Abstract
Multimodal representation learning produces high-dimensional embeddings that align diverse modalities in a shared latent space. While this enables strong generalization, it also introduces scalability challenges, both in terms of storage and downstream processing. A key open problem is how to achieve semantic compression, reducing the memory footprint of multimodal embeddings while preserving their ability to represent shared semantic content across modalities. In this paper, we prove a strong connection between reducing the modality gap, which is the residual separation of embeddings from different modalities, and the feasibility of post-training semantic compression. When the gap is sufficiently reduced, embeddings from different modalities but expressing the same semantics share a common portion of the space. Therefore, their centroid is a faithful representation of such a semantic concept. This enables replacing multiple embeddings with a single centroid, yielding significant memor