Sliced Inner Product Gromov-Wasserstein Distances

Fuente: arXiv
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Autores principales: Gong, Xiaoyun, Rioux, Gabriel, Goldfeld, Ziv
Formato: Preprint
Publicado: 2026
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author Gong, Xiaoyun
Rioux, Gabriel
Goldfeld, Ziv
author_facet Gong, Xiaoyun
Rioux, Gabriel
Goldfeld, Ziv
contents The Gromov-Wasserstein (GW) problem provides a framework for aligning heterogeneous datasets by matching their intrinsic geometry, but its statistical and computational scaling remains an issue for high-dimensional problems. Slicing techniques offer an appealing route to scalability, but, unlike Wasserstein distances, GW problems do not generally admit closed-form solutions in one-dimension. We resolve this problem for the GW problem with inner product cost (IGW), propose a sliced IGW distance that enjoys a natural rotational invariance property, and comprehensively study its structural and computational properties. Numerical experiments validating our theory are presented, followed by applications to heterogeneous clustering of text data and language model representation comparison.
format Preprint
id arxiv_https___arxiv_org_abs_2605_08546
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Sliced Inner Product Gromov-Wasserstein Distances
Gong, Xiaoyun
Rioux, Gabriel
Goldfeld, Ziv
Machine Learning
Optimization and Control
The Gromov-Wasserstein (GW) problem provides a framework for aligning heterogeneous datasets by matching their intrinsic geometry, but its statistical and computational scaling remains an issue for high-dimensional problems. Slicing techniques offer an appealing route to scalability, but, unlike Wasserstein distances, GW problems do not generally admit closed-form solutions in one-dimension. We resolve this problem for the GW problem with inner product cost (IGW), propose a sliced IGW distance that enjoys a natural rotational invariance property, and comprehensively study its structural and computational properties. Numerical experiments validating our theory are presented, followed by applications to heterogeneous clustering of text data and language model representation comparison.
title Sliced Inner Product Gromov-Wasserstein Distances
topic Machine Learning
Optimization and Control
url https://arxiv.org/abs/2605.08546