Contrastive Learning is Spectral Clustering on Similarity Graph

Zhiquan Tan, Yifan Zhang, Jingqin Yang, Yang Yuan

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Keywords: contrastive learning theory, self-supervised learning theory, representation learning theory, CLIP, multi-modal learning theory, markov random field, kernel method

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TL;DR: We prove that contrastive learning is equivalent to spectral clustering on the similarity graph and characterize multi-modal representation learning using this equivalence.

Abstract: Contrastive learning is a powerful self-supervised learning method, but we have a limited theoretical understanding of how it works and why it works. In this paper, we prove that contrastive learning with the standard InfoNCE loss is equivalent to spectral clustering on the similarity graph. Using this equivalence as the building block, we extend our analysis to the CLIP model and rigorously characterize how similar multi-modal objects are embedded together. Motivated by our theoretical insights, we introduce the Kernel-InfoNCE loss, incorporating mixtures of kernel functions that outperform the standard Gaussian kernel on several vision datasets.

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Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

Submission Number: 1212