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Domain adaptation (DA) aims to transfer knowledge from a label-rich source domain to a related but label-scarce target domain. The conventional DA strategy is to align the feature distributions of the two domains. Recently, increasing researches have focused on self-training or other semi-supervised algorithms to explore the data structure of the target domain. However, the bulk of them depend largely on confident samples in order to build reliable pseudo labels, prototypes or cluster centers. Representing the target data structure in such a way would overlook the huge low-confidence samples, resulting in sub-optimal transferability that is biased towards the samples similar to the source domain. To overcome this issue, we propose a novel contrastive learning method by processing low-confidence samples, which encourages the model to make use of the target data structure through the instance discrimination process. To be specific, we create positive and negative pairs only using low-confidence samples, and then re-represent the original features with the classifier weights rather than directly utilizing them, which can better encode the task-specific semantic information. Furthermore, we combine cross-domain mixup to augment the proposed contrastive loss. Consequently, the domain gap can be well bridged through contrastive learning of intermediate representations across domains. We evaluate the proposed method in both unsupervised and semi-supervised DA settings, and extensive experimental results on benchmarks reveal that our method is effective and achieves state-of-the-art performance. The code can be found in https://github.com/zhyx12/MixLRCo.