Title: Cross-Protein Wasserstein Transformer for Protein-Protein Interactions. Abstract: Previous studies reveal intimate relationships between the structure and function of proteins. Motivated by this, for protein-protein interactions (PPIs), we hypothesize that cross-protein structural correspondence, including both global correlation and local co-occurrence, poses a great influence. Accordingly, a novel deep learning framework named Cross-Protein Wasserstein Transformer (CPWT) is proposed to predict PPI sites through fine-grained cross-graph structural modeling. Considering the irregular architecture of acid sequences, for a pair of proteins, graphs are constructed to describe them. Then, a core Cross-Graph Transformer (CGT) module of two branches (e.g. ligand and receptor branches) is proposed for cross-protein structural modeling. Specifically, in this module, Wasserstein affinity across graphs is calculated through cross-graph query (i.e. ligand (query) - receptor (key) or the converse), based on which the multi-head attention is derived to adaptively mine fine-grained cues of PPI sites. By stacking CGT modules, the two branches in CGT are co-evolved in a deep architecture during forward inference, hence being powerful and advantageous in cross-protein structural representation and fine-grained learning. We verify the effectiveness of our CPWT framework by conducting comprehensive experiments on multiple PPI datasets, and further visualize the learned fine-grained saliencies for intuitive understanding.