Improving certified robustness via statistical learning with logical reasoning

Zhoulin Yang, Zhikuan Zhao, Boxin Wang, Jiawei Zhang, Linyi Li, Hengzhi Pei, Bojan Karlas, Ji Liu, Heng Guo, Ce Zhang, Bo Li

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract / Description of output

Intensive algorithmic efforts have been made to enable the rapid improvements of certificated robustness for complex ML models recently. However, current robustness certification methods are only able to certify under a limited perturbation radius. Given that existing pure data-driven statistical approaches have reached a bottleneck, in this paper, we propose to integrate statistical ML models with knowledge (expressed as logical rules) as a reasoning component using Markov logic networks (MLN, so as to further improve the overall certified robustness. This opens new research questions about certifying the robustness of such a paradigm, especially the reasoning component (e.g., MLN). As the first step towards understanding these questions, we first prove that the computational complexity of certifying the robustness of MLN is #P-hard. Guided by this hardness result, we then derive the first certified robustness bound for MLN by carefully analyzing different model regimes. Finally, we conduct extensive experiments on five datasets including both high-dimensional images and natural language texts, and we show that the certified robustness with knowledge-based logical reasoning indeed significantly outperforms that of the state-of-the-arts.
Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems 35 (NeurIPS 2022)
PublisherCurran Associates Inc
Pages34859-34873
Number of pages15
Volume35
ISBN (Print)9781713871088
Publication statusPublished - 1 Apr 2023
EventThe 36th Conference on Neural Information Processing Systems, 2022 - New Orleans, United States
Duration: 28 Nov 20229 Dec 2022
Conference number: 36
https://neurips.cc/Conferences/2022

Publication series

NameAdvances in Neural Information Processing Systems
ISSN (Print)1049-5258

Conference

ConferenceThe 36th Conference on Neural Information Processing Systems, 2022
Abbreviated titleNeurIPS 2022
Country/TerritoryUnited States
CityNew Orleans
Period28/11/229/12/22
Internet address

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