40 citations · 43 across the 7 of their papers we have counts for
7 papers
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…
Hold Me Tight: Stable Encoder-Decoder Design for Speech Enhancement
Daniel Haider, Felix Perfler, Vincent Lostanlen +2
Convolutional layers with 1-D filters are often used as frontend to encode audio signals. Unlike fixed time-frequency representations, they can adapt to the local characteristics o…
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,…
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…
Instabilities in Convnets for Raw Audio
Daniel Haider, Vincent Lostanlen, Martin Ehler +1
What makes waveform-based deep learning so hard? Despite numerous attempts at training convolutional neural networks (convnets) for filterbank design, they often fail to outperform…
Tight p-fusion frames
Christine Bachoc, Martin Ehler
Fusion frames enable signal decompositions into weighted linear subspace components. For positive integers p, we introduce p-fusion frames, a sharpening of the notion of fusion fra…