@article {2321, title = {Theory I: Why and When Can Deep Networks Avoid the Curse of Dimensionality?}, year = {2016}, month = {11/2016}, abstract = {

[formerly titled "Why and When Can Deep - but Not Shallow - Networks Avoid the Curse of Dimensionality: a Review"]

The paper reviews and extends an emerging body of theoretical results on deep learning including the conditions under which it can be exponentially better than shallow learning. A class of deep convolutional networks represent an important special case of these conditions, though weight sharing is not the main reason for their exponential advantage. Implications of a few key theorems are discussed, together with new results, open problems and conjectures.

}, author = {Tomaso Poggio and Hrushikesh Mhaskar and Lorenzo Rosasco and Brando Miranda and Qianli Liao} }