  We study a well known machine learning model -the perceptron- as a simple
model of jamming of hard objects. We exhibit two regimes: 1) a convex
optimisation regime where jamming is hypostatic and non-critical. 2) a non
convex optimisation regime where jamming is isostatic and critical. We
characterise the critical jamming phase through exponents describing the
distributions law of forces and gaps. Surprisingly we find that these exponents
coincide with the corresponding ones recently computed in high dimensional hard
spheres. In addition, modifying the perceptron to a random linear programming
problem, we show that isostaticity is not a sufficient condition for singular
force and gap distributions. For that, fragmentation of the space of solutions
(replica symmetry breaking) appears to be a crucial ingredient. We hypothesise
universality for a large class of non-convex constrained satisfaction problems
with continuous variables.
