Why and when can deep-but not shallow-networks avoid the curse of dimensionality: a review T Poggio, H Mhaskar, L Rosasco, B Miranda, Q Liao International Journal of Automation and Computing 14 (5), 503-519, 2017 | 685 | 2017 |
Neural networks for optimal approximation of smooth and analytic functions HN Mhaskar Neural computation 8 (1), 164-177, 1996 | 462 | 1996 |
Deep vs. shallow networks: An approximation theory perspective HN Mhaskar, T Poggio Analysis and Applications 14 (06), 829-848, 2016 | 428 | 2016 |
Approximation by superposition of sigmoidal and radial basis functions HN Mhaskar, CA Micchelli Advances in Applied mathematics 13 (3), 350-373, 1992 | 371 | 1992 |
Where does the sup norm of a weighted polynomial live? A Generalization of Incomplete Polynomials HN Mhaskar, EB Saff Constructive Approximation 1, 71-91, 1985 | 281 | 1985 |
Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature H Mhaskar, F Narcowich, J Ward Mathematics of computation 70 (235), 1113-1130, 2001 | 250 | 2001 |
When and why are deep networks better than shallow ones? H Mhaskar, Q Liao, T Poggio Proceedings of the AAAI conference on artificial intelligence 31 (1), 2017 | 242 | 2017 |
Extremal problems for polynomials with exponential weights HN Mhaskar, EB Saff Transactions of the American Mathematical Society 285 (1), 203-234, 1984 | 242 | 1984 |
Introduction to the theory of weighted polynomial approximation HN Mhaskar World Scientific, 1996 | 217 | 1996 |
Approximation properties of a multilayered feedforward artificial neural network HN Mhaskar Advances in Computational Mathematics 1 (1), 61-80, 1993 | 212 | 1993 |
Degree of approximation by neural and translation networks with a single hidden layer HN Mhaskar, CA Micchelli Advances in applied mathematics 16 (2), 151-183, 1995 | 180 | 1995 |
Learning functions: when is deep better than shallow H Mhaskar, Q Liao, T Poggio arXiv preprint arXiv:1603.00988, 2016 | 176 | 2016 |
A deep learning approach to diabetic blood glucose prediction HN Mhaskar, SV Pereverzyev, MD Van der Walt Frontiers in Applied Mathematics and Statistics 3, 14, 2017 | 141 | 2017 |
Fundamentals of approximation theory HN Mhaskar, DV Pai CRC Press, 2000 | 133 | 2000 |
Neural networks for localized approximation CK Chui, X Li, HN Mhaskar mathematics of computation 63 (208), 607-623, 1994 | 128 | 1994 |
Theory of deep learning III: explaining the non-overfitting puzzle T Poggio, K Kawaguchi, Q Liao, B Miranda, L Rosasco, X Boix, J Hidary, ... arXiv preprint arXiv:1801.00173, 2017 | 127 | 2017 |
A proof of Freud's conjecture for exponential weights DS Lubinsky, HN Mhaskar, EB Saff Constructive Approximation 4, 65-83, 1988 | 125 | 1988 |
On trigonometric wavelets CK Chui, HN Mhaskar Constructive Approximation 9, 167-190, 1993 | 119 | 1993 |
Diffusion polynomial frames on metric measure spaces M Maggioni, HN Mhaskar Applied and Computational Harmonic Analysis 24 (3), 329-353, 2008 | 107 | 2008 |
Dimension-independent bounds on the degree of approximation by neural networks HN Mhaskar, CA Micchelli IBM Journal of Research and Development 38 (3), 277-284, 1994 | 99 | 1994 |