LOT: Layer-wise Orthogonal Training on Improving l2 Certified Robustness

Recent studies show that training deep neural networks (DNNs) with Lipschitz constraints are able to enhance adversarial robustness and other model properties such as stability. In this paper, we propose a layer-wise orthogonal training method (LOT) to effectively train 1-Lipschitz convolution layers via parametrizing an orthogonal matrix with an unconstrained matrix. We then efficiently compute the inverse square root of a convolution kernel by transforming the input domain to the Fourier frequency domain. On the other hand, as existing works show that semisupervised training helps improve empirical robustness, we aim to bridge the gap and prove that semi-supervised learning also improves the certified robustness of Lipschitz-bounded models. We conduct comprehensive evaluations for LOT under different settings. We show that LOT significantly outperforms baselines regarding deterministic 2 certified robustness, and scales to deeper neural networks. Under the supervised scenario, we improve the state-of-the-art certified robustness for all architectures (e.g. from 59.04% to 63.50% on CIFAR-10 and from 32.57% to 34.59% on CIFAR-100 at radius ρ = 36/255 for 40-layer networks). With semisupervised learning over unlabelled data, we are able to improve state-of-the-art certified robustness on CIFAR-10 at ρ = 108/255 from 36.04% to 42.39%. In addition, LOT consistently outperforms baselines on different model architectures with only 1/3 evaluation time. 36th Conference on Neural Information Processing Systems (NeurIPS 2022).