Theoretical Refinement of CLIP by Utilizing Linear Structure of Optimal Similarity

In this study, we propose an enhancement to the similarity computation mechanism in multimodal contrastive pretraining frameworks such as CLIP. Prior theoretical research has demonstrated that the optimal similarity metrics between paired modalities should correspond to the pointwise mutual information (PMI) between the two modalities. However, the current implementations of CLIP and its variants fail to fully utilize the underlying linear structure of PMI. We therefore propose KME-CLIP, which leverages this structure through the inner product in a reproducing kernel Hilbert space (RKHS). We theoretically prove that, under our assumptions, the KME-CLIP similarity can bring the contrastive loss arbitrarily close to its optimal value, which is attained by PMI, as the size of the point set grows, and we empirically evaluate KME-CLIP against CLIP and its kernel-based variants across several retrieval and classification tasks.