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The neural network with $1$-Lipschitz property based on $\ell_\infty$-distneuron has a theoretical guarantee in certified $\ell_\infty$ robustness.However, due to the inherent difficulties in the training of the network, thecertified accuracy of previous work is limited. In this paper, we propose twoapproaches to deal with these difficuties. Aiming at the characteristics of thetraining process based on $\ell_\infty$-norm neural network, we introduce theEMA method to improve the training process. Considering the randomness of thetraining algorithm, we propose an ensemble method based on trained base modelsthat have the $1$-Lipschitz property and gain significant improvement in thesmall parameter network. Moreover, we give the theoretical analysis of theensemble method based on the $1$-Lipschitz property on the certifiedrobustness, which ensures the effectiveness and stability of the algorithm. Ourcode is available athttps://github.com/Theia-4869/EMA-and-Ensemble-Lip-Networks.

Boosting Certified $\ell_\infty$ Robustness with EMA Method and Ensemble Model