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Beyond Procrustes distances: a multilinear Gromov-Wasserstein distance capturing chirality

arXiv · AI, language, vision and robotics · article · Aug 27, 2026 · UTC

Efficiently and robustly analyzing shape data is critical across many scientific disciplines. While chirality is a fundamental property in numerous applications - most notably in molecular science - existing shape analysis metrics fail to distinguish between a shape and its mirror image. To address this gap, we introduce a multilinear generalization of the Gromov-Wasserstein objective. Under mild assumptions, this objective yields a distance between shapes, represented as probability distributions quotiented by a symmetry group $G$. In particular, for $G = SO(d)$, we introduce the Chiral Gromo

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