Emergent learning in physical systems as feedback-based aging in a glassy landscape

TL;DR

This paper explores how physical networks learn linear transformations through a process resembling aging in glassy systems, revealing insights into physical learning mechanisms and memory formation.

Contribution

It demonstrates that learning in physical systems can be understood as an aging process, linking physical properties to information encoding and memory in disordered systems.

Findings

Learning dynamics resemble aging and relaxation in glassy systems

Correlation length increases with learning, indicating memory formation

Mean-squared error follows a non-exponential decay pattern

Abstract

By training linear physical networks to learn linear transformations, we discern how their physical properties evolve due to weight update rules. Our findings highlight a striking similarity between the learning behaviors of such networks and the processes of aging and memory formation in disordered and glassy systems. We show that the learning dynamics resembles an aging process, where the system relaxes in response to repeated application of the feedback boundary forces in presence of an input force, thus encoding a memory of the input-output relationship. With this relaxation comes an increase in the correlation length, which is indicated by the two-point correlation function for the components of the network. We also observe that the square root of the mean-squared error as a function of epoch takes on a non-exponential form, which is a typical feature of glassy systems. This physical interpretation suggests that by encoding more detailed information into input and feedback boundary forces, the process of emergent learning can be rather ubiquitous and, thus, serve as a very early physical mechanism, from an evolutionary standpoint, for learning in biological systems.