117 citations · 442 across the 44 of their papers we have counts for
4 papers · 2 filters
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…
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…
Learning Functions: When Is Deep Better Than Shallow
Hrushikesh Mhaskar, Qianli Liao, Tomaso Poggio
While the universal approximation property holds both for hierarchical and shallow networks, we prove that deep (hierarchical) networks can approximate the class of compositional f…