Title: Bi-tuning of Pre-trained Representations. Abstract: It is common within the deep learning community to first pre-train a deep neural network from a large-scale dataset and then fine-tune the pre-trained model to a specific downstream task. Recently, both supervised and unsupervised pre-training approaches to learning representations have achieved remarkable advances, which exploit the discriminative knowledge of labels and the intrinsic structure of data, respectively. It follows natural intuition that both discriminative knowledge and intrinsic structure of the downstream task can be useful for fine-tuning, however, existing fine-tuning methods mainly leverage the former and discard the latter. A question arises: How to fully explore the intrinsic structure of data for boosting fine-tuning? In this paper, we propose Bi-tuning, a general learning framework to fine-tuning both supervised and unsupervised pre-trained representations to downstream tasks. Bi-tuning generalizes the vanilla fine-tuning by integrating two heads upon the backbone of pre-trained representations: a classifier head with an improved contrastive cross-entropy loss to better leverage the label information in an instance-contrast way, and a projector head with a newly-designed categorical contrastive learning loss to fully exploit the intrinsic structure of data in a category-consistent way. Comprehensive experiments confirm that Bi-tuning achieves state-of-the-art results for fine-tuning tasks of both supervised and unsupervised pre-trained models by large margins (e.g.~10.7\% absolute rise in accuracy on CUB in low-data regime).