Multi-label recognition (MLR) with incomplete labels is very challenging. Recent works strive to explore the image-to-label correspondence in the vision-language model, \ie, CLIP, to compensate for insufficient annotations. In spite of promising performance, they generally overlook the valuable prior about the label-to-label correspondence. In this paper, we advocate remedying the deficiency of label supervision for the MLR with incomplete labels by deriving a structured semantic prior about the label-to-label correspondence via a semantic prior prompter. We then present a novel Semantic Correspondence Prompt Network (SCPNet), which can thoroughly explore the structured semantic prior. A Prior-Enhanced Self-Supervised Learning method is further introduced to enhance the use of the prior. Comprehensive experiments and analyses on several widely used benchmark datasets show that our method significantly outperforms existing methods on all datasets, well demonstrating the effectiveness and the superiority of our method. Our code will be available at https://github.com/jameslahm/SCPNet.

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