On a problem of Hornik
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| 024 | 7 | 0 | |a 10.1007/s10114-015-3759-x |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10114-015-3759-x | ||
| 245 | 0 | 0 | |a On a problem of Hornik |h [Elektronische Daten] |c [Ting Xie, Fei Cao] |
| 520 | 3 | |a In 1991, Hornik proved that the collection of single hidden layer feedforward neural networks (SLFNs) with continuous, bounded, and non-constant activation function σ is dense in C(K) where K is a compact set in ℝ s (see Neural Networks, 4(2), 251-257 (1991)). Meanwhile, he pointed out "Whether or not the continuity assumption can entirely be dropped is still an open quite challenging problem”. This paper replies in the affirmative to the problem and proves that for bounded and continuous almost everywhere (a.e.) activation function σ on ℝ, the collection of SLFNs is dense in C(K) if and only if σ is un-constant a.e.. | |
| 540 | |a Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 | ||
| 690 | 7 | |a Neural networks |2 nationallicence | |
| 690 | 7 | |a approximation |2 nationallicence | |
| 690 | 7 | |a activation function |2 nationallicence | |
| 700 | 1 | |a Xie |D Ting |u Department of Mathematics and Information Sciences, China Jiliang University, 310018, Hangzhou, P. R. China |4 aut | |
| 700 | 1 | |a Cao |D Fei |u Department of Mathematics and Information Sciences, China Jiliang University, 310018, Hangzhou, P. R. China |4 aut | |
| 773 | 0 | |t Acta Mathematica Sinica, English Series |d Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |g 31/7(2015-07-01), 1141-1148 |x 1439-8516 |q 31:7<1141 |1 2015 |2 31 |o 10114 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10114-015-3759-x |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10114-015-3759-x |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Xie |D Ting |u Department of Mathematics and Information Sciences, China Jiliang University, 310018, Hangzhou, P. R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Cao |D Fei |u Department of Mathematics and Information Sciences, China Jiliang University, 310018, Hangzhou, P. R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Acta Mathematica Sinica, English Series |d Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |g 31/7(2015-07-01), 1141-1148 |x 1439-8516 |q 31:7<1141 |1 2015 |2 31 |o 10114 | ||