@article {4185, title = {Theory I: Deep networks and the curse of dimensionality}, journal = {Bulletin of the Polish Academy of Sciences: Technical Sciences}, volume = {66}, year = {2018}, abstract = {
We review recent work characterizing the classes of functions for which deep learning can be exponentially better than shallow learning. Deep convolutional networks are a special case of these conditions, though weight sharing is not the main reason for their exponential advantage.
}, keywords = {convolutional neural networks, deep and shallow networks, deep learning, function approximation}, author = {Tomaso Poggio and Qianli Liao} } @article {2557, title = {Why and when can deep-but not shallow-networks avoid the curse of dimensionality: A review}, journal = {International Journal of Automation and Computing}, year = {2017}, month = {03/2017}, pages = {1-17}, abstract = {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.
}, keywords = {convolutional neural networks, deep and shallow networks, deep learning, function approximation, Machine Learning, Neural Networks}, doi = {10.1007/s11633-017-1054-2}, url = {http://link.springer.com/article/10.1007/s11633-017-1054-2?wt_mc=Internal.Event.1.SEM.ArticleAuthorOnlineFirst}, author = {Tomaso Poggio and Hrushikesh Mhaskar and Lorenzo Rosasco and Brando Miranda and Qianli Liao} } @article {3662, title = {Deep vs. shallow networks: An approximation theory perspective}, journal = {Analysis and Applications}, volume = {14}, year = {2016}, month = {01/2016}, pages = {829 - 848}, abstract = {