将嵌入从球面改到单纯形，CLIP 模态间隙最高缩小 99%
Closing the Modality Gap via Simplex-Constrained Representations
把 CLIP 的嵌入从球面挪到单纯形，模态间隙直接砍掉 97% 以上，检索还不掉点，想法挺巧。
一篇 arXiv 论文提出用几何方法解决 CLIP、CLAP 等多模态对比模型的模态间隙问题：把嵌入空间从单位球改为概率单纯形。方法通过轻量 softmax 适配器和 Total Variation 相似度，使两种模态落在同一坐标系。在五个多模态检索基准上，质心 l2 间隙减少 97--99%，检索性能达到或超过标准无约束模型。
Closing the Modality Gap via Simplex-Constrained Representations
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, $Δ^{d-1}$. 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.