# Theoretical Refinement of CLIP by Utilizing Linear Structure of Optimal Similarity

arXiv: https://arxiv.org/abs/2510.15508 · HTML: https://mlsanity.com/paper/2510.15508/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 50 references that are in the map.
- First posted on arXiv 17 Oct 2025.

## Builds on (most cited first, 30 of 36)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [BLIP: Bootstrapping Language-Image Pre-training for Unified Vision-Language Understanding and Generation](https://mlsanity.com/paper/2201.12086/) (2022)
- [Scaling Up Visual and Vision-Language Representation Learning With Noisy Text Supervision](https://mlsanity.com/paper/2102.05918/) (2021)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Fine-Grained Visual Classification of Aircraft](https://mlsanity.com/paper/1306.5151/) (2013)
- [Align before Fuse: Vision and Language Representation Learning with Momentum Distillation](https://mlsanity.com/paper/2107.07651/) (2021)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [Microsoft COCO Captions: Data Collection and Evaluation Server](https://mlsanity.com/paper/1504.00325/) (2015)
- [Flickr30k Entities: Collecting Region-to-Phrase Correspondences for Richer Image-to-Sentence Models](https://mlsanity.com/paper/1505.04870/) (2015)
- [Conceptual 12M: Pushing Web-Scale Image-Text Pre-Training To Recognize Long-Tail Visual Concepts](https://mlsanity.com/paper/2102.08981/) (2021)
- [FILIP: Fine-grained Interactive Language-Image Pre-Training](https://mlsanity.com/paper/2111.07783/) (2021)
- [Mind the Gap: Understanding the Modality Gap in Multi-modal Contrastive Representation Learning](https://mlsanity.com/paper/2203.02053/) (2022)
- [SLIP: Self-supervision meets Language-Image Pre-training](https://mlsanity.com/paper/2112.12750/) (2021)
- [Supervision Exists Everywhere: A Data Efficient Contrastive Language-Image Pre-training Paradigm](https://mlsanity.com/paper/2110.05208/) (2021)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [AudioCLIP: Extending CLIP to Image, Text and Audio](https://mlsanity.com/paper/2106.13043/) (2021)
- [MaskCLIP: Masked Self-Distillation Advances Contrastive Language-Image Pretraining](https://mlsanity.com/paper/2208.12262/) (2022)
- [Hyperbolic Image-Text Representations](https://mlsanity.com/paper/2304.09172/) (2023)
- [CyCLIP: Cyclic Contrastive Language-Image Pretraining](https://mlsanity.com/paper/2205.14459/) (2022)
- [Benchmarking Spatial Relationships in Text-to-Image Generation](https://mlsanity.com/paper/2212.10015/) (2022)
- [CLOOB: Modern Hopfield Networks with InfoLOOB Outperform CLIP](https://mlsanity.com/paper/2110.11316/) (2021)
- [The Neglected Tails in Vision-Language Models](https://mlsanity.com/paper/2401.12425/) (2024)
- [The Power of Contrast for Feature Learning: A Theoretical Analysis](https://mlsanity.com/paper/2110.02473/) (2021)
- [Understanding Transferable Representation Learning and Zero-shot Transfer in CLIP](https://mlsanity.com/paper/2310.00927/) (2023)
- [Positively Weighted Kernel Quadrature via Subsampling](https://mlsanity.com/paper/2107.09597/) (2021)

## Built on by (most cited first, 2 of 2)

- [The Geometric Mechanics of Contrastive Representation Learning: Alignment Potentials, Entropic Dispersion, and Cross-modal Divergence](https://mlsanity.com/paper/2601.19597/) (2026)
- [Expressivity In Multimodal Contrastive Learning](https://mlsanity.com/paper/2608.17203/) (2026)

## Abstract (arXiv)

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.