Antibodies are a critical part of the immune system, having the function of directly neutralising or tagging undesirable objects (the antigens) for future destruction. Being able to predict which amino acids belong to the paratope, the region on the antibody which binds to the antigen, can facilitate antibody design and contribute to the development of personalised medicine. The suitability of deep neural networks has recently been confirmed for this task, with Parapred outperforming all prior physical models. Our contribution is twofold: first, we significantly outperform the computational efficiency of Parapred by leveraging a trous convolutions and self-attention. Secondly, we implement cross-modal attention by allowing the antibody residues to attend over antigen residues. This leads to new state-of-the-art results on this task, along with insightful interpretations.