulten (eds.), Models of Neural Networks II, Springer (Berlin), 1994
E. Domany, J.L. van Hemmen and K. Schulten (eds.), Models of Neural Networks III, Springer (Berlin), 1995
J.G. Taylor, Mathematical Approaches to Neural Networks, North-Holland (Amsterdam), 1993
M. Mezard, G. Parisi and M.A. Virasoro, Spin-Glass Theory and Beyond, World-Scientific (Singapore), 1987
M.A. Arbib (ed.), Handbook of Brain Theory and Neural Networks, MIT Press (Cambridge Mass.), 1995
M. Anthony and N. Biggs, Computational Learning Theory, Cambridge U.P., 1992
G. Deco and D. Obradovic, An Information-theoretic Approach to Neural Computing, Springer (New-York), 1996
D.J.C. MacKay, Probably Networks and Plausible Predictions — a Review of Practical Bayesian Methods for Supervised Neural Networks, Network 6, 1995, p. 469
A.F. Murray (ed.), Applications of Neural Networks, Kluwer (Dordrecht), 1995
C.M. Bishop, Neural Networks for Pattern Recognition, Oxford U.P., 1995
G.W. Irwin, K. Warwick and K.J. Hunt (eds.), Neural Network Applications in Control, IEE London, 1995
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© 1998 Springer-Verlag London Limited
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Coolen, A.C.C. (1998). A Beginner’s Guide to the Mathematics of Neural Networks. In: Landau, L.J., Taylor, J.G. (eds) Concepts for Neural Networks. Perspectives in Neural Computing. Springer, London. https://doi.org/10.1007/978-1-4471-3427-5_2
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DOI: https://doi.org/10.1007/978-1-4471-3427-5_2
Publisher Name: Springer, London
Print ISBN: 978-3-540-76163-1
Online ISBN: 978-1-4471-3427-5
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