Seminars

John Hopfield and Geoffrey Hinton explain how ideas from physics helped establish computational models that store patterns and learn from data. Hopfield develops a physical perspective on collective computation, including associative memories in which network dynamics recover stored patterns from incomplete or distorted inputs. Hinton examines Boltzmann machines, connecting probabilistic neural networks and learning to concepts from statistical physics. Together, the lectures link energy landscapes, interacting units and stochastic behaviour with mechanisms for representation and computation. They provide the scientific background to the neural-network contributions recognised by the 2024 physics prize and the conceptual route from models of collective systems to machine learning.

The link between behavior, learning and the underlying connectome is a fundamental open problem in neuroscience. In my talk I will show how it is possible to develop a theory that bridges across these three levels (animal behavior, learning and network connectivity) based on the geometrical properties of neural activity. The central tool in my approach is the dimensionality of neural activity. I will link animal complex behavior to the geometry of neural representations, specifically their dimensionality; I will then show how learning shapes changes in such geometrical properties and how local connectivity properties can further regulate them. As a result, I will explain how the complexity of neural representations emerges from both behavioral demands (top-down approach) and learning or connectivity features (bottom-up approach). I will build these results regarding neural dynamics and representations starting from the analysis of neural recordings, by means of theoretical and computational tools that blend dynamical systems, artificial intelligence and statistical physics approaches.

Neural networks can learn and recognize subtle correlations in high dimensional inputs. However, neural networks are simply many-body systems with strong non-linearities and disordered interactions. Hence, many-body physical systems with similar interactions should be able to show neural network-like behavior. Here we show neural network-like behavior in the nucleation dynamics of promiscuously interacting molecules with multiple stable crystalline phases. Using a combination of theory and experiments, we show how the physics of the system dictates relationships between the difficulty of the pattern recognition task solved, time taken and accuracy. This work shows that high dimensional pattern recognition and learning are not special to software algorithms but can be achieved by the collective dynamics of sufficiently disordered molecular systems.