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{arxiv.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}
}