{"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/a-truncated-newton-method-for-optimal-1","title":"A Truncated Newton Method for Optimal Transport","arxiv_id":"2504.02067","date":"2025-04-02","proceeding":"International Conference on Learning Representations (ICLR) 2025 4","authors":["Mete Kemertas","Amir-Massoud Farahmand","Allan D. Jepson"],"abstract":"Developing a contemporary optimal transport (OT) solver requires navigating trade-offs among several critical requirements: GPU parallelization, scalability to high-dimensional problems, theoretical convergence guarantees, empirical performance in terms of precision versus runtime, and numerical stability in practice. With these challenges in mind, we introduce a specialized truncated Newton algorithm for entropic-regularized OT. In addition to proving that locally quadratic convergence is possible without assuming a Lipschitz Hessian, we provide strategies to maximally exploit the high rate of local convergence in practice. Our GPU-parallel algorithm exhibits exceptionally favorable runtime performance, achieving high precision orders of magnitude faster than many existing alternatives. This is evidenced by wall-clock time experiments on 24 problem sets (12 datasets $\\times$ 2 cost functions). The scalability of the algorithm is showcased on an extremely large OT problem with $n \\approx 10^6$, solved approximately under weak entopric regularization.","url_abs":"https://arxiv.org/abs/2504.02067v1","url_pdf":"https://arxiv.org/pdf/2504.02067v1.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":"a-truncated-newton-method-for-optimal-1","repo_url":"https://github.com/metekemertas/mdot_tnt","is_official":0,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":null,"task_name":"GPU"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2504.02067","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2504.02067"}},"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/metekemertas/mdot_tnt","reach":null}],"summary":{"unverified":1},"by_repo_kind":{"named_in_paper":{"samples":1,"ran":0,"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":"f5141b118dcc550a","entry":"TruncatedNewtonProjector","repo":"metekemertas/mdot_tnt","repo_kind":"named_in_paper","path":"mdot_tnt/truncated_newton.py","file_url":"https://github.com/metekemertas/mdot_tnt/blob/HEAD/mdot_tnt/truncated_newton.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NOASSERTION","inline_ok":false,"mcp_get_code":{"code_sha256":"f5141b118dcc550a"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}