{"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/intrinsic-multi-scale-evaluation-of","title":"The Shape of Data: Intrinsic Distance for Data Distributions","arxiv_id":"1905.11141","date":"2019-05-27","proceeding":"ICLR 2020 1","authors":["Anton Tsitsulin","Marina Munkhoeva","Davide Mottin","Panagiotis Karras","Alex Bronstein","Ivan Oseledets","Emmanuel Müller"],"abstract":"The ability to represent and compare machine learning models is crucial in order to quantify subtle model changes, evaluate generative models, and gather insights on neural network architectures. Existing techniques for comparing data distributions focus on global data properties such as mean and covariance; in that sense, they are extrinsic and uni-scale. We develop a first-of-its-kind intrinsic and multi-scale method for characterizing and comparing data manifolds, using a lower-bound of the spectral variant of the Gromov-Wasserstein inter-manifold distance, which compares all data moments. In a thorough experimental study, we demonstrate that our method effectively discerns the structure of data manifolds even on unaligned data of different dimensionalities; moreover, we showcase its efficacy in evaluating the quality of generative models.","url_abs":"https://arxiv.org/abs/1905.11141v2","url_pdf":"https://arxiv.org/pdf/1905.11141v2.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":"intrinsic-multi-scale-evaluation-of","repo_url":"https://github.com/xgfs/imd","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"intrinsic-multi-scale-evaluation-of","repo_url":"https://github.com/xgfs/msid","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1905.11141","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1905.11141"}},"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/xgfs/msid","reach":{"status":"ok","spdx":"MIT"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/xgfs/imd","reach":null}],"summary":{"unverified":6},"by_repo_kind":{"official":{"samples":6,"ran":0,"repositories":2}},"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":"bc55d5de8b21ccd5","entry":"construct_graph_kgraph","repo":"xgfs/msid","repo_kind":"official","path":"msid/laplacian.py","file_url":"https://github.com/xgfs/msid/blob/HEAD/msid/laplacian.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":"bc55d5de8b21ccd5"}},{"code_sha256_prefix":"376c89ad8aa69c59","entry":"construct_graph_sparse","repo":"xgfs/msid","repo_kind":"official","path":"msid/laplacian.py","file_url":"https://github.com/xgfs/msid/blob/HEAD/msid/laplacian.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":"376c89ad8aa69c59"}},{"code_sha256_prefix":"ab53c7b3b4f82a1c","entry":"msid_descriptor","repo":"xgfs/imd","repo_kind":"official","path":"msid/msid.py","file_url":"https://github.com/xgfs/imd/blob/HEAD/msid/msid.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":"ab53c7b3b4f82a1c"}},{"code_sha256_prefix":"2f515d9a7b30368a","entry":"msid_score","repo":"xgfs/imd","repo_kind":"official","path":"msid/msid.py","file_url":"https://github.com/xgfs/imd/blob/HEAD/msid/msid.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":"2f515d9a7b30368a"}},{"code_sha256_prefix":"e1f4191eaf345f1b","entry":"np_euc_cdist","repo":"xgfs/msid","repo_kind":"official","path":"msid/laplacian.py","file_url":"https://github.com/xgfs/msid/blob/HEAD/msid/laplacian.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":"e1f4191eaf345f1b"}},{"code_sha256_prefix":"b1d1a60c6f0908d8","entry":"slq_red_var","repo":"xgfs/msid","repo_kind":"official","path":"msid/slq.py","file_url":"https://github.com/xgfs/msid/blob/HEAD/msid/slq.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":"b1d1a60c6f0908d8"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}