Theory I: Why and When Can Deep Networks Avoid the Curse of Dimensionality?
[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 learni...
| Main Authors: | , , , , |
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| Format: | Technical Report |
| Language: | en_US |
| Published: |
Center for Brains, Minds and Machines (CBMM), arXiv
2016
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| Subjects: | |
| Online Access: | http://hdl.handle.net/1721.1/105443 |
| _version_ | 1811074614230515712 |
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| author | Poggio, Tomaso Mhaskar, Hrushikesh Rosasco, Lorenzo Miranda, Brando Liao, Qianli |
| author_facet | Poggio, Tomaso Mhaskar, Hrushikesh Rosasco, Lorenzo Miranda, Brando Liao, Qianli |
| author_sort | Poggio, Tomaso |
| collection | MIT |
| description | [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. |
| first_indexed | 2024-09-23T09:52:37Z |
| format | Technical Report |
| id | mit-1721.1/105443 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T09:52:37Z |
| publishDate | 2016 |
| publisher | Center for Brains, Minds and Machines (CBMM), arXiv |
| record_format | dspace |
| spelling | mit-1721.1/1054432019-04-12T17:17:11Z Theory I: Why and When Can Deep Networks Avoid the Curse of Dimensionality? Poggio, Tomaso Mhaskar, Hrushikesh Rosasco, Lorenzo Miranda, Brando Liao, Qianli Deep Learning deep convolutional networks [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. This work was supported by the Center for Brains, Minds and Machines (CBMM), funded by NSF STC award CCF – 1231216. 2016-11-28T17:38:30Z 2016-11-28T17:38:30Z 2016-11-23 Technical Report Working Paper Other http://hdl.handle.net/1721.1/105443 arXiv:1611.00740v5 en_US CBMM Memo Series;058 Attribution-NonCommercial-ShareAlike 3.0 United States http://creativecommons.org/licenses/by-nc-sa/3.0/us/ application/pdf application/pdf Center for Brains, Minds and Machines (CBMM), arXiv |
| spellingShingle | Deep Learning deep convolutional networks Poggio, Tomaso Mhaskar, Hrushikesh Rosasco, Lorenzo Miranda, Brando Liao, Qianli Theory I: Why and When Can Deep Networks Avoid the Curse of Dimensionality? |
| title | Theory I: Why and When Can Deep Networks Avoid the Curse of Dimensionality? |
| title_full | Theory I: Why and When Can Deep Networks Avoid the Curse of Dimensionality? |
| title_fullStr | Theory I: Why and When Can Deep Networks Avoid the Curse of Dimensionality? |
| title_full_unstemmed | Theory I: Why and When Can Deep Networks Avoid the Curse of Dimensionality? |
| title_short | Theory I: Why and When Can Deep Networks Avoid the Curse of Dimensionality? |
| title_sort | theory i why and when can deep networks avoid the curse of dimensionality |
| topic | Deep Learning deep convolutional networks |
| url | http://hdl.handle.net/1721.1/105443 |
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