Jamming far from jamming

The jamming transition is an important phenomenon in granular systems which has been extensively studied in the last 20 years. In the idealized setting of frictionless hard spheres, jamming is associated with critical behavior and marginal stability. This shows up in the jerky response to external perturbations characterized by scale-free avalanches.
However in order to be at jamming one needs to compress hard spheres up to random close packing. In this talk I will show that if one considers soft spheres interacting through the so called Hinge loss (a very popular cost function in machine learning), the jammed/overcompressed phase becomes critical as much as the jamming point. This is very different from previously considered interaction potentials (Harmonic or Hertzian soft spheres) where jamming criticality is lost as soon as the system is compressed beyond the critical point.
I will show how these findings can be rationalized through a simple mean field theory based on machine learning models and how to compute the critical exponents associated to the critical behavior of such systems.