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This paper refines the CLIP framework by theoretically leveraging the linear structure of pointwise mutual information within a reproducing kernel Hilbert space to optimize similarity computation. The proposed KME-CLIP method is shown to reduce contrastive loss closer to its optimal theoretical limit as data scales, offering a mathematically grounded improvement over current implementations.
Theoretical Refinement of CLIP by Utilizing Linear Structure of Optimal Similarity
arXiv:2510.15508v2 Announce Type: replace Abstract: 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.
Abstract: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.
Machine Learning (cs.LG); Numerical Analysis (math.NA); Machine Learning (stat.ML)
arXiv:2510.15508 [cs.LG]
(or arXiv:2510.15508v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2510.15508 Focus to learn more arXiv-issued DOI via DataCite
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