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In this paper, we study a constructive approximation by neural networks with positive integer weights. Like neural networks with real weights, we show that neural networks with positive integer weights can even approximate arbitrarily well for any continuous functions on compact subsets of $\mathbb{R}$. We give a numerical result to justify our theoretical result.
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참고문헌 (9)
참고문헌 신청
B. L. Kalman / 1995 / Why Tanh : Choosing a Sigmoidal Function / Lect. Notes Comput. Sc. 600 : 303 ~ 312
C. K. Chui / 1992 / Approximation by Ridge Functions and Neural Networks with One Hidden Layer / J. Approx. Theory 70 : 17 ~ 28
D. Chen / 1993 / Degree of Approximation by Superpositions of a Sigmoidal Function / Approx. Theory and Appl. 9 (3) : 17 ~ 28
G. Lewicki / 2004 / Approximation of Functions of Finite Variation by Superpositions of a Sigmoidal Function / Appl. Math. Lett 17 : 1147 ~ 1152
J. Killian / 1996 / The Dynamic Universality of Sigmoidal Neural Networks / Inform. Comput. 128 : 48 ~ 56
C. K. Chui / 1992 / Approximation by Ridge Functions and Neural Networks with One Hidden Layer / J. Approx. Theory 70 : 17 ~ 28
D. Chen / 1993 / Degree of Approximation by Superpositions of a Sigmoidal Function / Approx. Theory and Appl. 9 (3) : 17 ~ 28
G. Lewicki / 2004 / Approximation of Functions of Finite Variation by Superpositions of a Sigmoidal Function / Appl. Math. Lett 17 : 1147 ~ 1152
J. Killian / 1996 / The Dynamic Universality of Sigmoidal Neural Networks / Inform. Comput. 128 : 48 ~ 56
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