Papers › Fast and scalable Wasserstein-1 neural optimal transport solver for single-cell...
Fast and scalable Wasserstein-1 neural optimal transport solver for single-cell perturbation prediction
Yanshuo Chen, Zhengmian Hu, Wei Chen, Heng Huang
\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 (W₂) neural optimal transport solvers (\textit{e.g.}, CellOT) have been employed for this prediction task. However, W₂ 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 (W₁) dual formulation. Unlike W₂, the W₁ 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 W₁ 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 W₁ neural optimal transport solver can mimic the W₂ OT solvers in finding a unique and ``monotonic" map on 2D datasets. Moreover, the W₁ OT solver achieves performance on par with or surpasses W₂ OT solvers on real single-cell perturbation datasets. Furthermore, we show that W₁ OT solver achieves 25 ∼45× 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.
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