%0 Journal Article %J International Journal of Automation and Computing %D 2017 %T Why and when can deep-but not shallow-networks avoid the curse of dimensionality: A review %A Tomaso Poggio %A Hrushikesh Mhaskar %A Lorenzo Rosasco %A Brando Miranda %A Qianli Liao %K convolutional neural networks %K deep and shallow networks %K deep learning %K function approximation %K Machine Learning %K Neural Networks %X
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.
%B International Journal of Automation and Computing %P 1-17 %8 03/2017 %G eng %U http://link.springer.com/article/10.1007/s11633-017-1054-2?wt_mc=Internal.Event.1.SEM.ArticleAuthorOnlineFirst %R 10.1007/s11633-017-1054-2