Signal recovery from pooling representations

Joan Bruna; Arthur Szlam; Yann Lecun

Signal recovery from pooling representations

Joan Bruna, Arthur Szlam, Yann Lecun

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

In this work we compute lower Lipschitz bounds of lp pooling operators for p = 1,2, ∞ as well as lp pooling operators preceded by half- rectification layers. These give sufficient conditions for the design of invertible neural network layers. Numerical experiments on MNIST and image patches confirm that pooling layers can be inverted with phase recovery algorithms. Moreover, the regularity of the inverse pooling, controlled by the lower Lipschitz constant, is empirically verified with a nearest neighbor regression.

Original language	English (US)
Title of host publication	31st International Conference on Machine Learning, ICML 2014
Publisher	International Machine Learning Society (IMLS)
Pages	1585-1598
Number of pages	14
ISBN (Electronic)	9781634393973
State	Published - 2014
Event	31st International Conference on Machine Learning, ICML 2014 - Beijing, China Duration: Jun 21 2014 → Jun 26 2014

Publication series

Name	31st International Conference on Machine Learning, ICML 2014
Volume	2

Other

Other	31st International Conference on Machine Learning, ICML 2014
Country/Territory	China
City	Beijing
Period	6/21/14 → 6/26/14

ASJC Scopus subject areas

Artificial Intelligence
Computer Networks and Communications
Software

Cite this

Signal recovery from pooling representations. / Bruna, Joan; Szlam, Arthur; Lecun, Yann.
31st International Conference on Machine Learning, ICML 2014. International Machine Learning Society (IMLS), 2014. p. 1585-1598 (31st International Conference on Machine Learning, ICML 2014; Vol. 2).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

@inproceedings{08bd269157f744cab5d664de89941b5d,

title = "Signal recovery from pooling representations",

abstract = "In this work we compute lower Lipschitz bounds of lp pooling operators for p = 1,2, ∞ as well as lp pooling operators preceded by half- rectification layers. These give sufficient conditions for the design of invertible neural network layers. Numerical experiments on MNIST and image patches confirm that pooling layers can be inverted with phase recovery algorithms. Moreover, the regularity of the inverse pooling, controlled by the lower Lipschitz constant, is empirically verified with a nearest neighbor regression.",

author = "Joan Bruna and Arthur Szlam and Yann Lecun",

note = "Publisher Copyright: Copyright {\textcopyright} (2014) by the International Machine Learning Society (IMLS) All rights reserved.; 31st International Conference on Machine Learning, ICML 2014 ; Conference date: 21-06-2014 Through 26-06-2014",

year = "2014",

language = "English (US)",

series = "31st International Conference on Machine Learning, ICML 2014",

publisher = "International Machine Learning Society (IMLS)",

pages = "1585--1598",

booktitle = "31st International Conference on Machine Learning, ICML 2014",

}

TY - GEN

T1 - Signal recovery from pooling representations

AU - Bruna, Joan

AU - Szlam, Arthur

AU - Lecun, Yann

PY - 2014

Y1 - 2014

N2 - In this work we compute lower Lipschitz bounds of lp pooling operators for p = 1,2, ∞ as well as lp pooling operators preceded by half- rectification layers. These give sufficient conditions for the design of invertible neural network layers. Numerical experiments on MNIST and image patches confirm that pooling layers can be inverted with phase recovery algorithms. Moreover, the regularity of the inverse pooling, controlled by the lower Lipschitz constant, is empirically verified with a nearest neighbor regression.

AB - In this work we compute lower Lipschitz bounds of lp pooling operators for p = 1,2, ∞ as well as lp pooling operators preceded by half- rectification layers. These give sufficient conditions for the design of invertible neural network layers. Numerical experiments on MNIST and image patches confirm that pooling layers can be inverted with phase recovery algorithms. Moreover, the regularity of the inverse pooling, controlled by the lower Lipschitz constant, is empirically verified with a nearest neighbor regression.

UR - http://www.scopus.com/inward/record.url?scp=84919951531&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84919951531&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84919951531

T3 - 31st International Conference on Machine Learning, ICML 2014

SP - 1585

EP - 1598

BT - 31st International Conference on Machine Learning, ICML 2014

PB - International Machine Learning Society (IMLS)

T2 - 31st International Conference on Machine Learning, ICML 2014

Y2 - 21 June 2014 through 26 June 2014

ER -

Signal recovery from pooling representations

Abstract

Publication series

Other

ASJC Scopus subject areas

Other files and links

Fingerprint

Cite this