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  5. Theory I: Why and When Can Deep Networks Avoid the Curse of Dimensionality?

Theory I: Why and When Can Deep Networks Avoid the Curse of Dimensionality?

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Author(s)
Poggio, Tomaso
•
Mhaskar, Hrushikesh
•
Rosasco, Lorenzo
•
Miranda, Brando
•
Liao, Qianli
Date Issued
November 23, 2016
Publisher
Center for Brains, Minds and Machines (CBMM), arXiv
Citation
arXiv:1611.00740v5
Series/Report no.
CBMM Memo Series;058
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.
Subjects
Deep Learning
deep convolutional networks
Terms of Use
Attribution-NonCommercial-ShareAlike 3.0 United States
http://creativecommons.org/licenses/by-nc-sa/3.0/us/
Persistent DSpace Link
http://hdl.handle.net/1721.1/105443
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