Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables

Multi-modal contrastive learning as a self-supervised representation learning technique has achieved great success in foundation model training, such as CLIP~\citep{radford2021learning}. In this paper, we study the theoretical properties of the learned representations from multi-modal contrastive learning beyond linear representations and specific data distributions. Our analysis reveals that, enabled by temperature optimization, multi-modal contrastive learning not only maximizes mutual information between modalities but also adapts to intrinsic dimensions of data, which can be much lower than user-specified dimensions for representation vectors. Experiments on both synthetic and real-world datasets demonstrate the ability of contrastive learning to learn low-dimensional and informative representations, bridging theoretical insights and practical performance.

@article{gui2025_2505.12473,
  title={ Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variables },
  author={ Yu Gui and Cong Ma and Zongming Ma },
  journal={arXiv preprint arXiv:2505.12473},
  year={ 2025 }
}