A New Kind of Infinite Series and its Applications on Neural Networks

Abstract:

A new important theorem for function expansion and a new infinite series based on the new expansion is proposed. Unlike constant derivatives at a point by Taylors expansion, the terms are functions associated with derivatives. The expansion generated by a function is not the form of polynomials, which is different from Taylors expansion. Some application examples are given to show that the region of convergence is much larger than that obtained by Taylor's Series. As a kind of application, a new learning algorithm based on the new expansion for training neural networks is also proposed. The weight functions using the new expansion are more suitable for training those patterns obtained by some rational problems.

• Periodical: Applied Mechanics and Materials (Volumes 457-458)
• Pages: 761-764
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.457-458.761
• Online since: October 2013
• Authors: Dai Yuan Zhang
• Keywords: Expansion, Infinite Series, Neural Network (NN), Region of Convergence, Weight Function

References

[1] D. Y. Zhang: New theories and methods on neural networks. Beijing: Tsinghua University Press, 2006 (in Chinese).

[2] D. Y. Zhang: Systems Engineering and Electronics (in Chinese). Vol. 28 (2006), p.1434.

[3] D. Y. Zhang: Systems Engineering and Electronics (in Chinese). Vol. 30 (2008), p.2274.

[4] D. Y. Zhang: In: Proc. 2010 International Conference on Artificial Intelligence and Education, edited by C. Zhao, volume 2, IEEE Press, Hangzhou (2010).

[5] D. Y. Zhang: Applied Mechanics and Materials, edited by Y. H. Kim and P. Yarlagadda, Part 2 of Advances in Mechatronics and Control Engineering, Vol. 278-280 (2013), p.1301.

[6] D. Y. Zhang: Submitted to Annals of Mathematics (2013).