SPLITZ: Certifiable Robustness via Split Lipschitz Randomized Smoothing
<|reference_start|>SPLITZ: Certifiable Robustness via Split Lipschitz Randomized Smoothing: Certifiable robustness gives the guarantee that small perturbations around an input to a classifier will not change the prediction. There are two approaches to provide certifiable robustness to adversarial examples: a) explicitly training classifiers with small Lipschitz constants, and b) Randomized smoothing, which adds random noise to the input to create a smooth classifier. We propose \textit{SPLITZ}, a practical and novel approach which leverages the synergistic benefits of both the above ideas into a single framework. Our main idea is to \textit{split} a classifier into two halves, constrain the Lipschitz constant of the first half, and smooth the second half via randomization. Motivation for \textit{SPLITZ} comes from the observation that many standard deep networks exhibit heterogeneity in Lipschitz constants across layers. \textit{SPLITZ} can exploit this heterogeneity while inheriting the scalability of randomized smoothing. We present a principled approach to train \textit{SPLITZ} and provide theoretical analysis to derive certified robustness guarantees during inference. We present a comprehensive comparison of robustness-accuracy tradeoffs and show that \textit{SPLITZ} consistently improves upon existing state-of-the-art approaches on MNIST and CIFAR-10 datasets. For instance, with $\ell_2$ norm perturbation budget of \textbf{$\epsilon=1$}, \textit{SPLITZ} achieves $\textbf{43.2\%}$ top-1 test accuracy on CIFAR-10 dataset compared to state-of-art top-1 test accuracy $\textbf{39.8\%}<|reference_end|>
@article{zhong2024splitz:,
    title={SPLITZ: Certifiable Robustness via Split Lipschitz Randomized Smoothing},
    author={Meiyu Zhong, Ravi Tandon},
    journal={arXiv preprint arXiv:2407.02811},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.02811},
    primaryClass={cs.LG cs.IT math.IT}
}