6 citations · 10 across the 9 of their papers we have counts for
3 papers · 1 filter
Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black-Scholes Partial Differential Equations
Julius Berner, Philipp Grohs, Arnulf Jentzen
The development of new classification and regression algorithms based on empirical risk minimization (ERM) over deep neural network hypothesis classes, coined deep learning, revolu…
The universal approximation power of finite-width deep ReLU networks
Dmytro Perekrestenko, Philipp Grohs, Dennis Elbrächter +1
We show that finite-width deep ReLU neural networks yield rate-distortion optimal approximation (Bölcskei et al., 2018) of polynomials, windowed sinusoidal functions, one-dimension…
Gabor phase retrieval is severely ill-posed
Rima Alaifari, Philipp Grohs
The problem of reconstructing a function from the magnitudes of its frame coefficients has recently been shown to be never uniformly stable in infinite-dimensional spaces [5]. This…