117 citations · 442 across the 44 of their papers we have counts for
7 papers · 1 filter
Approximate quadrature measures on data--defined spaces
Hrushikesh N. Mhaskar
An important question in the theory of approximate integration is to study the conditions on the nodes and weights that allow an estimate of the form $$ \sup_{f…
Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review
Tomaso Poggio, Hrushikesh Mhaskar, Lorenzo Rosasco +2
The paper characterizes classes of functions for which deep learning can be exponentially better than shallow learning. Deep convolutional networks are a special case of these cond…
Deep vs. shallow networks : An approximation theory perspective
Hrushikesh Mhaskar, Tomaso Poggio
The paper briefy reviews several recent results on hierarchical architectures for learning from examples, that may formally explain the conditions under which Deep Convolutional Ne…
Local approximation using Hermite functions
H. N. Mhaskar
We develop a wavelet like representation of functions in based on their Fourier--Hermite coefficients; i.e., we describe an expansion of such functions where the…
Deep nets for local manifold learning
Charles K. Chui, H. N. Mhaskar
The problem of extending a function defined on a training data on an unknown manifold to the entire manifold and a tubular neighborhood of this manif…
A unified framework for harmonic analysis of functions on directed graphs and changing data
Hrushikesh N. Mhaskar
We present a general framework for studying harmonic analysis of functions in the settings of various emerging problems in the theory of diffusion geometry. The starting point of t…