Dual-guided Hierarchical Edge Localization for Large-scale Optimal Transport Across Dimensions
Optimal transport (OT) compares distributions and aligns datasets in machine learning, yet unregularized discrete OT requires a linear program with quadratically many transport variables. We propose HELLO, a hierarchical solver that casts large-scale discrete OT as edge localization and uses dual potentials to guide both coarse-to-fine initialization and within-level refinement. Initialization propagates coarse dual potentials across a recursive subsampling hierarchy to assign candidate edges. Refinement then iteratively inserts the largest dual violators in each row and column until the relative KKT residual meets a prescribed tolerance, while budgeted pruning ensures linear memory compl...
| Authors | Wenzhou Xia, Qiaoqiao Ding, Jingwei Liang et al. |
|---|---|
| Primary category | cs.LG |
| Published | 11 September 2026 |
| Last updated at source | 11 September 2026 |
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