[Submitted on 23 Oct 2026]
Abstract:While multimodal contrastive models like CLIP and CLAP successfully learn shared representations, their embeddings typically exhibit a persistent emph{modality gap}. We propose addressing this separation through a purely geometric approach: changing 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 acts as a structural prior; its nonnegative, unit-mass constraints serve as a cross-modal calibration that forces both modalities to ground themselves in the same coordinate system. By attaching lightweight softmax adapters and using Total Variation similarity, we reduce the centroid $ell_2$ gap by 97–99% across five multimodal retrieval benchmarks. This confirms that simplicial geometry induces genuine semantic alignment, matching or exceeding the retrieval performance of standard unconstrained models.
Submission history
From: Shubham Gupta [view email]
[v1] Fri, 23 Oct 2026 16:57:48 UTC (90 KB)
