Deep Contrastive Learning is Provably (almost) Principal Component Analysis

We show that Contrastive Learning (CL) under a family of loss functions (including InfoNCE) has a game-theoretical formulation, where the \emph{max player} finds representation to maximize contrastiveness, and the \emph{min player} puts weights on pairs of samples with similar representation. We show that the max player who does \emph{representation learning} reduces to Principal Component Analysis for deep linear network, and almost all local minima are global, recovering optimal PCA solutions. Experiments show that the formulation yields comparable (or better) performance on CIFAR10 and STL-10 when extending beyond InfoNCE, yielding novel contrastive losses. Furthermore, we extend our theoretical analysis to 2-layer ReLU networks, showing its difference from linear ones, and proving that feature composition is preferred over picking single dominant feature under strong augmentation.