{"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/phom-gem-persistent-homology-for-generative","title":"PHom-GeM: Persistent Homology for Generative Models","arxiv_id":"1905.09894","date":"2019-05-23","proceeding":null,"authors":["Jeremy Charlier","Radu State","Jean Hilger"],"abstract":"Generative neural network models, including Generative Adversarial Network (GAN) and Auto-Encoders (AE), are among the most popular neural network models to generate adversarial data. The GAN model is composed of a generator that produces synthetic data and of a discriminator that discriminates between the generator's output and the true data. AE consist of an encoder which maps the model distribution to a latent manifold and of a decoder which maps the latent manifold to a reconstructed distribution. However, generative models are known to provoke chaotically scattered reconstructed distribution during their training, and consequently, incomplete generated adversarial distributions. Current distance measures fail to address this problem because they are not able to acknowledge the shape of the data manifold, i.e. its topological features, and the scale at which the manifold should be analyzed. We propose Persistent Homology for Generative Models, PHom-GeM, a new methodology to assess and measure the distribution of a generative model. PHom-GeM minimizes an objective function between the true and the reconstructed distributions and uses persistent homology, the study of the topological features of a space at different spatial resolutions, to compare the nature of the true and the generated distributions. Our experiments underline the potential of persistent homology for Wasserstein GAN in comparison to Wasserstein AE and Variational AE. The experiments are conducted on a real-world data set particularly challenging for traditional distance measures and generative neural network models. PHom-GeM is the first methodology to propose a topological distance measure, the bottleneck distance, for generative models used to compare adversarial samples in the context of credit card transactions.","url_abs":"https://arxiv.org/abs/1905.09894v1","url_pdf":"https://arxiv.org/pdf/1905.09894v1.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":"phom-gem-persistent-homology-for-generative","repo_url":"https://github.com/dagrate/phomgem","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":null,"task_name":"Generative Adversarial Network"}],"methods":[{"method_slug":"ae","method_name":"AE"},{"method_slug":"convolution","method_name":"Convolution"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1905.09894","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1905.09894"}},"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/dagrate/phomgem","reach":null}],"summary":{"ran_honours":1},"by_repo_kind":{"official":{"samples":1,"ran":1,"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":1,"samples":[{"code_sha256_prefix":"006fbad2a74f254c","entry":"scaleX","repo":"dagrate/phomgem","repo_kind":"official","path":"TopWGAN_2.py","file_url":"https://github.com/dagrate/phomgem/blob/HEAD/TopWGAN_2.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":"006fbad2a74f254c"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}