Proliferation of non-linear excitations in the piecewise-linear perceptron

We investigate the properties of local minima energy landscape a continuous non-convex optimization problem, spherical perceptron with piecewise linear cost function and show that they are critical, marginally stable displaying set pseudogaps, singularities non-linear excitations whose appear to be in same universality class jammed packings hard spheres. The problem appears as an evolution purely has been recently investigated [1]. Its contains two non-analytic points where derivative jump. Correspondingly, non-convex/glassy phase, these give rise four pseudogaps force distribution this induces power laws gap well. In addition one can define extended notion isostaticity again isostatic phase. believe our results generalize naturally more complex cases proliferation number is increased.