Towards Evaluating and Training Verifiably Robust Neural Networks

TL;DR

This paper compares IBP and CROWN bounding methods for verifiable robustness in neural networks, introduces a new verification technique LBP, and proposes a novel activation function, achieving state-of-the-art results.

Contribution

It proves CROWN's bounds are tighter than IBP, introduces LBP for better verification, and designs ParamRamp activation for improved robustness.

Findings

LBP outperforms IBP in verified error rates.

CROWN provides tighter bounds than IBP with proper lines.

ParamRamp enhances neuron diversity and robustness.

Abstract

Recent works have shown that interval bound propagation (IBP) can be used to train verifiably robust neural networks. Reseachers observe an intriguing phenomenon on these IBP trained networks: CROWN, a bounding method based on tight linear relaxation, often gives very loose bounds on these networks. We also observe that most neurons become dead during the IBP training process, which could hurt the representation capability of the network. In this paper, we study the relationship between IBP and CROWN, and prove that CROWN is always tighter than IBP when choosing appropriate bounding lines. We further propose a relaxed version of CROWN, linear bound propagation (LBP), that can be used to verify large networks to obtain lower verified errors than IBP. We also design a new activation function, parameterized ramp function (ParamRamp), which has more diversity of neuron status than ReLU. We conduct extensive experiments on MNIST, CIFAR-10 and Tiny-ImageNet with ParamRamp activation and achieve state-of-the-art verified robustness. Code and the appendix are available at https://github.com/ZhaoyangLyu/VerifiablyRobustNN.