The Convergent Representation of Contrastive Vision-Language Models: Geometry, Modality Gap and Shared Space Alignment

Multimodal contrastive learning (MCL) aims to embed data from two modalities in a shared embedding space. However, in practice, image and text representations occupy completely separated regions of the embedding space, a phenomenon called the modality gap. Meanwhile, empirical findings on how the modality gap affects downstream performance remain inconsistent. These observations motivate two key questions: (1) What causes the modality gap? (2) What determines downstream performance? To address these questions, we develop the first theoretical framework for analyzing the geometry of convergent optimal representations (COR) of MCL when training is optimized. We prove that the modality gap emerges when image and text representations collapse into different subspaces, a phenomenon called dimension collapse. Our theory further reveals that although the modality gap prevents direct alignment between image and text representations, their projections onto the shared subspace can align. Moreover, we show that shared space alignment is a dominant factor in downstream performance, while the effect of the modality gap is limited. Inspired by these findings, we propose Shared Space Alignment (SSA) to improve MCL pretraining by enhancing alignment in the shared space without optimizing for modality gap reduction. Extensive empirical results validate our theoretical analysis and the proposed method.