# Weighted Point Set Embedding for Multimodal Contrastive Learning Toward Optimal Similarity Metric

arXiv: https://arxiv.org/abs/2404.19228 · HTML: https://mlsanity.com/paper/2404.19228/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 61 references that are in the map.
- First posted on arXiv 30 Apr 2024.

## Builds on (most cited first, 30 of 42)

- [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)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Flamingo: a Visual Language Model for Few-Shot Learning](https://mlsanity.com/paper/2204.14198/) (2022)
- [Scaling Up Visual and Vision-Language Representation Learning With Noisy Text Supervision](https://mlsanity.com/paper/2102.05918/) (2021)
- [Fine-Grained Visual Classification of Aircraft](https://mlsanity.com/paper/1306.5151/) (2013)
- [An Empirical Study of Training Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.02057/) (2021)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Conceptual 12M: Pushing Web-Scale Image-Text Pre-Training To Recognize Long-Tail Visual Concepts](https://mlsanity.com/paper/2102.08981/) (2021)
- [ImageBind: One Embedding Space To Bind Them All](https://mlsanity.com/paper/2305.05665/) (2023)
- [Learning Representations by Maximizing Mutual Information Across Views](https://mlsanity.com/paper/1906.00910/) (2019)
- [Contrastive Learning of Medical Visual Representations from Paired Images and Text](https://mlsanity.com/paper/2010.00747/) (2020)
- [A Theoretical Analysis of Contrastive Unsupervised Representation Learning](https://mlsanity.com/paper/1902.09229/) (2019)
- [SLIP: Self-supervision meets Language-Image Pre-training](https://mlsanity.com/paper/2112.12750/) (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)
- [On Mutual Information Maximization for Representation Learning](https://mlsanity.com/paper/1907.13625/) (2019)
- [Provable Guarantees for Self-Supervised Deep Learning with Spectral Contrastive Loss](https://mlsanity.com/paper/2106.04156/) (2021)
- [Contrastive Learning Inverts the Data Generating Process](https://mlsanity.com/paper/2102.08850/) (2021)
- [Wav2CLIP: Learning Robust Audio Representations From CLIP](https://mlsanity.com/paper/2110.11499/) (2021)
- [Contrastive learning, multi-view redundancy, and linear models](https://mlsanity.com/paper/2008.10150/) (2020)
- [Hyperbolic Image-Text Representations](https://mlsanity.com/paper/2304.09172/) (2023)

## Built on by (most cited first, 6 of 6)

- [Zero-Flow Encoders](https://mlsanity.com/paper/2602.00797/) (2026)
- [Theoretical Refinement of CLIP by Utilizing Linear Structure of Optimal Similarity](https://mlsanity.com/paper/2510.15508/) (2025)
- [The Geometric Mechanics of Contrastive Representation Learning: Alignment Potentials, Entropic Dispersion, and Cross-modal Divergence](https://mlsanity.com/paper/2601.19597/) (2026)
- [Robust LLM Watermarking with Minimal Semantic Distortion for IP Protection](https://mlsanity.com/paper/2605.23175/) (2026)
- [RE-TRIANGLE: Does TRIANGLE Enable Multimodal Alignment Beyond Cosine Similarity in Retrieval?](https://mlsanity.com/paper/2605.27436/) (2026)
- [Expressivity In Multimodal Contrastive Learning](https://mlsanity.com/paper/2608.17203/) (2026)

## Abstract (arXiv)

In typical multimodal contrastive learning, such as CLIP, encoders produce one point in the latent representation space for each input. However, one-point representation has difficulty in capturing the relationship and the similarity structure of a huge amount of instances in the real world. For richer classes of the similarity, we propose the use of weighted point sets, namely, sets of pairs of weight and vector, as representations of instances. In this work, we theoretically show the benefit of our proposed method through a new understanding of the contrastive loss of CLIP, which we call symmetric InfoNCE. We clarify that the optimal similarity that minimizes symmetric InfoNCE is the pointwise mutual information, and show an upper bound of excess risk on downstream classification tasks of representations that achieve the optimal similarity. In addition, we show that our proposed similarity based on weighted point sets consistently achieves the optimal similarity. To verify the effectiveness of our proposed method, we demonstrate pretraining of text-image representation models and classification tasks on common benchmarks.