{"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/2-wasserstein-approximation-via-restricted","title":"2-Wasserstein Approximation via Restricted Convex Potentials with Application to Improved Training for GANs","arxiv_id":"1902.07197","date":"2019-02-19","proceeding":null,"authors":["Amirhossein Taghvaei","Amin Jalali"],"abstract":"We provide a framework to approximate the 2-Wasserstein distance and the\noptimal transport map, amenable to efficient training as well as statistical\nand geometric analysis. With the quadratic cost and considering the Kantorovich\ndual form of the optimal transportation problem, the Brenier theorem states\nthat the optimal potential function is convex and the optimal transport map is\nthe gradient of the optimal potential function. Using this geometric structure,\nwe restrict the optimization problem to different parametrized classes of\nconvex functions and pay special attention to the class of input-convex neural\nnetworks. We analyze the statistical generalization and the discriminative\npower of the resulting approximate metric, and we prove a restricted\nmoment-matching property for the approximate optimal map. Finally, we discuss a\nnumerical algorithm to solve the restricted optimization problem and provide\nnumerical experiments to illustrate and compare the proposed approach with the\nestablished regularization-based approaches. We further discuss practical\nimplications of our proposal in a modular and interpretable design for GANs\nwhich connects the generator training with discriminator computations to allow\nfor learning an overall composite generator.","url_abs":"http://arxiv.org/abs/1902.07197v1","url_pdf":"http://arxiv.org/pdf/1902.07197v1.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":"2-wasserstein-approximation-via-restricted","repo_url":"https://github.com/facebookresearch/w2ot","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"jax","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1902.07197","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1902.07197"}},"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/facebookresearch/w2ot","reach":null}],"summary":{"unverified":1},"by_repo_kind":{},"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":"7fb9bfa9b31ec695","entry":"plot_conj","repo":null,"repo_kind":null,"path":null,"file_url":null,"link_basis":"identical_code_first_harvested_elsewhere","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":null,"inline_ok":false,"mcp_get_code":{"code_sha256":"7fb9bfa9b31ec695"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}