  Neural network quantization is becoming an industry standard to efficiently
deploy deep learning models on hardware platforms, such as CPU, GPU, TPU, and
FPGAs. However, we observe that the conventional quantization approaches are
vulnerable to adversarial attacks. This paper aims to raise people's awareness
about the security of the quantized models, and we designed a novel
quantization methodology to jointly optimize the efficiency and robustness of
deep learning models. We first conduct an empirical study to show that vanilla
quantization suffers more from adversarial attacks. We observe that the
inferior robustness comes from the error amplification effect, where the
quantization operation further enlarges the distance caused by amplified noise.
Then we propose a novel Defensive Quantization (DQ) method by controlling the
Lipschitz constant of the network during quantization, such that the magnitude
of the adversarial noise remains non-expansive during inference. Extensive
experiments on CIFAR-10 and SVHN datasets demonstrate that our new quantization
method can defend neural networks against adversarial examples, and even
achieves superior robustness than their full-precision counterparts while
maintaining the same hardware efficiency as vanilla quantization approaches. As
a by-product, DQ can also improve the accuracy of quantized models without
adversarial attack.
