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A common\nrequirement is robustness to adversarial perturbations in a neighbourhood\naround an input. In this paper we focus on the $L_0$ norm and aim to compute,\nfor a trained DNN and an input, the maximal radius of a safe norm ball around\nthe input within which there are no adversarial examples. Then we define global\nrobustness as an expectation of the maximal safe radius over a test data set.\nWe first show that the problem is NP-hard, and then propose an approximate\napproach to iteratively compute lower and upper bounds on the network's\nrobustness. The approach is \\emph{anytime}, i.e., it returns intermediate\nbounds and robustness estimates that are gradually, but strictly, improved as\nthe computation proceeds; \\emph{tensor-based}, i.e., the computation is\nconducted over a set of inputs simultaneously, instead of one by one, to enable\nefficient GPU computation; and has \\emph{provable guarantees}, i.e., both the\nbounds and the robustness estimates can converge to their optimal values.\nFinally, we demonstrate the utility of the proposed approach in practice to\ncompute tight bounds by applying and adapting the anytime algorithm to a set of\nchallenging problems, including global robustness evaluation, competitive $L_0$\nattacks, test case generation for DNNs, and local robustness evaluation on\nlarge-scale ImageNet DNNs. We release the code of all case studies via GitHub.","url_abs":"http://arxiv.org/abs/1804.05805v2","url_pdf":"http://arxiv.org/pdf/1804.05805v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"global-robustness-evaluation-of-deep-neural","repo_url":"https://github.com/L0-TRE/L0-TRE","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"global-robustness-evaluation-of-deep-neural","repo_url":"https://github.com/Accountable-Machine-Intelligence-Lab/DeepTRE","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"BSD-3-Clause"}}],"tasks":[{"task_slug":null,"task_name":"GPU"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1804.05805","atlas_url":"https://app.syntology.ai/?focus=1804.05805","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1804.05805"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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