Sliced Inner Product Gromov-Wasserstein Distances

• URL: http://arxiv.org/abs/2605.08546v1
• Date: Fri, 08 May 2026 23:15:59 GMT
• Title: Sliced Inner Product Gromov-Wasserstein Distances
• Abstract summary: 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.<n>We propose a sliced IGW distance that enjoys a natural rotational invariance property, and study its structural and computational properties.<n> Numerical experiments validating our theory are presented, followed by applications to heterogeneous clustering of text data and language model representation comparison.
• Score: 17.413570378872453
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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