Hierarchical Randomized Smoothing
This work addresses the problem of making machine learning models provably robust to targeted attacks on specific parts of data, such as pixels or nodes, for applications in security-critical domains, representing an incremental improvement over existing randomized smoothing methods.
The paper tackles the challenge of certifying robustness against perturbations on subsets of entities in complex data, such as pixels in images, by introducing hierarchical randomized smoothing, which achieves stronger robustness guarantees while maintaining high accuracy, with experimental results showing superior robustness-accuracy trade-offs in image and node classification.
Real-world data is complex and often consists of objects that can be decomposed into multiple entities (e.g. images into pixels, graphs into interconnected nodes). Randomized smoothing is a powerful framework for making models provably robust against small changes to their inputs - by guaranteeing robustness of the majority vote when randomly adding noise before classification. Yet, certifying robustness on such complex data via randomized smoothing is challenging when adversaries do not arbitrarily perturb entire objects (e.g. images) but only a subset of their entities (e.g. pixels). As a solution, we introduce hierarchical randomized smoothing: We partially smooth objects by adding random noise only on a randomly selected subset of their entities. By adding noise in a more targeted manner than existing methods we obtain stronger robustness guarantees while maintaining high accuracy. We initialize hierarchical smoothing using different noising distributions, yielding novel robustness certificates for discrete and continuous domains. We experimentally demonstrate the importance of hierarchical smoothing in image and node classification, where it yields superior robustness-accuracy trade-offs. Overall, hierarchical smoothing is an important contribution towards models that are both - certifiably robust to perturbations and accurate.