# Discretization based Solutions for Secure Machine Learning against Adversarial Attacks

## TL;DR

Discretizing inputs and using binary neural networks significantly enhances the robustness of deep learning models against adversarial attacks with minimal accuracy loss, across multiple datasets.

## Contribution

The paper demonstrates that input discretization and binary neural networks improve adversarial robustness without extensive adversarial training.

## Key findings

- 2-bit input discretization yields maximal robustness with ~1-2% accuracy loss.
- Binary Neural Networks are inherently more robust than full precision models.
- Combining discretization with BNNs further enhances security against adversarial attacks.

## Abstract

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 DLNs against adversarial attacks. Specifically, discretizing the input space (or allowed pixel levels from 256 values or 8-bit to 4 values or 2-bit) extensively improves the adversarial robustness of 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 BNNs furthers the robustness even waiving the need for adversarial training for 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-bit input discretization that incurs an adversarial accuracy loss of just ~1-2% as compared to clean test accuracy.