Towards Certifying L-infinity Robustness using Neural Networks with L-inf-dist Neurons

Code

• github.com/zbh2047/L_inf-dist-net
  OfficialIn paperpytorch★ 42
• github.com/zbh2047/L_inf-dist-net-v2
  pytorch★ 22

Abstract

It is well-known that standard neural networks, even with a high classification accuracy, are vulnerable to small _-norm bounded adversarial perturbations. Although many attempts have been made, most previous works either can only provide empirical verification of the defense to a particular attack method, or can only develop a certified guarantee of the model robustness in limited scenarios. In this paper, we seek for a new approach to develop a theoretically principled neural network that inherently resists _ perturbations. In particular, we design a novel neuron that uses _-distance as its basic operation (which we call _-dist neuron), and show that any neural network constructed with _-dist neurons (called _-dist net) is naturally a 1-Lipschitz function with respect to _-norm. This directly provides a rigorous guarantee of the certified robustness based on the margin of prediction outputs. We then prove that such networks have enough expressive power to approximate any 1-Lipschitz function with robust generalization guarantee. We further provide a holistic training strategy that can greatly alleviate optimization difficulties. Experimental results show that using _-dist nets as basic building blocks, we consistently achieve state-of-the-art performance on commonly used datasets: 93.09% certified accuracy on MNIST (=0.3), 35.42% on CIFAR-10 (=8/255) and 16.31% on TinyImageNet (=1/255).

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