Hierarchical Verification for Adversarial Robustness

Cong Han Lim, Raquel Urtasun, Ersin Yumer
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:6072-6082, 2020.

Abstract

We introduce a new framework for the exact point-wise ℓp robustness verification problem that exploits the layer-wise geometric structure of deep feed-forward networks with rectified linear activations (ReLU networks). The activation regions of the network partition the input space, and one can verify the ℓp robustness around a point by checking all the activation regions within the desired radius. The GeoCert algorithm (Jordan et al., NeurIPS 2019) treats this partition as a generic polyhedral complex in order to detect which region to check next. In contrast, our LayerCert framework considers the nested hyperplane arrangement structure induced by the layers of the ReLU network and explores regions in a hierarchical manner. We show that, under certain conditions on the algorithm parameters, LayerCert provably reduces the number and size of the convex programs that one needs to solve compared to GeoCert. Furthermore, our LayerCert framework allows the incorporation of lower bounding routines based on convex relaxations to further improve performance. Experimental results demonstrate that LayerCert can significantly reduce both the number of convex programs solved and the running time over the state-of-the-art.

Cite this Paper


BibTeX
@InProceedings{pmlr-v119-lim20b, title = {Hierarchical Verification for Adversarial Robustness}, author = {Lim, Cong Han and Urtasun, Raquel and Yumer, Ersin}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {6072--6082}, year = {2020}, editor = {Hal Daumé III and Aarti Singh}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/lim20b/lim20b.pdf}, url = { http://proceedings.mlr.press/v119/lim20b.html }, abstract = {We introduce a new framework for the exact point-wise ℓp robustness verification problem that exploits the layer-wise geometric structure of deep feed-forward networks with rectified linear activations (ReLU networks). The activation regions of the network partition the input space, and one can verify the ℓp robustness around a point by checking all the activation regions within the desired radius. The GeoCert algorithm (Jordan et al., NeurIPS 2019) treats this partition as a generic polyhedral complex in order to detect which region to check next. In contrast, our LayerCert framework considers the nested hyperplane arrangement structure induced by the layers of the ReLU network and explores regions in a hierarchical manner. We show that, under certain conditions on the algorithm parameters, LayerCert provably reduces the number and size of the convex programs that one needs to solve compared to GeoCert. Furthermore, our LayerCert framework allows the incorporation of lower bounding routines based on convex relaxations to further improve performance. Experimental results demonstrate that LayerCert can significantly reduce both the number of convex programs solved and the running time over the state-of-the-art.} }
Endnote
%0 Conference Paper %T Hierarchical Verification for Adversarial Robustness %A Cong Han Lim %A Raquel Urtasun %A Ersin Yumer %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-lim20b %I PMLR %P 6072--6082 %U http://proceedings.mlr.press/v119/lim20b.html %V 119 %X We introduce a new framework for the exact point-wise ℓp robustness verification problem that exploits the layer-wise geometric structure of deep feed-forward networks with rectified linear activations (ReLU networks). The activation regions of the network partition the input space, and one can verify the ℓp robustness around a point by checking all the activation regions within the desired radius. The GeoCert algorithm (Jordan et al., NeurIPS 2019) treats this partition as a generic polyhedral complex in order to detect which region to check next. In contrast, our LayerCert framework considers the nested hyperplane arrangement structure induced by the layers of the ReLU network and explores regions in a hierarchical manner. We show that, under certain conditions on the algorithm parameters, LayerCert provably reduces the number and size of the convex programs that one needs to solve compared to GeoCert. Furthermore, our LayerCert framework allows the incorporation of lower bounding routines based on convex relaxations to further improve performance. Experimental results demonstrate that LayerCert can significantly reduce both the number of convex programs solved and the running time over the state-of-the-art.
APA
Lim, C.H., Urtasun, R. & Yumer, E.. (2020). Hierarchical Verification for Adversarial Robustness. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:6072-6082 Available from http://proceedings.mlr.press/v119/lim20b.html .

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