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As an effective data augmentation method, Mixup synthesizes an extra amount of samples through linear interpolations. Despite its theoretical dependency on data properties, Mixup reportedly performs well as a regularizer and calibrator contributing reliable robustness and generalization to deep model training. In this paper, inspired by Universum Learning which uses out-of-class samples to assist the target tasks, we investigate Mixup from a largely under-explored perspective - the potential to generate in-domain samples that belong to none of the target classes, that is, universum. We find that in the framework of supervised contrastive learning, Mixup-induced universum can serve as surprisingly high-quality hard negatives, greatly relieving the need for large batch sizes in contrastive learning. With these findings, we propose Universum-inspired supervised Contrastive learning (UniCon), which incorporates Mixup strategy to generate Mixup-induced universum as universum negatives and pushes them apart from anchor samples of the target classes. We extend our method to the unsupervised setting, proposing Unsupervised Universum-inspired contrastive model (Un-Uni). Our approach not only improves Mixup with hard labels, but also innovates a novel measure to generate universum data. With a linear classifier on the learned representations, UniCon shows state-of-the-art performance on various datasets. Specially, UniCon achieves 81.7% top-1 accuracy on CIFAR-100, surpassing the state of art by a significant margin of 5.2% with a much smaller batch size, typically, 256 in UniCon vs. 1024 in SupCon using ResNet-50. Un-Uni also outperforms SOTA methods on CIFAR-100. The code of this paper is released on https://github.com/hannaiiyanggit/UniCon.