← Back to all news
arXiv Machine Learning By Sjoerd Dirksen, Patrick Finke, Paul Geuchen, Dominik St\"oger, Felix Voigtlaender

Near-optimal estimates for the $\ell^p$-Lipschitz constants of deep random ReLU neural networks

Read the original on arXiv Machine Learning →

This paper investigates the ρ^p-Lipschitz constants of deep ReLU neural networks with random weights drawn from a He‑style initialization. For zero‑bias networks, it provides high‑probability upper and lower bounds that differ by at most a logarithmic factor in depth, and shows a sharp contrast between the regimes p∈[1,2) and p∈[2,∞], with the former behaving like the Euclidean norm of a Gaussian vector and the latter like its dual norm. The analysis is extended to networks with non‑zero biases from symmetric distributions, yielding bounds that differ by a logarithmic factor in width and a linear factor in depth.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

Related stories

arXiv Machine Learning
Aug 28

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

The paper establishes high‑probability bounds on mixed input derivatives for wide random neural networks whose activation derivatives grow factorially, with a focus on anh networks initialized with Xavier weights. For scalar‑output anh networks with Gaussian weights, the authors prove that when the hidden width exceeds a depth‑dependent threshold, the derivative of any order satisfies a bound that is independent of depth for first‑order derivatives and grows at most polynomially with depth for higher‑order mixed derivatives. These results yield high‑probability estimates for the Euclidean Lipschitz constant and weighted Sobolev norms, linking the regularity of network realizations to quasi‑Monte Carlo integration and its potential impact on QMC‑based training.

By Josef Dick, Michael Feischl, Fabian Zehetgruber
More like this →