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A Random Matrix and Concentration Inequalities framework for Neural Networks Analysis

Abstract: 

Our article provides a theoretical analysis of the asymptotic performance of a regression or classification task performed by a simple random neural network. This result is obtained by leveraging a new framework at the crossroads between random matrix theory and the concentration of measure theory. This approach is of utmost interest for neural network analysis at large in that it naturally dismisses the difficulty induced by the non-linear activation functions, so long that these are Lipschitz functions. As an application, we provide formulas for the limiting law of the random neural network output and compare them conclusively to those obtained practically on handwritten digits databases.

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Paper Details

Authors:
Romain Couillet
Submitted On:
13 April 2018 - 5:38pm
Short Link:
Type:
Poster
Event:
Presenter's Name:
louart
Paper Code:
ICASSP18001
Document Year:
2018
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Document Files

conc_measure_NN_ICASSP18(3).pdf

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[1] Romain Couillet, "A Random Matrix and Concentration Inequalities framework for Neural Networks Analysis", IEEE SigPort, 2018. [Online]. Available: http://sigport.org/2767. Accessed: Apr. 24, 2019.
@article{2767-18,
url = {http://sigport.org/2767},
author = {Romain Couillet },
publisher = {IEEE SigPort},
title = {A Random Matrix and Concentration Inequalities framework for Neural Networks Analysis},
year = {2018} }
TY - EJOUR
T1 - A Random Matrix and Concentration Inequalities framework for Neural Networks Analysis
AU - Romain Couillet
PY - 2018
PB - IEEE SigPort
UR - http://sigport.org/2767
ER -
Romain Couillet. (2018). A Random Matrix and Concentration Inequalities framework for Neural Networks Analysis. IEEE SigPort. http://sigport.org/2767
Romain Couillet, 2018. A Random Matrix and Concentration Inequalities framework for Neural Networks Analysis. Available at: http://sigport.org/2767.
Romain Couillet. (2018). "A Random Matrix and Concentration Inequalities framework for Neural Networks Analysis." Web.
1. Romain Couillet. A Random Matrix and Concentration Inequalities framework for Neural Networks Analysis [Internet]. IEEE SigPort; 2018. Available from : http://sigport.org/2767