On Lipschitz Bounds of General Convolutional Neural Networks
By Dongmian Zou, Radu V. Balan, Maneesh Kumar Singh. 2018
60 citations recorded by the source corpus.
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.
Subfields: Artificial Intelligence, Computational Mechanics
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Klas Leino
- Matt Fredrikson
- George Pappas
- Manfred Morari
- Mahyar Fazlyab
- Hamed Hassani
- Zifan Wang
- Alexander Robey
In Computational Mechanics
Citations in the corpus
- Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks (2019, background): “Bounding Lipschitz constants for the specific case of convolutional neural networks (CNNs) has also been addressed in [5, 44, 6].”
- Globally-Robust Neural Networks (2021, background): “For more complicated networks, there is a growing body of work on computing layer-wise Lipschitz bounds for various types of layers that are commonly used in neural networks (Zou et al., 2019; Fazlyab et al., 2019; Sedghi et al., 2019; Singla & Feizi, 2019; Miyato et al., 2018).”