  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.
