Author

Josef Dick

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Preprint Oct 2026

The $L\log L$-Luxemburg Discrepancy for Nonnegative Weights Suffers from the Curse of Dimensionality

We study the normalized discrepancy in the Luxemburg norm generated by $\Phi(s)=s\log(1+s)$. For arbitrary nonnegative quadrature weights, we prove that the associated information complexity suffers from the curse of dimensionality: for every $\varepsilon\in(0,1)$, there exist constants $c_\varepsilon>0$ and $d_0=d_0(\...

Josef Dick, F. Pillichshammer · 0 citations

Preprint Aug 2026

High Probability Derivative Bounds for Random tanh Neural Networks on a Hypercube

High-probability bounds for mixed input derivatives of wide random neural networks whose activation derivatives satisfy a factorial growth bound are established and the derivative estimates are connected to quasi-Monte Carlo integration and indicate how such regularity can enter the analysis of QMC-based training.

Josef Dick, Michael Feischl, Fabian Zehetgruber · 0 citations