On the exact solution of the Parity-N problem using ordered neural networks

Neural Networks

Volumn 13, Issue 6, 2000, Pages 643-649

  Lavretsky, E ^a  

^a BOEING COMPANY   (United States)

Author keywords

Fully feedforward connected network; Function approximation; Neural network; Ordered neural network; Parity N solution

Indexed keywords

APPROXIMATION THEORY; BOOLEAN FUNCTIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; THEOREM PROVING; VECTORS;

FUNCTION APPROXIMATION; NEURAL NETWORK ACTIVATION FUNCTION; ORDERED NEURAL NETWORK; PARITY-N PROBLEM;

FEEDFORWARD NEURAL NETWORKS;

ARCHITECTURE; ARTICLE; ARTIFICIAL NEURAL NETWORK; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; PRIORITY JOURNAL; PROBLEM SOLVING;

MODELS, NEUROLOGICAL; NEURAL NETWORKS (COMPUTER);

EID: 0034233399     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-6080(00)00038-1     Document Type: Article

References (13)

1. Barron A.R. Universal approximation bounds for superpositions of a sigmoidal function. IEEE Transactions on Information Theory. 39:1993;930-945.
2. Brown D.A. N-bit parity networks. Neural Networks. 6:1993;607-608.
3. Cybenko G. Approximation by superpositions of a sigmoidal function. Mathematical Contributions, Signals and Systems. 2:1989;303-314.
4. Hecht-Nielsen, R. (1989). Kolmogorov's mapping neural network existence theorem. In: Proceedings of the International Joint Conference in Neural Networks, vol. 3 (pp. 11-14) Washington, DC: IEEE.
5. Hertz J., Krogh A., Palmer R. Introduction to the theory of neural computation. 1991;Addison-Wesley, Redwood City, CA.
6. Hohil M.E., Liu D., Smith S.H. Solving the N-bit parity problem using neural networks. Neural Networks. 12:1999;1321-1323.
7. Lavretsky, E. (1999). Ordered neural networks: formulation, development, design and application. In: Proceedings of the 37th Aerospace Sciences Meeting & Exhibit, AIAA Paper 99-0106, January, Reno, NV.
8. Lavretsky, E. (2000). Neural networks for function approximation and control system design. PhD Thesis, Claremont Graduate University, Department of Mathematics. Claremont, CA.
9. McCulloch W.S., Pitts W. A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics. 9:1943;127-147.
10. Minor J.M. Parity with two layer feedforward nets. Neural Networks. 6:1993;705-707.
11. Scarselli F., Tsoi A.C. Universal approximation using feedforward neural networks: a survey of some existing methods and some new results. Neural Networks. 11:1998;15-37.
12. Stork D.G., Allen J.D. How to solve the N-bit parity problem with two hidden units. Neural Networks. 5:1992;923-926.
13. Werbos, P. J. (1974). Beyond regression: new tools for prediction and analysis in the behavior sciences. PhD Thesis, Harvard University, Committee on Applied Mathematics.