# Expressivity In Multimodal Contrastive Learning

arXiv: https://arxiv.org/abs/2608.17203 · HTML: https://mlsanity.com/paper/2608.17203/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Prompt learning and adaptation of CLIP, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 99 of its 125 references that are in the map.
- First posted on arXiv 17 Aug 2026.

## Placed in

- Multimodal LLMs / vision-language models / [Prompt learning and adaptation of CLIP](https://mlsanity.com/mllm/prompt-learning-and-adaptation-of-clip/)

## Builds on (most cited first, 30 of 99)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [BLIP-2: Bootstrapping Language-Image Pre-training with Frozen Image Encoders and Large Language Models](https://mlsanity.com/paper/2301.12597/) (2023)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Improved Baselines with Visual Instruction Tuning](https://mlsanity.com/paper/2310.03744/) (2023)
- [Flamingo: a Visual Language Model for Few-Shot Learning](https://mlsanity.com/paper/2204.14198/) (2022)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Scaling Up Visual and Vision-Language Representation Learning With Noisy Text Supervision](https://mlsanity.com/paper/2102.05918/) (2021)
- [Align before Fuse: Vision and Language Representation Learning with Momentum Distillation](https://mlsanity.com/paper/2107.07651/) (2021)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Big Self-Supervised Models are Strong Semi-Supervised Learners](https://mlsanity.com/paper/2006.10029/) (2020)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [CoCa: Contrastive Captioners are Image-Text Foundation Models](https://mlsanity.com/paper/2205.01917/) (2022)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [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)
- [CogVLM: Visual Expert for Pretrained Language Models](https://mlsanity.com/paper/2311.03079/) (2023)
- [CLIP4Clip: An Empirical Study of CLIP for End to End Video Clip Retrieval](https://mlsanity.com/paper/2104.08860/) (2021)
- [CLIPort: What and Where Pathways for Robotic Manipulation](https://mlsanity.com/paper/2109.12098/) (2021)
- [NExT-GPT: Any-to-Any Multimodal LLM](https://mlsanity.com/paper/2309.05519/) (2023)
- [Hypersim: A Photorealistic Synthetic Dataset for Holistic Indoor Scene Understanding](https://mlsanity.com/paper/2011.02523/) (2020)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [A Theoretical Analysis of Contrastive Unsupervised Representation Learning](https://mlsanity.com/paper/1902.09229/) (2019)
- [Image Segmentation Using Text and Image Prompts](https://mlsanity.com/paper/2112.10003/) (2021)
- [MotionCLIP: Exposing Human Motion Generation to CLIP Space](https://mlsanity.com/paper/2203.08063/) (2022)
- [Understanding Dimensional Collapse in Contrastive Self-supervised Learning](https://mlsanity.com/paper/2110.09348/) (2021)

## Abstract (arXiv)

Contrastive learning has become a cornerstone of modern representation learning, powering CLIP-style models that underpin text-to-image generation, vision-language models, and retrieval across a rapidly growing range of modalities. Despite this empirical success, the expressive power of these architectures remains poorly understood. To gain insight, we study expressivity by adopting a population-level, density-estimation viewpoint: each architecture comprises a parameterized set of densities whose parameters may be chosen to approximate the joint distribution of the modalities. This isolates a question of pure representational capacity: which joint distributions can a given contrastive family of parameterizations approximate to arbitrary accuracy? We show that expressivity is sharply architecture-dependent. For two modalities, the simple two-tower CLIP architecture is a universal approximator. A natural generalization of CLIP, widely used in practice when three or more modalities are present, is based on a loss found by summing over all pairwise similarities. This provably cannot represent arbitrary joint distributions, although we prove that it remains expressive enough to match all pairwise conditionals. Motivated by this gap, we propose Hadamard-CLIP, which adds a single learned weight vector on top of the existing encoders and restores universal approximation of the joint for any number of modalities while preserving CLIP's fast, precomputable-embedding retrieval.