  Diverse many-body systems, from soap bubbles to suspensions to polymers,
learn and remember patterns in the drives that push them far from equilibrium.
This learning may be leveraged for computation, memory, and engineering. Until
now, many-body learning has been detected with thermodynamic properties, such
as work absorption and strain. We progress beyond these macroscopic properties
first defined for equilibrium contexts: We quantify statistical mechanical
learning using representation learning, a machine-learning model in which
information squeezes through a bottleneck. By calculating properties of the
bottleneck, we measure four facets of many-body systems' learning:
classification ability, memory capacity, discrimination ability, and novelty
detection. Numerical simulations of a classical spin glass illustrate our
technique. This toolkit exposes self-organization that eludes detection by
thermodynamic measures: Our toolkit more reliably and more precisely detects
and quantifies learning by matter while providing a unifying framework for
many-body learning.
