{"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/empirically-measuring-concentration","title":"Empirically Measuring Concentration: Fundamental Limits on Intrinsic Robustness","arxiv_id":"1905.12202","date":"2019-05-29","proceeding":"NeurIPS 2019 12","authors":["Saeed Mahloujifar","Xiao Zhang","Mohammad Mahmoody","David Evans"],"abstract":"Many recent works have shown that adversarial examples that fool classifiers can be found by minimally perturbing a normal input. Recent theoretical results, starting with Gilmer et al. (2018b), show that if the inputs are drawn from a concentrated metric probability space, then adversarial examples with small perturbation are inevitable. A concentrated space has the property that any subset with $\\Omega(1)$ (e.g., 1/100) measure, according to the imposed distribution, has small distance to almost all (e.g., 99/100) of the points in the space. It is not clear, however, whether these theoretical results apply to actual distributions such as images. This paper presents a method for empirically measuring and bounding the concentration of a concrete dataset which is proven to converge to the actual concentration. We use it to empirically estimate the intrinsic robustness to $\\ell_\\infty$ and $\\ell_2$ perturbations of several image classification benchmarks. Code for our experiments is available at https://github.com/xiaozhanguva/Measure-Concentration.","url_abs":"https://arxiv.org/abs/1905.12202v2","url_pdf":"https://arxiv.org/pdf/1905.12202v2.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":"empirically-measuring-concentration","repo_url":"https://github.com/xiaozhanguva/Measure-Concentration","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"image-classification","task_name":"Image Classification"},{"task_slug":"image-classification","task_name":"image-classification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1905.12202","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1905.12202"}},"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. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/xiaozhanguva/Measure-Concentration","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"unverified":4},"by_repo_kind":{"official":{"samples":4,"ran":0,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"9ee5d436c364d9e2","entry":"cifar_loaders","repo":"xiaozhanguva/Measure-Concentration","repo_kind":"official","path":"load_data.py","file_url":"https://github.com/xiaozhanguva/Measure-Concentration/blob/HEAD/load_data.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"9ee5d436c364d9e2"}},{"code_sha256_prefix":"454ac42f2c881b9f","entry":"fashion_mnist_loaders","repo":"xiaozhanguva/Measure-Concentration","repo_kind":"official","path":"load_data.py","file_url":"https://github.com/xiaozhanguva/Measure-Concentration/blob/HEAD/load_data.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"454ac42f2c881b9f"}},{"code_sha256_prefix":"dbe1f4a2578f7918","entry":"knn_graph","repo":"xiaozhanguva/Measure-Concentration","repo_kind":"official","path":"preliminary.py","file_url":"https://github.com/xiaozhanguva/Measure-Concentration/blob/HEAD/preliminary.py","link_basis":"plan_row","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"dbe1f4a2578f7918"}},{"code_sha256_prefix":"53b5f8ddae846a11","entry":"mnist_loaders","repo":"xiaozhanguva/Measure-Concentration","repo_kind":"official","path":"load_data.py","file_url":"https://github.com/xiaozhanguva/Measure-Concentration/blob/HEAD/load_data.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"53b5f8ddae846a11"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}