Towards adversarial robustness with 01 loss neural networks

Motivated by the general robustness properties of the 01 loss we propose a single hidden layer 01 loss neural network trained with stochastic coordinate descent as a defense against adversarial attacks in machine learning. One measure of a model's robustness is the minimum distortion required to make the input adversarial. This can be approximated with the Boundary Attack (Brendel et. al. 2018) and HopSkipJump (Chen et. al. 2019) methods. We compare the minimum distortion of the 01 loss network to the binarized neural network and the standard sigmoid activation network with cross-entropy loss all trained with and without Gaussian noise on the CIFAR10 benchmark binary classification between classes 0 and 1. Both with and without noise training we find our 01 loss network to have the largest adversarial distortion of the three models by non-trivial margins. To further validate these results we subject all models to substitute model black box attacks under different distortion thresholds and find that the 01 loss network is the hardest to attack across all distortions. At a distortion of 0.125 both sigmoid activated cross-entropy loss and binarized networks have almost 0% accuracy on adversarial examples whereas the 01 loss network is at 40%. Even though both 01 loss and the binarized network use sign activations their training algorithms are different which in turn give different solutions for robustness. Finally we compare our network to simple convolutional models under substitute model black box attacks and find their accuracies to be comparable. Our work shows that the 01 loss network has the potential to defend against black box adversarial attacks better than convex loss and binarized networks.