dc.contributor.author Eiras, Francisco dc.contributor.author Alfarra, Motasem dc.contributor.author Kumar, M. Pawan dc.contributor.author Torr, Philip H. S. dc.contributor.author Dokania, Puneet K. dc.contributor.author Ghanem, Bernard dc.contributor.author Bibi, Adel dc.date.accessioned 2021-07-14T06:27:31Z dc.date.available 2021-07-14T06:27:31Z dc.date.issued 2021-07-09 dc.identifier.uri http://hdl.handle.net/10754/670194 dc.description.abstract Randomized smoothing has recently emerged as an effective tool that enables certification of deep neural network classifiers at scale. All prior art on randomized smoothing has focused on isotropic $\ell_p$ certification, which has the advantage of yielding certificates that can be easily compared among isotropic methods via $\ell_p$-norm radius. However, isotropic certification limits the region that can be certified around an input to worst-case adversaries, \ie it cannot reason about other "close", potentially large, constant prediction safe regions. To alleviate this issue, (i) we theoretically extend the isotropic randomized smoothing $\ell_1$ and $\ell_2$ certificates to their generalized anisotropic counterparts following a simplified analysis. Moreover, (ii) we propose evaluation metrics allowing for the comparison of general certificates - a certificate is superior to another if it certifies a superset region - with the quantification of each certificate through the volume of the certified region. We introduce ANCER, a practical framework for obtaining anisotropic certificates for a given test set sample via volume maximization. Our empirical results demonstrate that ANCER achieves state-of-the-art $\ell_1$ and $\ell_2$ certified accuracy on both CIFAR-10 and ImageNet at multiple radii, while certifying substantially larger regions in terms of volume, thus highlighting the benefits of moving away from isotropic analysis. Code used in our experiments is available in https://github.com/MotasemAlfarra/ANCER. dc.publisher arXiv dc.relation.url https://arxiv.org/pdf/2107.04570.pdf dc.rights Archived with thanks to arXiv dc.title ANCER: Anisotropic Certification via Sample-wise Volume Maximization dc.type Preprint dc.contributor.department Electrical Engineering dc.contributor.department Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division dc.contributor.department Electrical Engineering Program dc.eprint.version Pre-print dc.contributor.institution University of Oxford, United Kingdom dc.contributor.institution Five AI Limited, United Kingdom dc.identifier.arxivid 2107.04570 kaust.person Alfarra, Motasem kaust.person Ghanem, Bernard refterms.dateFOA 2021-07-14T06:28:11Z
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