Molecular recognition, the selective interaction between the elements of two different populations, plays a central role in regulating key processes in biology as, for example, immune responses where T cell receptors have the task of recognizing peptide antigens. Despite advances in sequencing technologies, predicting whether a TCR-antigen pair will bind remains a major challenge due to the experimental limitations in data collection. Data-driven approaches exploiting neural networks have shown to be promising in this regard, therefore understanding the amount and type of data on interacting partners necessary for generalisation is a question of great interest. In this thesis we translate this problem into the language of statistical physics and study two different settings of data collection exploiting the well-known teacher-student model and replica trick.