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.Comment: 11 pages, 7 figure