The paper introduces EGGroW, efficient algorithms for computing geodesic Gromov-Wasserstein distances using entropic Sinkhorn-like methods, GenusSink techniques, and random features. It addresses the cubic time complexity of traditional GWD calculations on dense intra-space distance matrices, enabling scalable comparisons of probabilistic distributions on general geodesic manifolds and graph shortest‑path distances. The authors demonstrate EGGroW’s effectiveness in downstream tasks such as 3D pose estimation and partial 3D template recovery, showing accurate results where Euclidean‑based methods fail while maintaining a light computational footprint.
By Krzysztof Marcin Choromanski, Derek Long, Ananya Parashar, Dwaipayan Saha
arXiv:2605. 14981v2 Announce Type: replace Abstract: Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system.
By Ao Xu, Tieru Wu
The paper introduces a Nested Inductive Bias framework that uses a two‑stage diffeomorphic composition to pull back non‑Euclidean target geometries onto symmetric positive definite (SPD) manifolds. This approach allows the construction of curvature‑aligned Riemannian classifiers that respect both matrix constraints and the intrinsic relational geometry of data. Empirical results on kinematic, signal processing, and synthetic benchmarks show that class separability degrades when metric curvature does not match the data distribution, and the authors also propose the Rational Conformal Metric (RCM) for robust vectorized architectures.
By Tushar Das
The paper presents a new duality formulation for the Gromov‑Wasserstein distance that applies to all finitely supported metric‑measure spaces, with and without entropic regularization. Using this duality, the authors derive sample‑complexity bounds and limit distributions for empirical GW distances, and introduce algorithms with formal convergence guarantees. These results enable a principled, efficient method for testing isomorphism between distributions on graphs with a fixed number of nodes based on samples.
By Gabriel Rioux, Joanna Marks, Riccardo Passeggeri, Ziv Goldfeld
RW-Flow presents a new one‑step generative framework for data on compact manifolds, leveraging Wasserstein gradient flows. The authors derive a necessary and sufficient identifiability condition for velocity fields on compact, connected Riemannian manifolds, showing that a symmetric, Lipschitz‑continuous cost function yields identifiability iff its Gibbs kernel is nondegenerate. Experiments on geospatial events, protein and RNA torsion angles, and discretized manifolds demonstrate that RW‑Flow surpasses existing one‑step methods across most benchmark settings.
By Ualibyek Nurgulan, Seungwoo Yoo, Prin Phunyaphibarn, Minhyuk Sung
arXiv:2609.25659v1 Announce Type: new
Abstract: Many scientific datasets, such as molecular conformational ensembles or single-cell tissue measurements, are naturally modeled as meta-distributions: d...
By Doron Haviv, Edward De Brouwer, Rishabh Anand, Rex Ying, A\"icha Bentaieb, Gabriele Scalia, Hector Corrada Bravo
arXiv:2608. 27774v1 Announce Type: cross Abstract: Efficiently and robustly analyzing shape data is critical across many scientific disciplines.
By Cl\'ement Soubrier, Geoffrey Woollard, Andrew Warren, Khanh Dao Duc
arXiv:2512.03579v2 Announce Type: replace
Abstract: Optimal transport (OT) and Gromov-Wasserstein (GW) alignment provide interpretable geometric frameworks for comparing, transforming, and aggregatin...
By Sanjit Dandapanthula, Aleksandr Podkopaev, Shiva Prasad Kasiviswanathan, Aaditya Ramdas, Ziv Goldfeld
The paper introduces a geometric framework for measuring how far empirical datasets deviate from the Gaussian family using optimal transport theory. It defines two new quantities—the relative Wasserstein angle and the orthogonal projection distance—based on the cone structure of the relative translation invariant quadratic Wasserstein space, and shows that the usual moment‑matching Gaussian is not generally the $W_2$‑nearest Gaussian. Closed‑form expressions are derived for one‑dimensional and several location–scale families, while a numerical approximation is proposed for higher dimensions, with experiments demonstrating convergence, stability, and the angle’s robustness as a non‑Gaussianity indicator.
By Binshuai Wang, Peng Wei
The paper introduces MS‑WDRO, a multi‑source Wasserstein distributionally robust optimization framework for reconstructing complex network topologies from scarce target‑domain data and abundant heterogeneous source data. It fuses sources via a weighted Wasserstein barycenter, builds an ambiguity set around it, and solves a regularized Laplacian estimator using a provably convergent ADMM scheme. The authors provide finite‑sample guarantees, demonstrate that naive aggregation is suboptimal, and show through experiments on synthetic data and the ABIDE I neuroimaging dataset that MS‑WDRO outperforms seven baselines in graph recovery, sample efficiency, and diagnostic utility, especially when target samples are limited.
By Chuansen Peng, Yifan Xia, Jinshan Zhong, Xiaojing Shen
arXiv:2606. 02047v1 Announce Type: cross Abstract: We introduce Convex Distance Operator Transport (CDOT), the first convex optimal transport framework that aligns distributions across heterogeneous domains by jointly preserving feature correspondence and intrinsic geometric structure.
By Junhyoung Chung, Euijong Song, Won Hwa Kim, Gunwoong Park
arXiv:2607. 03145v1 Announce Type: cross Abstract: The informativeness of a training set is as consequential as its size, yet most sampling strategies remain agnostic to the intrinsic geometry of the data distribution.
By Alexandre L. M. Levada