4 papers
Quantitative estimates: How well does the discrete Fourier transform approximate the Fourier transform on
Martin Ehler, Karlheinz Gröchenig, Andreas Klotz
In order to compute the Fourier transform of a function on the real line numerically, one samples on a grid and then takes the discrete Fourier transform. We derive exact e…
Aliasing in Convnets: A Frame-Theoretic Perspective
Daniel Haider, Vincent Lostanlen, Martin Ehler +2
Using a stride in a convolutional layer inherently introduces aliasing, which has implications for numerical stability and statistical generalization. While techniques such as the…
Geodesic cycles on the Sphere: -designs and Marcinkiewicz-Zygmund Inequalities
Martin Ehler, Karlheinz Gröchenig, Clemens Karner
A geodesic cycle is a closed curve that connects finitely many points along geodesics. We study geodesic cycles on the sphere in regard to their role in equal-weight quadrature rul…
Injectivity of ReLU-layers: Tools from Frame Theory
Daniel Haider, Martin Ehler, Peter Balazs
Injectivity is the defining property of a mapping that ensures no information is lost and any input can be perfectly reconstructed from its output. By performing hard thresholding,…