We study the problem of training and certifying adversarially robust quantized neural networks (QNNs). Quantization is a technique for making neural networks more efficient by running them using low-bit integer arithmetic and is therefore commonly adopted in industry. Recent work has shown that floating-point neural networks that have been verified to be robust can become vulnerable to adversarial attacks after quantization, and certification of the quantized representation is necessary to guarantee robustness. In this work, we present quantization-aware interval bound propagation (QA-IBP), a novel method for training robust QNNs. Inspired by advances in robust learning of non-quantized networks, our training algorithm computes the gradient of an abstract representation of the actual network. Unlike existing approaches, our method can handle the discrete semantics of QNNs. Based on QA-IBP, we also develop a complete verification procedure for verifying the adversarial robustness of QNNs, which is guaranteed to terminate and produce a correct answer. Compared to existing approaches, the key advantage of our verification procedure is that it runs entirely on GPU or other accelerator devices. We demonstrate experimentally that our approach significantly outperforms existing methods and establish the new state-of-the-art for training and certifying the robustness of QNNs.

本文研究了在保证噪声攻击后的量化神经网络的训练和认证问题，并提出了一个能够完全利用 GPU 加速的 QA-IBP 训练方法和验证流程，大大优于现有方法，已成为量化神经网络鲁棒性训练和认证新的标准。 

量化感知区间边界传播用于训练可证明鲁棒性的量化神经网络