{"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/recovery-guarantees-for-compressible-signals","title":"Recovery Guarantees for Compressible Signals with Adversarial Noise","arxiv_id":"1907.06565","date":"2019-07-15","proceeding":null,"authors":["Jasjeet Dhaliwal","Kyle Hambrook"],"abstract":"We provide recovery guarantees for compressible signals that have been corrupted with noise and extend the framework introduced in \\cite{bafna2018thwarting} to defend neural networks against $\\ell_0$-norm, $\\ell_2$-norm, and $\\ell_{\\infty}$-norm attacks. Our results are general as they can be applied to most unitary transforms used in practice and hold for $\\ell_0$-norm, $\\ell_2$-norm, and $\\ell_\\infty$-norm bounded noise. In the case of $\\ell_0$-norm noise, we prove recovery guarantees for Iterative Hard Thresholding (IHT) and Basis Pursuit (BP). For $\\ell_2$-norm bounded noise, we provide recovery guarantees for BP and for the case of $\\ell_\\infty$-norm bounded noise, we provide recovery guarantees for Dantzig Selector (DS). These guarantees theoretically bolster the defense framework introduced in \\cite{bafna2018thwarting} for defending neural networks against adversarial inputs. Finally, we experimentally demonstrate the effectiveness of this defense framework against an array of $\\ell_0$, $\\ell_2$ and $\\ell_\\infty$ norm attacks.","url_abs":"https://arxiv.org/abs/1907.06565v3","url_pdf":"https://arxiv.org/pdf/1907.06565v3.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":"recovery-guarantees-for-compressible-signals","repo_url":"https://github.com/jasjeetIM/recovering_compressible_signals","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"tf","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}