Discretization based Solutions for Secure Machine Learning against Adversarial Attacks

Adversarial examples are perturbed inputs that are designed (from a deep learning network’s (DLN) parameter gradients) to mislead the DLN during test time. Intuitively, constraining the dimensionality of inputs or parameters of a network reduces the “space” in which adversarial examples exist. Guided by this intuition, we demonstrate that discretization greatly improves the robustness of the DLNs against adversarial attacks. Specifically, discretizing the input space (or allowed pixel levels from 256 values or 8<inline-formula> <tex-math notation="LaTeX">$bit$ </tex-math></inline-formula> to 4 values or 2<inline-formula> <tex-math notation="LaTeX">$bit$ </tex-math></inline-formula>) extensively improves the adversarial robustness of the DLNs for a substantial range of perturbations for minimal loss in test accuracy. Furthermore, we find that binary neural networks (BNNs) and related variants are intrinsically more robust than their full precision counterparts in adversarial scenarios. Combining input discretization with the BNNs furthers the robustness, even waiving the need for adversarial training for the certain magnitude of perturbation values. We evaluate the effect of discretization on MNIST, CIFAR10, CIFAR100, and ImageNet datasets. Across all datasets, we observe maximal adversarial resistance with 2<inline-formula> <tex-math notation="LaTeX">$bit$ </tex-math></inline-formula> input discretization that incurs an adversarial accuracy loss of just ~1% – 2% as compared to clean test accuracy against single-step attacks. We also show standalone discretization remains vulnerable to stronger multi-step attack scenarios necessitating the use of adversarial training with discretization as an improved defense strategy.