Dual Convex Composition for CLIP Interpretability

Concept decompositions of CLIP need both inspectable provenance and a clear scale for their activations. We present DCC-CLIP, which constructs each concept as a convex mixture of in-domain sample embeddings and reconstructs each sample as a convex mixture of concepts. A cosine objective fits the directional representation while the two weight systems expose dictionary provenance and sample composition. We establish hull containment, sparse representability, and fixed-weight perturbation bounds, distinguishing these properties from semantic interpretability and optimizer stability. Experiments compare adapted NMF/CRAFT and PCA on image classification and image–text alignment. DCC-CLIP obtains reconstruction cosine similarities from 0.947 to 0.993 across the reported dataset–backbone pairs. Semantic consistency, discriminative retention, and insertion/deletion evaluations examine complementary aspects of the resulting explanations. Code is provided in the supplementary material.