Lecture 11 PDF

Three-layer feedforward networks

Mappings by three–layer feedforward networks: mathematical analysis

Mapping by 3–layer feedforward networks

• Hecht–Nielsen, Robert (1987) Kolmogorov’s mapping neural network existence theorem. Proceedings, IEEE First International Conference on Neural Networks, San Diego: SOS Press. pp. III:11–14. CC
  • http://en.wikipedia.org/wiki/Hilbert%27s_problems
  • http://en.wikipedia.org/wiki/Hilbert%27s_thirteenth_problem

• Duda, Richard O., Hart, Peter E., and Stork, David (2001) Pattern Classification. Second Edition. New York: Wiley. Section 6.2.2: Expressive power of multilayer networks, pp. 287-288

• Hornik, Kurt, Stinchcombe, Maxwell, and White, Halbert (1989) Multi–layer feedforward networks are universal approximators. Neural Networks, 2, 359–366. CC

• Cybenko, George (1989) Approximation by superpositions of a sigmoidal function. Mathematics of Control, Signals, and Systems, 2, 303–314. CC

Reference book: Mathematical analysis

• Rudin, Walter (1964) Principles of Mathematical Analysis. New York: McGraw–Hill.