The Hyperspherical Geometry of CLIP Latent Space: A Semantic Mixture Model

Contrastive Language-Image Pretraining learns a shared representation space through large-scale contrastive learning. However, existing methods that enforce global consistency regularization overlook a key challenge: the inherent information asymmetry between images and text: captions typically describe only one specific aspect of an image, thus images with similar visual content can be paired with completely divergent textual content and semantic information. Consequently, global regularizers inadvertently impose constraints between visually similar images whose captions describe divergent aspects, introducing semantic distortion into the representation space. We propose AspectCLIP, a framework that reformulates consistency regularization to respect this one-to-many structure. AspectCLIP first partitions training samples into attribute clusters based on textual similarity to identify aspect-coherent groups, then applies full cyclic consistency within each cluster while restricting cross-cluster regularization to prototype-level comparisons. This aspect-guided regularization enforces strict geometric alignment only when images and texts describe a consistent facet, while allowing flexibility across divergent aspects. Extensive experiments on downstream tasks demonstrate that AspectCLIP consistently outperforms traditional methods and achieves a more structured representation space.

Dense vision-language understanding, including object localization, region recognition, and open-vocabulary semantic segmentation, requires associating language concepts with spatially grounded visual regions. CLIP provides a strong foundation for these tasks by learning a shared image-text embedding space from large-scale contrastive pre-training. However, its image-level objective aligns text with a CLS-derived global representation, leaving local vision-language correspondence only indirectly constrained. Existing methods either introduce additional supervision, external models, or task-specific adaptation, while training-free approaches mainly recover dense responses from existing patch features without examining where local semantics become most accessible within CLIP. We introduce TraceCLIP, a training-free framework that recovers latent patch-level semantic evidence by isolating the patch-specific terms written into the CLS attention output. TraceCLIP further converts contribution-derived semantic responses into a semantic-geodesic topology gate that calibrates final-layer patch affinity for dense feature reconstruction. Diagnostic experiments show that these contribution features exhibit strong local semantic discrimination and text-conditioned spatial alignment. On eight zero-shot semantic segmentation benchmarks, TraceCLIP achieves gains of 1.3 to 4.5 points in average mIoU over the strongest prior training-free methods across both backbones and background settings, without additional training, external vision foundation models, or region-level supervision. More broadly, these findings suggest that spatially localized semantics may remain accessible within the internal construction of globally aligned representations.

Vision-language foundation models such as CLIP and SigLIP provide widely used representations for multimodal learning systems. While these models are typically compared through downstream performance, such evaluations often do not explain how their representations differ structurally. In this work, we study this problem through the task of Contrastive Embedding Clustering: identifying sample subsets that are weakly clustered under one representation but strongly clustered under another. We propose \emph{Kernel Optimization for Discrepancy Analysis (KODA)}, a kernel-based framework for contrastive representation comparison and alignment. KODA constructs unified multimodal kernels through modality-wise kernel composition and formulates discrepancy discovery as a constrained optimization problem that searches for coherent structures in one representation while suppressing coherence in a reference representation. This yields interpretable discrepancy directions associated with specific sample subsets and modality interactions. To scale KODA to large vision-language datasets, we develop randomized low-dimensional approximations of joint kernels using random projections, including Random Fourier Features for shift-invariant kernels. Empirically, KODA identifies consistent and interpretable discrepancy structures across vision-language representations and provides sample subsets for representation alignment. The code is available at https://github.com/yokiwuuu/KODA.