Parametrizing Convex Sets Using Sublinear Neural Networks

ArXi:2605.03520v1 Announce Type: cross We propose a neural parameterization of convex sets by learning sublinear (positively homogeneous and convex) functions. Our networks implicitly represent both the and gauge functions of a convex body. We prove a universal approximation theorem for convex sets under this parametrization. Empirically, we nstrate the method on shape optimization and inverse design tasks, achieving accurate reconstruction of target shapes.