# SRRM: Improving Recursive Transport Surrogates in the Small-Discrepancy Regime

arXiv: https://arxiv.org/abs/2603.18781 · HTML: https://mlsanity.com/paper/2603.18781/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 34 references that are in the map.
- First posted on arXiv 19 Mar 2026.

## Builds on (most cited first, 15 of 15)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [Max-Sliced Wasserstein Distance and its use for GANs](https://mlsanity.com/paper/1904.05877/) (2019)
- [Large-scale optimal transport map estimation using projection pursuit](https://mlsanity.com/paper/2106.05838/) (2021)
- [Efficient Approximation of Gromov-Wasserstein Distance Using Importance Sparsification](https://mlsanity.com/paper/2205.13573/) (2022)
- [Hilbert Curve Projection Distance for Distribution Comparison](https://mlsanity.com/paper/2205.15059/) (2022)
- [Gaussian Herding across Pens: An Optimal Transport Perspective on Global Gaussian Reduction for 3DGS](https://mlsanity.com/paper/2506.09534/) (2025)
- [A Review on Modern Computational Optimal Transport Methods with Applications in Biomedical Research](https://mlsanity.com/paper/2008.02995/) (2020)
- [Applications of No-Collision Transportation Maps in Manifold Learning](https://mlsanity.com/paper/2304.00199/) (2023)
- [Importance Sparsification for Sinkhorn Algorithm](https://mlsanity.com/paper/2306.06581/) (2023)
- [No-collision Transportation Maps](https://mlsanity.com/paper/1912.02317/) (2019)
- [Extensible grids: uniform sampling on a space-filling curve](https://mlsanity.com/paper/1406.4549/) (2014)
- [HiMAP: Hilbert Mass-Addressed Parameterization for Multivariate Barycenters and Fre'chet Regression](https://mlsanity.com/paper/2603.03674/) (2026)

## Abstract (arXiv)

Recursive partitioning methods provide computationally efficient surrogates for the Wasserstein distance, yet their statistical behavior and their resolution in the small-discrepancy regime remain insufficiently understood. We study Recursive Rank Matching (RRM) as a representative instance of this class under a population-anchored reference. In this setting, we establish consistency and an explicit convergence rate for the anchored empirical RRM under the quadratic cost. We then identify a dominant mismatch mechanism responsible for the loss of resolution in the small-discrepancy regime. Based on this analysis, we introduce Selective Recursive Rank Matching (SRRM), which suppresses the resulting dominant mismatches and yields a higher-fidelity practical surrogate for the Wasserstein distance at moderate additional computational cost.