Parametrizing Convex Sets Using Sublinear Neural Networks

Eloi Martinet

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arXiv · 2605.03520

Parametrizing Convex Sets Using Sublinear Neural Networks

Eloi Martinet

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Abstract

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

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Eloi Martinet. 2026-05-05. Parametrizing Convex Sets Using Sublinear Neural Networks. https://arxiv.org/abs/2605.03520

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