{"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/fast-and-scalable-wasserstein-1-neural","title":"Fast and scalable Wasserstein-1 neural optimal transport solver for single-cell perturbation prediction","arxiv_id":"2411.00614","date":"2024-11-01","proceeding":null,"authors":["Yanshuo Chen","Zhengmian Hu","Wei Chen","Heng Huang"],"abstract":"\\textbf{Motivation:} Predicting single-cell perturbation responses requires mapping between two unpaired single-cell data distributions. Optimal transport (OT) theory provides a principled framework for constructing such mappings by minimizing transport cost. Recently, Wasserstein-2 ($W_2$) neural optimal transport solvers (\\textit{e.g.}, CellOT) have been employed for this prediction task. However, $W_2$ OT relies on the general Kantorovich dual formulation, which involves optimizing over two conjugate functions, leading to a complex min-max optimization problem that converges slowly. \\\\ \\textbf{Results:} To address these challenges, we propose a novel solver based on the Wasserstein-1 ($W_1$) dual formulation. Unlike $W_2$, the $W_1$ dual simplifies the optimization to a maximization problem over a single 1-Lipschitz function, thus eliminating the need for time-consuming min-max optimization. While solving the $W_1$ dual only reveals the transport direction and does not directly provide a unique optimal transport map, we incorporate an additional step using adversarial training to determine an appropriate transport step size, effectively recovering the transport map. Our experiments demonstrate that the proposed $W_1$ neural optimal transport solver can mimic the $W_2$ OT solvers in finding a unique and ``monotonic\" map on 2D datasets. Moreover, the $W_1$ OT solver achieves performance on par with or surpasses $W_2$ OT solvers on real single-cell perturbation datasets. Furthermore, we show that $W_1$ OT solver achieves $25 \\sim 45\\times$ speedup, scales better on high dimensional transportation task, and can be directly applied on single-cell RNA-seq dataset with highly variable genes. \\\\ \\textbf{Availability and Implementation:} Our implementation and experiments are open-sourced at https://github.com/poseidonchan/w1ot.","url_abs":"https://arxiv.org/abs/2411.00614v2","url_pdf":"https://arxiv.org/pdf/2411.00614v2.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":"fast-and-scalable-wasserstein-1-neural","repo_url":"https://github.com/poseidonchan/w1ot","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2411.00614","atlas_url":"https://app.syntology.ai/?focus=2411.00614","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}