Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지

DEGREE OF APPROXIMATION TO A SMOOTH FUNCTION BY GENERALIZED TRANSLATION NETWORKS

  • HAHM, NAHMWOO (Department of Mathematics University of Incheon) ;
  • YANG, MEEHYEA (Department of Mathematics University of Incheon) ;
  • HONG, BUM IL (Department of Mathematics and Institute of Natural Sciences Kyung Hee University)
  • Received : 2005.04.28
  • Published : 2005.06.25
Download PDF
⟨ Previous Next ⟩

Abstract

We obtain the approximation order to a smooth function on a compact subset of $\mathbb{R}$ by generalized translation networks. In our study, the activation function is infinitely many times continuously differentiable function but it does not have special properties around ${\infty}$ and $-{\infty}$ like a sigmoidal activation function. Using the Jackson's Theorem, we get the approximation order. Especially, we obtain the approximation order by a neural network with a fixed threshold.

Keywords

Acknowledgement

Supported by : UNIVERSITY OF INCHEON

References

  1. J. Approximation Theory and Appl. v.9 Degree of Approximation by Superpositions of a Sigmoidal function Chen, D.
  2. IEEE Trans. Neural Networks v.6 Approximation Capability in C($R^n$) by Multilayer Feedforward Networks and Related Problems Chen, T.;Chen, H.
  3. J. Approximation Theory v.70 Approximation by Ridge Functions and Neural networks with One Hidden layer Chui, C.K.;Li, X.
  4. Mathematics of Control, Signal and Systems v.2 Approximation by Superposition of Sigmoidal Function Cybenko, G.
  5. Neural Networks v.7 Multilayer Feedforward Networks with a Nonpolynomial Activation Function Can Approximate Any Function Leshno, M.;Lin, V.Y.;Pinkus, A.;Schoken, S.
  6. Moscow University Mathematics Bulletin v.53 no.1 On Sigmoidal Functions Medvedeva, M.V.
  7. Neural Computation v.9 no.1 Neural Networks for Functional Approximation and System Identification Mhaskar, H.N.;Hahm, N.
  8. Applied Mathematics Letters v.15 Approximation Order to a Function in C(R) by Superposition of a Sigmoidal Function Hahm, N.;Hong, B.I.
  9. Advances in Applied Mathematics v.16 Degree of Approximation by Neural and Translation Networks with a Single Hidden Layer Mhaskar, H.N.;Micchelli, C.A.
  10. Theory of Approximation of Functions of a Real Variable Timan, A.F.