Forum Numerica - Elena Agliari - The many lives of the Hopfield model: from dreams to generalization

In the first part of the seminar, I will review the main features of the Hopfield model and provide an overview of its numerous and diverse applications. Next, inspired by biological information processing, I will introduce reinforcement and removal mechanisms occurring in the mammalian brain during sleep and recast them in terms of suitable hyperparameters. This enriched framework is shown to efficiently handle structured datasets, enabling both retrieval and generalization, depending on the chosen setup. Our theoretical picture, developed using tools from statistical mechanics and random matrix theory, is corroborated by numerical simulations. 

Elena Agliari is a Professor of Mathematical Physics at Sapienza University of Rome, where she explores the structure of complexity across physical, biological, and learning systems. After earning her degree and PhD in Physics from the University of Parma, she conducted research in Freiburg and Paris before settling in Rome. Her research bridges the statistical mechanics of disordered systems, mathematical approaches to machine learning, and biological modelling. She has authored or co-authored over one hundred papers in leading international journals and has delivered nearly one hundred invited talks worldwide, including colloquia and lectures in high-profile summer school. She has coordinated multiple funded research projects and currently co-leads the Co’ Scienza Lab at Sapienza. She serves as Main Editor of Physica A and Editor-in-Chief of the Journal of Statistical Physics, and has previously served on the Advisory Panel of the Journal of Physics A and the Editorial Board of Physical Review Letters.