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Recent advances in contrastive learning have enlightened diverse applications across various semi-supervised fields. Jointly training supervised learning and unsupervised learning with a shared feature encoder becomes a common scheme. Though it benefits from taking advantage of both feature-dependent information from self-supervised learning and label-dependent information from supervised learning, this scheme remains suffering from bias of the classifier. In this work, we systematically explore the relationship between self-supervised learning and supervised learning, and study how self-supervised learning helps robust data-efficient deep learning. We propose hyperspherical consistency regularization (HCR), a simple yet effective plug-and-play method, to regularize the classifier using feature-dependent information and thus avoid bias from labels. Specifically, HCR first projects logits from the classifier and feature projections from the projection head on the respective hypersphere, then it enforces data points on hyperspheres to have similar structures by minimizing binary cross entropy of pairwise distances' similarity metrics. Extensive experiments on semi-supervised and weakly-supervised learning demonstrate the effectiveness of our method, by showing superior performance with HCR.