通过正交变换对齐嵌入模型，实现跨模型兼容与性能提升
When Embedding Models Meet: Procrustes Bounds and Applications
- 基于点积近似保持性，推导出嵌入对齐的紧致误差上界
- 提出Procrustes后处理方法，使不同模型嵌入可直接互换
- 在模型重训练、文本检索和多模态搜索中表现卓越
在相似数据上独立训练的嵌入模型虽能生成稳定表征，但彼此不可直接互换，影响模型重训练、部分升级及多模态搜索等应用。本文研究何时可通过正交变换对齐两组嵌入。我们证明：若成对点积近似保持，则存在一个等距变换可紧密对齐两组嵌入，并给出精确的对齐误差上界。由此提出简单有效的Procrustes后处理方法，使嵌入空间几何结构不变的前提下实现模型间兼容。实验证明该方法在模型重训练兼容性维护、多模型文本检索融合以及混合模态搜索中均取得当前最优性能。
原文摘要 · Abstract (English)
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.
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