Integer-arithmetic-only Certified Robustness for Quantized Neural Networks

Abstract

Adversarial data examples have drawn significant attention from the machine learning and security communities. A line of work on tackling adversarial examples is certified robustness via randomized smoothing that can provide a theoretical robustness guarantee. However, such a mechanism usually uses floating-point arithmetic for calculations in inference and requires large memory footprints and daunting computational costs. These defensive models cannot run efficiently on edge devices nor be deployed on integer-only logical units such as Turing Tensor Cores or integer-only ARM processors. To overcome these challenges, we propose an integer randomized smoothing approach with quantization to convert any classifier into a new smoothed classifier, which uses integer-only arithmetic for certified robustness against adversarial perturbations. We prove a tight robustness guarantee under ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> -norm for the proposed approach. We show our approach can obtain a comparable accuracy and 4× ∼ 5× speedup over floating-point arithmetic certified robust methods on general-purpose CPUs and mobile devices on two distinct datasets (CIFAR-10 and Caltech-101).