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The robustness of neural network classifiers is important in thesafety-critical domain and can be quantified by robustness verification. Atpresent, efficient and scalable verification techniques are always sound butincomplete, and thus, the improvement of verified robustness results is the keycriterion to evaluate the performance of incomplete verification approaches.The multi-variate function MaxPool is widely adopted yet challenging to verify.In this paper, we present Ti-Lin, a robustness verifier for MaxPool-based CNNswith Tight Linear Approximation. Following the sequel of minimizing theover-approximation zone of the non-linear function of CNNs, we are the first topropose the provably neuron-wise tightest linear bounds for the MaxPoolfunction. By our proposed linear bounds, we can certify larger robustnessresults for CNNs. We evaluate the effectiveness of Ti-Lin on differentverification frameworks with open-sourced benchmarks, including LeNet,PointNet, and networks trained on the MNIST, CIFAR-10, Tiny ImageNet andModelNet40 datasets. Experimental results show that Ti-Lin significantlyoutperforms the state-of-the-art methods across all networks with up to 78.6%improvement in terms of the certified accuracy with almost the same timeconsumption as the fastest tool. Our code is available athttps://github.com/xiaoyuanpigo/Ti-Lin-Hybrid-Lin.

Tightening Robustness Verification of MaxPool-based Neural Networks via Minimizing the Over-Approximation Zone