{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/adversarial-robustness-guarantees-for-random","title":"Adversarial Robustness Guarantees for Random Deep Neural Networks","arxiv_id":"2004.05923","date":"2020-04-13","proceeding":null,"authors":["Giacomo De Palma","Bobak T. Kiani","Seth Lloyd"],"abstract":"The reliability of deep learning algorithms is fundamentally challenged by the existence of adversarial examples, which are incorrectly classified inputs that are extremely close to a correctly classified input. We explore the properties of adversarial examples for deep neural networks with random weights and biases, and prove that for any $p\\ge1$, the $\\ell^p$ distance of any given input from the classification boundary scales as one over the square root of the dimension of the input times the $\\ell^p$ norm of the input. The results are based on the recently proved equivalence between Gaussian processes and deep neural networks in the limit of infinite width of the hidden layers, and are validated with experiments on both random deep neural networks and deep neural networks trained on the MNIST and CIFAR10 datasets. The results constitute a fundamental advance in the theoretical understanding of adversarial examples, and open the way to a thorough theoretical characterization of the relation between network architecture and robustness to adversarial perturbations.","url_abs":"https://arxiv.org/abs/2004.05923v2","url_pdf":"https://arxiv.org/pdf/2004.05923v2.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":"adversarial-robustness-guarantees-for-random","repo_url":"https://github.com/bkiani/Adversarial-robustness-guarantees-for-random-deep-neural-networks","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"tf","reach":null}],"tasks":[{"task_slug":"adversarial-robustness","task_name":"Adversarial Robustness"},{"task_slug":"gaussian-processes","task_name":"Gaussian Processes"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2004.05923","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2004.05923"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+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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