arXiv Machine Learning By Dominik Schnaus, Thomas Dag\`es, Daniel Cremers, Xi Wang, Phillip Isola

Shared Geometry As A Rosetta Stone: Cross-Modal Alignment Without Paired Data

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The paper proposes that independently trained multimodal models often share a common geometric structure, allowing cross‑modal alignment without paired data. Using a Wasserstein Procrustes approach with a coarse geometric initialization, the authors align two disjoint embedding sets by estimating a single orthogonal map, achieving consistent alignment across datasets and modalities. While paired examples can further improve performance, the method already outperforms existing techniques in the few‑pair regime and enables text‑to‑image generation without paired data.

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