TY - JOUR
T1 - Provable approximation properties for deep neural networks
AU - Shaham, Uri
AU - Cloninger, Alexander
AU - Coifman, Ronald R.
N1 - Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2018/5
Y1 - 2018/5
N2 - We discuss approximation of functions using deep neural nets. Given a function f on a d-dimensional manifold Γ⊂Rm, we construct a sparsely-connected depth-4 neural network and bound its error in approximating f. The size of the network depends on dimension and curvature of the manifold Γ the complexity of f, in terms of its wavelet description, and only weakly on the ambient dimension m. Essentially, our network computes wavelet functions, which are computed from Rectified Linear Units (ReLU).
AB - We discuss approximation of functions using deep neural nets. Given a function f on a d-dimensional manifold Γ⊂Rm, we construct a sparsely-connected depth-4 neural network and bound its error in approximating f. The size of the network depends on dimension and curvature of the manifold Γ the complexity of f, in terms of its wavelet description, and only weakly on the ambient dimension m. Essentially, our network computes wavelet functions, which are computed from Rectified Linear Units (ReLU).
KW - Function approximation
KW - Neural nets
KW - Wavelets
UR - http://www.scopus.com/inward/record.url?scp=84964515172&partnerID=8YFLogxK
U2 - 10.1016/j.acha.2016.04.003
DO - 10.1016/j.acha.2016.04.003
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AN - SCOPUS:84964515172
SN - 1063-5203
VL - 44
SP - 537
EP - 557
JO - Applied and Computational Harmonic Analysis
JF - Applied and Computational Harmonic Analysis
IS - 3
ER -