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A note on the expressive power of deep rectified linear unit networks in high‐dimensional spaces
Author(s) -
Chen Liang,
Wu Congwei
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5575
Subject(s) - mathematics , curse of dimensionality , bandlimiting , class (philosophy) , unit (ring theory) , power (physics) , multivariate statistics , algorithm , artificial intelligence , mathematical analysis , fourier transform , computer science , statistics , physics , mathematics education , quantum mechanics
We investigate the ability of deep deep rectified linear unit (ReLU) networks to approximate multivariate functions. Specially, we establish the approximation error estimate on a class of bandlimited functions; in this case, ReLU networks can overcome the “curse of dimensionality.”