Towards Large Certified Radius in Randomized Smoothing using Quasiconcave Optimization

TL;DR

This paper introduces a quasiconcave optimization-based method for randomized smoothing that significantly increases certified robustness radii for neural networks with minimal additional computational cost.

Contribution

It leverages quasiconvex problem structure to efficiently compute optimal certified radii, improving robustness certification in a data-specific manner.

Findings

Significantly larger certified radii on CIFAR-10 and ImageNet.

Low computational overhead compared to existing methods.

Effective input-specific robustness certification.

Abstract

Randomized smoothing is currently the state-of-the-art method that provides certified robustness for deep neural networks. However, due to its excessively conservative nature, this method of incomplete verification often cannot achieve an adequate certified radius on real-world datasets. One way to obtain a larger certified radius is to use an input-specific algorithm instead of using a fixed Gaussian filter for all data points. Several methods based on this idea have been proposed, but they either suffer from high computational costs or gain marginal improvement in certified radius. In this work, we show that by exploiting the quasiconvex problem structure, we can find the optimal certified radii for most data points with slight computational overhead. This observation leads to an efficient and effective input-specific randomized smoothing algorithm. We conduct extensive experiments and empirical analysis on CIFAR-10 and ImageNet. The results show that the proposed method significantly enhances the certified radii with low computational overhead.