Quadratic Characterizations for Reachability Analysis of Neural Networks
Quadratic constraints (QCs) are widely used to characterize nonlinearities and uncertainties, but generic analytical characterizations can be conservative on bounded domains. This paper develops a framework for constructing verified quadratic characterizations of scalar relations in the two-dimensional real plane. Candidate quadratic inequalities are locally generated by solving convex quadratic programs using samples from the relation and exterior sample points. They are then verified globally using sum-of-squares certificates over an exact semialgebraic description or, in the case of nonpolynomial relations, over relaxed polynomial descriptions. The resulting verified constraints define...
| Authors | Elias Khalife, Mazen Farhood, Pierre-Loic Garoche |
|---|---|
| Primary category | cs.LG |
| Published | 19 May 2026 |
| Last updated at source | 9 October 2026 |
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