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Fast Alignment of Embeddings: Computational Guarantees for Anisotropic Procrustes-Wasserstein

NeurIPS 2026 · Point clouds › Point cloud classification · approach: Equivariant point cloud networks

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Studies computational guarantees for the Procrustes-Wasserstein problem under a planted anisotropic Gaussian model, where two point clouds are related by an unknown relabeling and orthogonal transformation.

Problem

Matching unlabeled point clouds related by a latent orthogonal transformation (Procrustes-Wasserstein) for representation alignment and domain adaptation, where computational theory is limited.

Approach

Analyzes a planted Gaussian model in which Y is obtained from X via an unknown permutation and an unknown orthogonal transformation, with anisotropic (non-isotropic) covariance, to derive computational guarantees for fast alignment; details beyond the abstract are not available.

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