Object parts serve as crucial intermediate representations in various downstream tasks, but part-level representation learning still has not received as much attention as other vision tasks. Previous research has established that Vision Transformer can learn instance-level attention without labels, extracting high-quality instance-level representations for boosting downstream tasks. In this paper, we achieve unsupervised part-specific attention learning using a novel paradigm and further employ the part representations to improve part discovery performance. Specifically, paired images are generated from the same image with different geometric transformations, and multiple part representations are extracted from these paired images using a novel module, named PartFormer. These part representations from the paired images are then exchanged to improve geometric transformation invariance. Subsequently, the part representations are aligned with the feature map extracted by a feature map encoder, achieving high similarity with the pixel representations of the corresponding part regions and low similarity in irrelevant regions. Finally, the geometric and semantic constraints are applied to the part representations through the intermediate results in alignment for part-specific attention learning, encouraging the PartFormer to focus locally and the part representations to explicitly include the information of the corresponding parts. Moreover, the aligned part representations can further serve as a series of reliable detectors in the testing phase, predicting pixel masks for part discovery. Extensive experiments are carried out on four widely used datasets, and our results demonstrate that the proposed method achieves competitive performance and robustness due to its part-specific attention.