Speaker: Elena Agliari (Università di Roma Sapienza)
The Hopfield model and the quest for lost memories
The Hopfield network is a paradigmatic model for both biological neural networks (where it mimics associative memory) and artificial neural networks (where it is used for retrieval tasks). Since its introduction in the 1980s, it has been extensively studied by mathematicians and physicists alike, and its profound impact was recognized with the 2024 Nobel Prize in Physics awarded to John J. Hopfield. In the first part of this talk, I will review its key properties from a mathematical standpoint, focusing on foundational aspects such as the proof of the existence of the thermodynamic limit for the model’s free energy. In the second part, I will explore several extensions and variations of the model that address contemporary challenges, including AI sustainability and the issue of model collapse.
Where: Sapienza Università di Roma, Dipartimento di Matematica, Aula Consiglio
