{"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/optimal-neural-network-approximation-of","title":"Optimal Neural Network Approximation of Wasserstein Gradient Direction via Convex Optimization","arxiv_id":"2205.13098","date":"2022-05-26","proceeding":null,"authors":["Yifei Wang","Peng Chen","Mert Pilanci","Wuchen Li"],"abstract":"The computation of Wasserstein gradient direction is essential for posterior sampling problems and scientific computing. The approximation of the Wasserstein gradient with finite samples requires solving a variational problem. We study the variational problem in the family of two-layer networks with squared-ReLU activations, towards which we derive a semi-definite programming (SDP) relaxation. This SDP can be viewed as an approximation of the Wasserstein gradient in a broader function family including two-layer networks. By solving the convex SDP, we obtain the optimal approximation of the Wasserstein gradient direction in this class of functions. Numerical experiments including PDE-constrained Bayesian inference and parameter estimation in COVID-19 modeling demonstrate the effectiveness of the proposed method.","url_abs":"https://arxiv.org/abs/2205.13098v1","url_pdf":"https://arxiv.org/pdf/2205.13098v1.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":"optimal-neural-network-approximation-of","repo_url":"https://github.com/ai-submit/optimalwasserstein","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"},{"task_slug":"parameter-estimation","task_name":"parameter estimation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2205.13098","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2205.13098"}},"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/ai-submit/optimalwasserstein","reach":null}],"summary":{"ran_honours":1,"ran_draft_wrong":1,"ran_violates":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":3,"samples":[{"code_sha256_prefix":"1dbace35862da027","entry":"relu","repo":null,"repo_kind":null,"path":null,"file_url":null,"link_basis":"identical_code_first_harvested_elsewhere","language":"python","status":"ran_honours","verification_level":2,"contract_check":"HONOURS","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":null,"inline_ok":false,"mcp_get_code":{"code_sha256":"1dbace35862da027"}},{"code_sha256_prefix":"eb374d9c8042009d","entry":"cvx_nn_gen_mask","repo":"ai-submit/optimalwasserstein","repo_kind":"official","path":"WGD_cvxNN_toy/cvx_nn.py","file_url":"https://github.com/ai-submit/optimalwasserstein/blob/HEAD/WGD_cvxNN_toy/cvx_nn.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"eb374d9c8042009d"}},{"code_sha256_prefix":"05d5f59ee175fe31","entry":"drelu","repo":null,"repo_kind":null,"path":null,"file_url":null,"link_basis":"identical_code_first_harvested_elsewhere","language":"python","status":"ran_violates","verification_level":1,"contract_check":"VIOLATES","metamorphic_tier":"deterministic","behaviour_fingerprint":true,"licence":null,"inline_ok":false,"mcp_get_code":{"code_sha256":"05d5f59ee175fe31"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}