Fastened CROWN: Tightened Neural Network Robustness Certificates

TL;DR

This paper introduces FROWN, an optimization-based method that enhances neural network robustness certificates, making them tighter and more efficient, demonstrated through extensive experiments on various networks.

Contribution

It proves the optimality of deterministic CROWN solutions and proposes FROWN to tighten robustness certificates efficiently.

Findings

FROWN significantly improves robustness certificates.

FROWN reduces computational costs compared to linear programming methods.

Experiments show larger safe regions for neural networks using FROWN.

Abstract

The rapid growth of deep learning applications in real life is accompanied by severe safety concerns. To mitigate this uneasy phenomenon, much research has been done providing reliable evaluations of the fragility level in different deep neural networks. Apart from devising adversarial attacks, quantifiers that certify safeguarded regions have also been designed in the past five years. The summarizing work of Salman et al. unifies a family of existing verifiers under a convex relaxation framework. We draw inspiration from such work and further demonstrate the optimality of deterministic CROWN (Zhang et al. 2018) solutions in a given linear programming problem under mild constraints. Given this theoretical result, the computationally expensive linear programming based method is shown to be unnecessary. We then propose an optimization-based approach \textit{FROWN} (\textbf{F}astened C\textbf{ROWN}): a general algorithm to tighten robustness certificates for neural networks. Extensive experiments on various networks trained individually verify the effectiveness of FROWN in safeguarding larger robust regions.