Modern communication networks are rapidly evolving into sophisticated systems combining communication and computing capabilities. Computation at the network edge is the key to supporting many emerging applications. However, large scale adoption of edge intelligence technology will result in a surge of data and computation in mobile networks, which, in turn, will exacerbate their already significant energy consumption. SONATA tames this growing energy demand by combining memristive hardware and energy harvesting technologies with novel machine learning algorithms and physical layer communication techniques. The goal is to reduce the energy requirements of edge learning systems drastically and, also, to make them robust against stochastic failures, due to unreliable hardware or energy sources. To work towards this goal, CTTC has teamed up in SONATA with Imperial College London, Bilkent University and Pázmány Péter Catholic University.