arXiv Statistics ML By Misha Oberski, Valentijn Oldenburg, Xanthos Kekkos, Soham Chaudhuri, Emma Oosterhuis, Floris de Kam, Sagi Schwartz, Alison Pouplin, Federica Valeau

How Geometry Shapes Generative Model Evaluation on Riemannian Manifolds

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arXiv Machine Learning
Oct 2

RW-Flow: One-Step Generation on Compact Manifolds via Wasserstein Gradient Flows

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 Machine Learning
Oct 21

A Likely Geometry of Generative Models

arXiv:2510.26266v3 Announce Type: replace Abstract: The geometry of generative models serves as the basis for interpolation, model inspection, and more. Unfortunately, most generative models lack a p...

By Frederik M\"obius Rygaard, Shen Zhu, Yinzhu Jin, S{\o}ren Hauberg, Tom Fletcher
arXiv Machine Learning
Oct 7

Constant-Curvature Sliced Gromov-Wasserstein for Heterogeneous Cross-Curvature Alignment

The paper introduces Constant‑Curvature Sliced Gromov‑Wasserstein (CCSGW), a new divergence for aligning probability distributions on heterogeneous constant‑curvature spaces such as hyperbolic and spherical manifolds. It extends sliced Gromov‑Wasserstein by adding geodesic‑based one‑dimensional projections for spherical spaces, enabling efficient and principled comparison across manifolds with different curvatures while preserving intrinsic geometric relationships. The authors provide theoretical analysis showing that CCSGW controls intrinsic geometric discrepancy and demonstrate consistent performance gains when integrated into mixed‑curvature learning tasks like graph anomaly detection, node classification, and multimodal learning.

By Shanglin Li, Wenjing Lu, Muyang Li, Nicu Sebe, Ziheng Chen