The Physical Effects of Learning

Understand

Interacting many-body physical systems ranging from neural networks in the brain to folding proteins to self-modifying electrical circuits can learn to perform diverse tasks.

• This learning, both in nature and in engineered systems, can occur through evolutionary selection or through dynamical rules that drive active learning from experience.
• Here, we show that \added{learning in linear physical networks with weak input signals} leaves architectural imprints on the Hessian of a physical system.
• Compared to a generic organization of the system components, (a) the effective physical dimension of the response to inputs decreases, (b) the response of physical degrees of freedom to random perturbations (or system ``susceptibility'') increases, and (c) the low-eigenvalue eigenvectors of the Hessian align with the task.