Understanding the peptide presentation mechanism of Major Histocompatibility Complex (MHC) is crucial to study the recognition of pathogens, the treatment of autoimmune diseases and in developing cancer immunotherapies. To comprehend these mechanisms and design effective therapies at affordable costs, it is fundamental to be able to precisely predictin silicowhich peptides can be bound by each MHC. Many computational approaches have been developed to identify MHC-binding peptides based on their sequences, however, they present biases and their performance on less-studied MHC alleles with limited experimental binding data is severely restricted by their sequence-based (SeqB) nature. We reason that structure-based (StrB) methods could learn the physico-chemical and geometrical rules of peptide-MHC (pMHC) complexes conserved among the alleles, thus generalizing better. We designed three supervised StrB geometric deep learning (GDL) methods, showing superior generalization across all StrB methods over two SeqB methods when the test data is distant from the training data. To further explore data efficiency, we designed a novel self-supervised GDL approach trained only on ∼1K x-ray structures, 3D-SSL, which predicts binding affinities without seeing any during training. Finally, we showcase our StrB method on a case study from the HPV vaccine design to show how StrB methods are robust to biases in the binding data. These findings highlight the potentials of structure-based methods in efficiently utilizing limited data, enhancing generalizability. This study bears important implications on data hungry fields, for example, the long-standing T cell receptor (TCR) specificity challenge.