{"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/representation-topology-divergence-a-method-1","title":"Representation Topology Divergence: A Method for Comparing Neural Network Representations","arxiv_id":"2201.00058","date":"2021-12-31","proceeding":null,"authors":["Serguei Barannikov","Ilya Trofimov","Nikita Balabin","Evgeny Burnaev"],"abstract":"Comparison of data representations is a complex multi-aspect problem that has not enjoyed a complete solution yet. We propose a method for comparing two data representations. We introduce the Representation Topology Divergence (RTD), measuring the dissimilarity in multi-scale topology between two point clouds of equal size with a one-to-one correspondence between points. The data point clouds are allowed to lie in different ambient spaces. The RTD is one of the few TDA-based practical methods applicable to real machine learning datasets. Experiments show that the proposed RTD agrees with the intuitive assessment of data representation similarity and is sensitive to its topological structure. We apply RTD to gain insights on neural networks representations in computer vision and NLP domains for various problems: training dynamics analysis, data distribution shift, transfer learning, ensemble learning, disentanglement assessment.","url_abs":"https://arxiv.org/abs/2201.00058v2","url_pdf":"https://arxiv.org/pdf/2201.00058v2.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":"representation-topology-divergence-a-method-1","repo_url":"https://github.com/ilyatrofimov/rtd","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"representation-topology-divergence-a-method-1","repo_url":"https://github.com/ilyatrofimov/sftd","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"Apache-2.0"}},{"paper_slug":"representation-topology-divergence-a-method-1","repo_url":"https://github.com/nikitabalabin/topdis","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"disentanglement","task_name":"Disentanglement"},{"task_slug":"ensemble-learning","task_name":"Ensemble Learning"},{"task_slug":"transfer-learning","task_name":"Transfer Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2201.00058","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2201.00058"}},"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/nikitabalabin/topdis","reach":null},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/ilyatrofimov/rtd","reach":{"status":"ok"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/ilyatrofimov/sftd","reach":{"status":"ok","spdx":"Apache-2.0"}}],"summary":{"ran_honours":1,"unverified":6},"by_repo_kind":{"listed":{"samples":7,"ran":1,"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":2,"samples":[{"code_sha256_prefix":"230251fbc53d99a1","entry":"lp_loss","repo":"nikitabalabin/topdis","repo_kind":"listed","path":"BetaTCVAE_TopDis/rtd.py","file_url":"https://github.com/nikitabalabin/topdis/blob/HEAD/BetaTCVAE_TopDis/rtd.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"230251fbc53d99a1"}},{"code_sha256_prefix":"8e50af8dd2a65977","entry":"augmentation","repo":"ilyatrofimov/sftd","repo_kind":"listed","path":"SHAPR_torch+SFTD/shapr/data_generator.py","file_url":"https://github.com/ilyatrofimov/sftd/blob/HEAD/SHAPR_torch%2BSFTD/shapr/data_generator.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"8e50af8dd2a65977"}},{"code_sha256_prefix":"e1cd310a804b6dd7","entry":"auto_property","repo":"ilyatrofimov/sftd","repo_kind":"listed","path":"SHAPR_torch+SFTD/shapr/_settings.py","file_url":"https://github.com/ilyatrofimov/sftd/blob/HEAD/SHAPR_torch%2BSFTD/shapr/_settings.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"e1cd310a804b6dd7"}},{"code_sha256_prefix":"12c61458f7a34695","entry":"get_indicies","repo":"nikitabalabin/topdis","repo_kind":"listed","path":"BetaTCVAE_TopDis/rtd.py","file_url":"https://github.com/nikitabalabin/topdis/blob/HEAD/BetaTCVAE_TopDis/rtd.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"12c61458f7a34695"}},{"code_sha256_prefix":"c1f885bc16f810ac","entry":"get_test_image","repo":"ilyatrofimov/sftd","repo_kind":"listed","path":"SHAPR_torch+SFTD/shapr/data_generator.py","file_url":"https://github.com/ilyatrofimov/sftd/blob/HEAD/SHAPR_torch%2BSFTD/shapr/data_generator.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"c1f885bc16f810ac"}},{"code_sha256_prefix":"b746f94350810053","entry":"graph2matrix","repo":"ilyatrofimov/sftd","repo_kind":"listed","path":"sftd/sftd.py","file_url":"https://github.com/ilyatrofimov/sftd/blob/HEAD/sftd/sftd.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"b746f94350810053"}},{"code_sha256_prefix":"bdc2d395cd0ad8b6","entry":"import_image","repo":"ilyatrofimov/sftd","repo_kind":"listed","path":"SHAPR_torch+SFTD/shapr/utils.py","file_url":"https://github.com/ilyatrofimov/sftd/blob/HEAD/SHAPR_torch%2BSFTD/shapr/utils.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"bdc2d395cd0ad8b6"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}