LipBaB: Computing Exact Lipschitz Constant of ReLU Networks

被引：5

作者：

Bhowmick, Aritra ^{[1
]}

D'Souza, Meenakshi ^{[1
]}

Raghavan, G. Srinivasa ^{[1
]}

机构：

[1] Int Inst Informat Technol Bangalore, Bangalore, Karnataka, India

来源：

ARTIFICIAL NEURAL NETWORKS AND MACHINE LEARNING - ICANN 2021, PT IV | 2021年 / 12894卷

关键词：

D O I：

10.1007/978-3-030-86380-7_13

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

The Lipschitz constant of neural networks plays an important role in several contexts of deep learning ranging from robustness certification and regularization to stability analysis of systems with neural network controllers. Obtaining tight bounds of the Lipschitz constant is therefore important. We introduce LipBaB, a branch and bound framework to compute certified bounds of the local Lipschitz constant of deep neural networks with ReLU activation functions up to any desired precision. It is based on iteratively upper-bounding the norm of the Jacobians, corresponding to different activation patterns of the network caused within the input domain. Our algorithm can provide provably exact computation of the Lipschitz constant for any p-norm.

引用

页码：151 / 162

页数：12