Lorenzo Chicchi — Università di Firenze #
Learning with Attractors: A Dynamical Systems Approach to Classification and Generation #
In recent years, machine learning has achieved remarkable success, yet many of its models remain difficult to interpret. In this talk, I present an alternative perspective in which learning is formulated in terms of dynamical systems with explicitly designed attractors. Within this framework, data are treated as initial conditions of a continuous-time evolution, and classification emerges from the asymptotic state reached by the system. Each class is associated with a stable attractor, and learning amounts to shaping the interactions so that trajectories converge to the appropriate equilibrium.
Moreover, the introduction of stochasticity transforms deterministic attractors into probability distributions, providing a direct link to generative modeling. The same dynamical system can therefore be used not only to classify data, but also to generate new samples by exploiting the structure of the learned attractors.
This framework offers a transparent and physically grounded interpretation of learning processes, where information is encoded in the geometry of the dynamical landscape. I will discuss recent results and outline how this perspective may contribute to bridging machine learning and theoretical physics.