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Analysis of Global Convergence and Learning Parameters of the Back-Propagation Algorithm for Quadratic Functions

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4682))

Abstract

This paper analyzes global convergence and learning parameters of the back-propagation algorithm for quadratic functions. Some global convergence conditions of the steepest descent algorithm are obtained by directly analyzing the exact momentum equations for quadratic cost functions. In addition, in order to guarantee the convergence for a given learning task, the method is obtained to choose the proper learning parameters. The results presented in this paper are the improvement and extension of the existed ones in some existing works.

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References

  1. Phansalkar, V.V., Sastry, P.S.: Analysis of the Back-propagation Algorithm with Momentum. IEEE Trans. Neural Networks 5, 505–506 (1994)

    Article  Google Scholar 

  2. Rumelhart, D.E., Hinton, G.E., Williams, R.J.: Learning Representations by Back-propagating Errors. Nature 323, 533–536 (1986)

    Article  Google Scholar 

  3. Hagan, M.T., Demuth, H.B., Beale, M.H.: Neural Network Design. PWS, Boston, MA (1996)

    Google Scholar 

  4. Torii, M., Hagan, M.T.: Stability of Steepest Descent with Momentum for Quadratic Functions. IEEE Trans. Neural Networks 13, 752–756 (2002)

    Article  Google Scholar 

  5. Hagiwara, M., Sato, A.: Analysis of Momentum Term in Back-propagation. IEICE Trans. Inform. Syst. 8, 1–6 (1995)

    Google Scholar 

  6. Sato, A.: Analytical Study of the Momentum Term in A Backpropagation Algorithm. In: Proc. ICANN91, pp. 617–622 (1991)

    Google Scholar 

  7. Qian, N.: On the Momentum Term in Gradient Descent Learning Algorithms. Neural Networks 12, 145–151 (1999)

    Article  Google Scholar 

  8. Zeng, Z.G., Huang, D.S., Wang, Z.F.: Global Convergence of Steepest Descent for Quadratic Functions. In: Yang, Z.R., Yin, H., Everson, R.M. (eds.) IDEAL 2004. LNCS, vol. 3177, pp. 672–677. Springer, Heidelberg (2004)

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De-Shuang Huang Laurent Heutte Marco Loog

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© 2007 Springer-Verlag Berlin Heidelberg

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Zeng, Z. (2007). Analysis of Global Convergence and Learning Parameters of the Back-Propagation Algorithm for Quadratic Functions. In: Huang, DS., Heutte, L., Loog, M. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence. ICIC 2007. Lecture Notes in Computer Science(), vol 4682. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74205-0_2

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  • DOI: https://doi.org/10.1007/978-3-540-74205-0_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74201-2

  • Online ISBN: 978-3-540-74205-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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