16 citations · 41 across the 6 of their papers we have counts for
8 papers
Upper bounds on the number of causal pieces in spiking neural networks
Dominik Dold, Dennis Elbrächter, Philipp Petersen
The input space of single-spike neural networks decomposes into causal pieces, and the number of causal pieces has been shown to provide a lower bound on the approximation error fo…
Compositional Approximation Can Strictly Outperform Superpositional Approximation
Dennis Elbrächter, Philipp Petersen
Many classically studied function classes are known to be approximated optimally by superpositional methods, i.e. with approximants constructed as the linear combination of element…
Redistributor: Transforming Empirical Data Distributions
Pavol Harar, Dennis Elbrächter, Monika Dörfler +1
We present an algorithm and package, Redistributor, which forces a collection of scalar samples to follow a desired distribution. When given independent and identically distributed…
Towards a regularity theory for ReLU networks -- chain rule and global error estimates
Julius Berner, Dennis Elbrächter, Philipp Grohs +1
Although for neural networks with locally Lipschitz continuous activation functions the classical derivative exists almost everywhere, the standard chain rule is in general not app…
How degenerate is the parametrization of neural networks with the ReLU activation function?
Julius Berner, Dennis Elbrächter, Philipp Grohs
Neural network training is usually accomplished by solving a non-convex optimization problem using stochastic gradient descent. Although one optimizes over the networks parameters,…
The Oracle of DLphi
Dominik Alfke, Weston Baines, Jan Blechschmidt +24
We present a novel technique based on deep learning and set theory which yields exceptional classification and prediction results. Having access to a sufficiently large amount of l…
Deep Neural Network Approximation Theory
Dennis Elbrächter, Dmytro Perekrestenko, Philipp Grohs +1
This paper develops fundamental limits of deep neural network learning by characterizing what is possible if no constraints are imposed on the learning algorithm and on the amount…
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…