Search Results for author: Dennis Elbrächter

Found 6 papers, 1 papers with code

Redistributor: Transforming Empirical Data Distributions

1 code implementation25 Oct 2022 Pavol Harar, Dennis Elbrächter, Monika Dörfler, Kory D. Johnson

We present an algorithm and package, Redistributor, which forces a collection of scalar samples to follow a desired distribution.

How degenerate is the parametrization of neural networks with the ReLU activation function?

no code implementations NeurIPS 2019 Julius Berner, Dennis Elbrächter, Philipp Grohs

Approximation capabilities of neural networks can be used to deal with the latter non-convexity, which allows us to establish that for sufficiently large networks local minima of a regularized optimization problem on the realization space are almost optimal.

Towards a regularity theory for ReLU networks -- chain rule and global error estimates

no code implementations13 May 2019 Julius Berner, Dennis Elbrächter, Philipp Grohs, Arnulf Jentzen

Although for neural networks with locally Lipschitz continuous activation functions the classical derivative exists almost everywhere, the standard chain rule is in general not applicable.

Deep Neural Network Approximation Theory

no code implementations8 Jan 2019 Dennis Elbrächter, Dmytro Perekrestenko, Philipp Grohs, Helmut Bölcskei

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 of training data.

Handwritten Digit Recognition Image Classification +1

The universal approximation power of finite-width deep ReLU networks

no code implementations ICLR 2019 Dmytro Perekrestenko, Philipp Grohs, Dennis Elbrächter, Helmut Bölcskei

We show that finite-width deep ReLU neural networks yield rate-distortion optimal approximation (B\"olcskei et al., 2018) of polynomials, windowed sinusoidal functions, one-dimensional oscillatory textures, and the Weierstrass function, a fractal function which is continuous but nowhere differentiable.

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