Overcoming the convex barrier for simplex input
Recent progress in neural network verification has challenged the notion of a convex barrier, that is, an inherent weakness in the convex relaxation of the output of a neural network. Specifically, there now exists a tight relaxation for verifying the robustness of a neural network to `∞ input pertu...
| Главные авторы: | , , , |
|---|---|
| Формат: | Conference item |
| Язык: | English |
| Опубликовано: |
NeurIPS Proceedings
2021
|
| _version_ | 1826307352178982912 |
|---|---|
| author | Behl, HS Kumar, MP Torr, P Dvijotham, K |
| author_facet | Behl, HS Kumar, MP Torr, P Dvijotham, K |
| author_sort | Behl, HS |
| collection | OXFORD |
| description | Recent progress in neural network verification has challenged the notion of a convex
barrier, that is, an inherent weakness in the convex relaxation of the output of
a neural network. Specifically, there now exists a tight relaxation for verifying
the robustness of a neural network to `∞ input perturbations, as well as efficient
primal and dual solvers for the relaxation. Buoyed by this success, we consider
the problem of developing similar techniques for verifying robustness to input
perturbations within the probability simplex. We prove a somewhat surprising
result that, in this case, not only can one design a tight relaxation that overcomes
the convex barrier, but the size of the relaxation remains linear in the number of
neurons, thereby leading to simpler and more efficient algorithms. We establish
the scalability of our overall approach via the specification of `1 robustness for
CIFAR-10 and MNIST classification, where our approach improves the state of the
art verified accuracy by up to 14.4%. Furthermore, we establish its accuracy on
a novel and highly challenging task of verifying the robustness of a multi-modal
(text and image) classifier to arbitrary changes in its textual input. |
| first_indexed | 2024-03-07T07:00:59Z |
| format | Conference item |
| id | oxford-uuid:ffbd7430-bb77-4dc5-acc5-c89da5efd8a0 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:00:59Z |
| publishDate | 2021 |
| publisher | NeurIPS Proceedings |
| record_format | dspace |
| spelling | oxford-uuid:ffbd7430-bb77-4dc5-acc5-c89da5efd8a02022-03-27T13:47:24ZOvercoming the convex barrier for simplex inputConference itemhttp://purl.org/coar/resource_type/c_5794uuid:ffbd7430-bb77-4dc5-acc5-c89da5efd8a0EnglishSymplectic ElementsNeurIPS Proceedings2021Behl, HSKumar, MPTorr, PDvijotham, KRecent progress in neural network verification has challenged the notion of a convex barrier, that is, an inherent weakness in the convex relaxation of the output of a neural network. Specifically, there now exists a tight relaxation for verifying the robustness of a neural network to `∞ input perturbations, as well as efficient primal and dual solvers for the relaxation. Buoyed by this success, we consider the problem of developing similar techniques for verifying robustness to input perturbations within the probability simplex. We prove a somewhat surprising result that, in this case, not only can one design a tight relaxation that overcomes the convex barrier, but the size of the relaxation remains linear in the number of neurons, thereby leading to simpler and more efficient algorithms. We establish the scalability of our overall approach via the specification of `1 robustness for CIFAR-10 and MNIST classification, where our approach improves the state of the art verified accuracy by up to 14.4%. Furthermore, we establish its accuracy on a novel and highly challenging task of verifying the robustness of a multi-modal (text and image) classifier to arbitrary changes in its textual input. |
| spellingShingle | Behl, HS Kumar, MP Torr, P Dvijotham, K Overcoming the convex barrier for simplex input |
| title | Overcoming the convex barrier for simplex input |
| title_full | Overcoming the convex barrier for simplex input |
| title_fullStr | Overcoming the convex barrier for simplex input |
| title_full_unstemmed | Overcoming the convex barrier for simplex input |
| title_short | Overcoming the convex barrier for simplex input |
| title_sort | overcoming the convex barrier for simplex input |
| work_keys_str_mv | AT behlhs overcomingtheconvexbarrierforsimplexinput AT kumarmp overcomingtheconvexbarrierforsimplexinput AT torrp overcomingtheconvexbarrierforsimplexinput AT dvijothamk overcomingtheconvexbarrierforsimplexinput |