Author

Moritz Grillo

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#machine learning Sep 2025

Parameterized Hardness of Zonotope Containment and Neural Network Verification

It is proved that, for all $\ell\ge 2$, deciding positivity (and thus surjectivity) of a function computed by an $\ell$-layer ReLU network is W[$\ell-1$]-hard when parameterized by the input dimension $d$.

Vincent Froese, Moritz Grillo, Christoph Hertrich et al. · arXiv.org · 9 citations · ⚡2

Jul 2026

Shallower ReLU Network Representations via Exact Linear Algebra

It is proved that $\max_n(x)$ is exactly representable with two hidden layers for every $n\leq 12$, and these results improve upon [Bakaev, Brunck, Hertrich, Stade, Yehudayoff, STOC'26], who proved analogous logarithmic bounds with base three.

Kilian Ruess, G. Averkov, Florestan Brunck et al. · arXiv.org · 2 citations · ⚡1

Preprint Aug 2026

Parameterized Complexity of $L_p$-Lipschitz Constants for Input Convex Neural Networks and $L_p$-Norm Maximization over Zonotopes

These results resolve the corresponding questions regarding the parameterized complexity status for zonotope norm maximization and two-layer ICNN Lipschitz constants.

Aritra Das, Vincent Froese, Moritz Grillo et al. · 1 citation