Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898219 | Applied and Computational Harmonic Analysis | 2018 | 21 Pages |
Abstract
We discuss approximation of functions using deep neural nets. Given a function f on a d-dimensional manifold ÎâRm, 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 Î, 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).
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Uri Shaham, Alexander Cloninger, Ronald R. Coifman,