Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 66, Issue 3, Pages 1738-1759Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2019.2961812
Keywords
Lipschitz bounds; convolutional neural networks; scattering networks; linear programming; adversarial perturbation
Funding
- NSF [DMS-1413249, DMS1816608]
- Army Research Office (ARO) [W911NF16-1-0008]
- Laboratory for Telecommunication Sciences (LTS) [H9823031D00560049]
Ask authors/readers for more resources
Many convolutional neural networks (CNN's) have a feed-forward structure. In this paper, we model a general framework for analyzing the Lipschitz bounds of CNN's and propose a linear program that estimates these bounds. Several CNN's, including the scattering networks, the AlexNet and the GoogleNet, are studied numerically. In these practical numerical examples, estimations of local Lipschitz bounds are compared to these theoretical bounds. Based on the Lipschitz bounds, we next establish concentration inequalities for the output distribution with respect to a stationary random input signal. The Lipschitz bound is further used to perform nonlinear discriminant analysis that measures the separation between features of different classes.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available