Abstract
This paper considers a structure of three-layer feedforward networks that approximate polynomial functions. The feedforward network has some system parameters such as the coupling coefficients and the biases. The structure of the feedforward network is determined by the system parameters. For any polynomial function, a simple calculation method of the parameters is proposed when the three-layer feedforward network sufficiently approximates the polynomial function. Moreover, it is shown that the obtained feedforward network smoothly approximates the polynomial function.
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References
Bagheri, A., Karimi, T., Amanifard, N.: Tracking performance control of a cable communicated underwater vehicle using adaptive neural network controllers. Applied Soft Computing 10(3), 908–918 (2010)
Cybenko, C.: Approximation by superpositions of sigmodial function. Mathematics of Control, Signals and Systems 2, 303–314 (1989)
Funahashi, K.: On the approximate realization of continuous mapping by neural networks. Neural Networks 2(3), 183–191 (1989)
Hornik, K., Stinchcombe, M., White, H.: Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks. Neural Networks 3, 551–560 (1990)
Leshno, M., Lin, V.Y., Pinkus, A., Schocken, S.: Multilayer feedforward networks with a nonpolynomial activation function can approximate any function. Neural Networks 6, 861–867 (1993)
Meltser, M., Shoham, M., Manevitz, L.M.: Approximating functions by neural networks: a constructive solution in the uniform norm. Neural Networks 9(6), 965–978 (1996)
Scarselli, F., Tsoi, A.C.: Universal approximation using feedforward neural networks: a survey of some existing methods, and some new results. Neural Networks 11(1), 15–37 (1998)
Souza, R.M.G.P., Moreira, J.M.L.: Neural network correlation for power peak factor estimation. Annals of Nuclear Energy 33(7), 594–608 (2006)
Suzuki, S.: Constructive function-approximation by three-layer artificial neural networks. Neural Networks 11, 1049–1058 (1998)
Toda, N., Funahashi, K., Usui, S.: Polynomial functions can be realized by finite size multilayer feedforward neural networks. In: 1991 IEEE International Joint Conference on Neural Networks, Singapore, vol. 1, pp. 343–348 (1991)
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Nakamura, Y., Nakagawa, M. (2010). Three-Layer Feedforward Structures Smoothly Approximating Polynomial Functions. In: Diamantaras, K., Duch, W., Iliadis, L.S. (eds) Artificial Neural Networks – ICANN 2010. ICANN 2010. Lecture Notes in Computer Science, vol 6354. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15825-4_54
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DOI: https://doi.org/10.1007/978-3-642-15825-4_54
Publisher Name: Springer, Berlin, Heidelberg
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