When Embedding Models Meet: Procrustes Bounds and Applications
This addresses interoperability challenges in practical applications such as model retraining and multimodal search, but it is incremental as it builds on existing Procrustes methods.
The paper tackles the problem of aligning embedding models trained separately on similar data to enable interoperability, showing that if pairwise dot products are preserved, an isometry exists for close alignment, and it demonstrates effectiveness in applications like text retrieval and mixed-modality search with state-of-the-art performance.
Embedding models trained separately on similar data often produce representations that encode stable information but are not directly interchangeable. This lack of interoperability raises challenges in several practical applications, such as model retraining, partial model upgrades, and multimodal search. Driven by these challenges, we study when two sets of embeddings can be aligned by an orthogonal transformation. We show that if pairwise dot products are approximately preserved, then there exists an isometry that closely aligns the two sets, and we provide a tight bound on the alignment error. This insight yields a simple alignment recipe, Procrustes post-processing, that makes two embedding models interoperable while preserving the geometry of each embedding space. Empirically, we demonstrate its effectiveness in three applications: maintaining compatibility across retrainings, combining different models for text retrieval, and improving mixed-modality search, where it achieves state-of-the-art performance.