Recent breakthroughs in Artificial Intelligence require an exponential growth (×4 per year) of computing power and, therefore, of energy consumption, raising huge ecological and social concerns. Little research has been done si far in the field of theoretical machine learning to address this pressing problem. Inspiration can be drawn from the brain of organisms, which have evolved under strong metabolic constraints for hundreds of millions of years. Recently, computational neuroscientists proposed empirical learning rules to curb energy consumption and applied them to few data sets or contexts. The purpose of this internship is to develop statistical mechanics tools to reach a deep understanding of the learning dynamics induced by those rules and, eventually, to improve them.