Antibody-antigen binding relies on the specific interaction of amino acids at the paratope-epitope interface. The predictability of antibody-antigen binding is a prerequisite for de novo antibody and (neo-)epitope design. A fundamental premise for the predictability of antibody-antigen binding is the existence of paratope-epitope interaction motifs that are universally shared among antibody-antigen structures. In a dataset of non-redundant antibody-antigen structures, we identify structural interaction motifs, which together compose a commonly shared structure-based vocabulary of paratope-epitope interactions. We show that this vocabulary enables the machine learnability of antibody-antigen binding on the paratope-epitope level using generative machine learning. The vocabulary (1) is compact, less than 104 motifs; (2) distinct from non-immune protein-protein interactions; and (3) mediates specific oligo- and polyreactive interactions between paratope-epitope pairs. Our work leverages combined structure- and sequence-based learning to demonstrate that machine-learning-driven predictive paratope and epitope engineering is feasible.