Title: Rethinking Positive Sampling for Contrastive Learning with Kernel. Abstract:   Data augmentation is a crucial component in unsupervised contrastive learning (CL). It determines how positive samples are defined and, ultimately, the quality of the representation. Even if efforts have been made to find efficient augmentations for ImageNet, CL underperforms compared to supervised methods and it is still an open problem in other applications, such as medical imaging, or in datasets with easy-to-learn but irrelevant imaging features. In this work, we propose a new way to define positive samples using kernel theory along with a novel loss called \textit{decoupled uniformity}. We propose to integrate prior information, learnt from generative models viewed as feature extractor, or given as auxiliary attributes, into contrastive learning, to make it less dependent on data augmentation.  We draw a connection between contrastive learning and the conditional mean embedding theory to derive tight bounds on the downstream classification loss.  In an unsupervised setting, we empirically demonstrate that CL benefits from generative models, such as VAE and GAN, to less rely on data augmentations. We validate our framework on vision and medical datasets including CIFAR10, CIFAR100, STL10, ImageNet100, CheXpert and a brain MRI dataset. In the weakly supervised setting, we demonstrate that our formulation provides state-of-the-art results.