Parametrizing Convex Sets Using Sublinear Neural Networks
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915980786008064 |
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| author | Martinet, Eloi |
| author_facet | Martinet, Eloi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03520 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Parametrizing Convex Sets Using Sublinear Neural Networks Martinet, Eloi Optimization and Control Artificial Intelligence Machine Learning Numerical Analysis 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. |
| title | Parametrizing Convex Sets Using Sublinear Neural Networks |
| topic | Optimization and Control Artificial Intelligence Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2605.03520 |