The robustness of neural network classifiers is becoming important in the safety-critical domain and can be quantified by robustness verification. However, at present, efficient and scalable verification techniques are always sound but incomplete. Therefore, the improvement of certified robustness bounds is the key criterion to evaluate the superiority of robustness verification approaches. In this paper, we present a Tight Linear approximation approach for robustness verification of Convolutional Neural Networks(Ti-Lin). For general CNNs, we first provide a new linear constraints for S-shaped activation functions, which is better than both existing Neuron-wise Tightest and Network-wise Tightest tools. We then propose Neuron-wise Tightest linear bounds for Maxpool function. We implement Ti-Lin, the resulting verification method. We evaluate it with 48 different CNNs trained on MNIST, CIFAR-10, and Tiny ImageNet datasets. Experimental results show that Ti-Lin significantly outperforms other five state-of-the-art methods(CNN-Cert, DeepPoly, DeepCert, VeriNet, Newise). Concretely, Ti-Lin certifies much more precise robustness bounds on pure CNNs with Sigmoid/Tanh/Arctan functions and CNNs with Maxpooling function with at most 63.70% and 253.54% improvement, respectively.

本文提出了一种紧线性逼近方法(Ti-Lin)来验证卷积神经网络的稳健性，使用MNIST，CIFAR-10和Tiny ImageNet数据集对Ti-Lin进行评估，结果表明Ti-Lin明显优于其他五种最先进的方法，对纯CNN具有Sigmoid/Tanh/Arctan函数和具有Maxpooling功能的CNN的稳健性边界水平提高了最多63.70％和253.54％。

利用紧线性逼近证明卷积神经网络的鲁棒性