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

Certifying Robustness of Convolutional Neural Networks with Tight Linear Approximation