Lp APPROXIMATION CAPABILITIES OF SUM-OF-PRODUCT AND SIGMA-PI-SIGMA NEURAL NETWORKS
2007 ◽
Vol 17
(05)
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pp. 419-424
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Keyword(s):
This paper studies the Lp approximation capabilities of sum-of-product (SOPNN) and sigma-pi-sigma (SPSNN) neural networks. It is proved that the set of functions that are generated by the SOPNN with its activation function in [Formula: see text] is dense in [Formula: see text] for any compact set [Formula: see text], if and only if the activation function is not a polynomial almost everywhere. It is also shown that if the activation function of the SPSNN is in [Formula: see text], then the functions generated by the SPSNN are dense in [Formula: see text] if and only if the activation function is not a constant (a.e.).
Keyword(s):
2019 ◽
Vol 12
(3)
◽
pp. 156-161
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Keyword(s):