  The introduction of transient learning degrees of freedom into a system can
lead to novel material design and training protocols that guide a system into a
desired metastable state. In this approach, some degrees of freedom, which were
not initially included in the system dynamics, are first introduced and
subsequently removed from the energy minimization process once the desired
state is reached. Using this conceptual framework, we create stable jammed
packings that exist in exceptionally deep energy minima marked by the absence
of low-frequency quasilocalized modes; this added stability persists in the
thermodynamic limit. The inclusion of particle radii as transient degrees of
freedom leads to deeper and much more stable minima than does the inclusion of
particle stiffnesses. This is because particle radii couple to the jamming
transition whereas stiffnesses do not. Thus different choices for the added
degrees of freedom can lead to very different training outcomes.
