Multimodal contrastive models such as CLIP and CLAP learn shared representations, yet their embeddings typically exhibit a persistent modality gap. This work introduces a purely geometric remedy: shift the embedding domain from the unit sphere $S^{d-1}$ to the probability simplex $\Delta^{d-1}$. Although both manifolds share the same intrinsic dimension, the simplex’s non‑negative, unit‑mass constraints act as a structural prior that calibrates across modalities, forcing them into a common coordinate system. We attach lightweight softmax adapters to the model and employ Total Variation similarity. Across five multimodal retrieval benchmarks, the centroid $\ell_2$ gap is reduced by 97%–99%, confirming that simplicial geometry induces genuine semantic alignment and even surpasses the retrieval performance of standard unconstrained models.
Review