Canonicalizing Multimodal Contrastive Representation Learning
This work addresses the challenge of ensuring consistency and enabling backward-compatible upgrades in multimodal AI systems, with incremental theoretical and practical contributions.
The paper tackles the problem of aligning representation spaces across independently trained multimodal contrastive models, showing that an orthogonal map can systematically relate their embedding spaces for both images and text, with theoretical proof and empirical validation across models like CLIP, SigLIP, and FLAVA.
As models and data scale, independently trained networks often induce analogous notions of similarity. But, matching similarities is weaker than establishing an explicit correspondence between the representation spaces, especially for multimodal models, where consistency must hold not only within each modality, but also for the learned image-text coupling. We therefore ask: given two independently trained multimodal contrastive models (with encoders $(f, g)$ and $(\widetilde{f},\widetilde{g})$) -- trained on different distributions and with different architectures -- does a systematic geometric relationship exist between their embedding spaces? If so, what form does it take, and does it hold uniformly across modalities? In this work, we show that across model families such as CLIP, SigLIP, and FLAVA, this geometric relationship is well approximated by an orthogonal map (up to a global mean shift), i.e., there exists an orthogonal map $Q$ where $Q^\top Q = I$ such that $\widetilde{f}(x)\approx Q f(x)$ for paired images $x$. Strikingly, the same $Q$ simultaneously aligns the text encoders i.e., $\widetilde{g}(y)\approx Q g(y)$ for texts $y$. Theoretically, we prove that if the multimodal kernel agrees across models on a small anchor set i.e. $\langle f(x), g(y)\rangle \approx \langle \widetilde{f}(x), \widetilde{g}(y)\rangle$, then the two models must be related by a single orthogonal map $Q$ and the same $Q$ maps images and text across models. More broadly, this finding enables backward-compatible model upgrades, avoiding costly re-embedding, and has implications for the privacy of learned representations. Our project page: https://canonical-multimodal.github.io/