Show simple item record

dc.contributor.authorEiras, Francisco
dc.contributor.authorAlfarra, Motasem
dc.contributor.authorKumar, M. Pawan
dc.contributor.authorTorr, Philip H. S.
dc.contributor.authorDokania, Puneet K.
dc.contributor.authorGhanem, Bernard
dc.contributor.authorBibi, Adel
dc.date.accessioned2021-07-14T06:27:31Z
dc.date.available2021-07-14T06:27:31Z
dc.date.issued2021-07-09
dc.identifier.urihttp://hdl.handle.net/10754/670194
dc.description.abstractRandomized 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.publisherarXiv
dc.relation.urlhttps://arxiv.org/pdf/2107.04570.pdf
dc.rightsArchived with thanks to arXiv
dc.titleANCER: Anisotropic Certification via Sample-wise Volume Maximization
dc.typePreprint
dc.contributor.departmentElectrical Engineering
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentElectrical Engineering Program
dc.eprint.versionPre-print
dc.contributor.institutionUniversity of Oxford, United Kingdom
dc.contributor.institutionFive AI Limited, United Kingdom
dc.identifier.arxivid2107.04570
kaust.personAlfarra, Motasem
kaust.personGhanem, Bernard
refterms.dateFOA2021-07-14T06:28:11Z


Files in this item

Thumbnail
Name:
Preprintfile1.pdf
Size:
5.522Mb
Format:
PDF
Description:
Pre-print

This item appears in the following Collection(s)

Show simple item record