Institution ::

Lehrstuhl für Mathematik - Reliable Machine Learning

2023

• 

  

  Koppensteiner, Sarah ; Van Velthoven, Jordy Timo ; Voigtlaender, Felix:
  Anisotropic Triebel–Lizorkin spaces and wavelet coefficient decay over one-parameter dilation groups, I.
  In: Monatshefte für Mathematik. 201 (2023). - S. 375-429.
  ISSN 0026-9255 ; 1436-5081
  10.1007/s00605-023-01827-0
  (Peer-Review-Journal)
• 

  

  Koppensteiner, Sarah ; Van Velthoven, Jordy Timo ; Voigtlaender, Felix:
  Anisotropic Triebel–Lizorkin spaces and wavelet coefficient decay over one-parameter dilation groups, II.
  In: Monatshefte für Mathematik. 201 (2023). - S. 431-464.
  ISSN 0026-9255 ; 1436-5081
  10.1007/s00605-023-01824-3
  (Peer-Review-Journal)
• 

  

  Caragea, Andrei ; Lee, Dae Gwan ; Philipp, Friedrich ; Voigtlaender, Felix:
  A Balian–Low type theorem for Gabor Riesz sequences of arbitrary density.
  In: Mathematische Zeitschrift. 303 (2023) 2: 48. - 23 S.
  ISSN 1432-1823 ; 0025-5874
  10.1007/s00209-022-03182-6
  (Peer-Review-Journal)
• 

  

  Matt, Hannes ; Steenebrügge, Daniel ; Mosel, Heiko von der:
  Banach gradient flows for various families of knot energies.
  In: Journal of evolution equations : JEE. 23 (2023): 31.
  ISSN 1424-3202 ; 1424-3199
  10.1007/s00028-022-00863-x
  (Peer-Review-Journal)
• 

  

  Abreu, Daniel Luìs ; Mouayn, Zouhair ; Voigtlaender, Felix:
  A fractal uncertainty principle for Bergman spaces and analytic wavelets.
  In: Journal of mathematical analysis and applications. 519 (2023) 1: 126699.
  ISSN 0022-247x ; 1096-0813
  10.1016/j.jmaa.2022.126699
  (Peer-Review-Journal)
• 

  

  Lee, Dae Gwan ; Philipp, Friedrich ; Voigtlaender, Felix:
  A Note on the Invertibility of the Gabor Frame Operator on Certain Modulation Spaces.
  In: The journal of Fourier analysis and applications. 29 (2023): 3.
  ISSN 1069-5869 ; 1531-5851
  10.1007/s00041-022-09980-0
  (Peer-Review-Journal)
• 

  Voigtlaender, Felix:
  The universal approximation theorem for complex-valued neural networks.
  In: Applied and computational harmonic analysis. 64 (2023). - S. 33-61.
  ISSN 1063-5203 ; 1096-603x
  10.1016/j.acha.2022.12.002
  (Peer-Review-Journal)

2022

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  Gribonval, Rémi ; Kutyniok, Gitta ; Nielsen, Morten ; Voigtlaender, Felix:
  Approximation Spaces of Deep Neural Networks.
  In: Constructive approximation. 55 (2022). - S. 259-367.
  ISSN 0176-4276 ; 1432-0940
  10.1007/s00365-021-09543-4
  (Peer-Review-Journal)
• 

  Lee, Dae Gwan ; Pfander, Götz E. ; Walnut, David:
  Bases of complex exponentials with restricted supports.
  In: Journal of mathematical analysis and applications. 521 (2022) 2: 126917.
  ISSN 0022-247x ; 1096-0813
  10.1016/j.jmaa.2022.126917
  (Peer-Review-Journal)
• 

  

  Van Velthoven, Jordy Timo ; Voigtlaender, Felix:
  Coorbit spaces and dual molecules : The quasi-Banach case.
  2022. - 61 S.
  arXiv:2203.07959
• 

  

  Romero, José Luis ; Van Velthoven, Jordy Timo ; Voigtlaender, Felix:
  Invertibility of Frame Operators on Besov-Type Decomposition Spaces.
  In: The journal of geometric analysis. 32 (2022) 5: 149.
  ISSN 1559-002x ; 1050-6926
  10.1007/s12220-022-00887-2
  (Peer-Review-Journal)
• 

  

  Caragea, Andrei ; Petersen, Philipp ; Voigtlaender, Felix:
  Neural network approximation and estimation of classifiers with classification boundary in a Barron class.
  2022. - 42 S.
  arXiv:2011.09363
• 

  Caragea, Andrei ; Lee, Dae Gwan ; Maly, Johannes ; Pfander, Götz E. ; Voigtlaender, Felix:
  Quantitative approximation results for complex-valued neural networks.
  In: SIAM Journal on Mathematics of Data Science. 4 (2022) 2. - S. 553-580.
  ISSN 2577-0187
  0.1137/21M1429540
  (Peer-Review-Journal)

2021

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  Grohs, Philipp ; Klotz, Andreas ; Voigtlaender, Felix:
  Phase Transitions in Rate Distortion Theory and Deep Learning.
  In: Foundations of computational mathematics. (16. November 2021). - 64 S.
  ISSN 1615-3375 ; 1615-3383
  10.1007/s10208-021-09546-4
  (Peer-Review-Journal)
• 

  

  Koppensteiner, Sarah ; Van Velthoven, Jordy Timo ; Voigtlaender, Felix:
  Anisotropic Triebel-Lizorkin spaces and wavelet coefficient decay over one-parameter dilation groups.
  2021. - 40 S.
  arXiv:2104.14361
• 

  

  Voigtlaender, Felix:
  A General Version of Price’s Theorem.
  In: Journal of theoretical probability. 34 (2021). - S. 1474-1485.
  ISSN 0894-9840 ; 1572-9230
  10.1007/s10959-020-01017-w
  (Peer-Review-Journal)
• 

  

  Almira, J. M. ; Lopez-de-Teruel, P. E. ; Romero-Lopez, D. J. ; Voigtlaender, Felix:
  Negative results for approximation using single layer and multilayer feedforward neural networks.
  In: Journal of mathematical analysis and applications. 494 (2021) 1: 124584.
  ISSN 0022-247x ; 1096-0813
  10.1016/j.jmaa.2020.124584
  (Peer-Review-Journal)
• 

  

  Lee, Dae Gwan ; Philipp, Friedrich ; Voigtlaender, Felix:
  A note on the invertibility of the Gabor frame operator on certain modulation spaces.
  2021. - 17 S.
  arXiv:2106.02365
• 

  

  Romero, José Luis ; Van Velthoven, Jordy Timo ; Voigtlaender, Felix:
  On dual molecules and convolution-dominated operators.
  In: Journal of functional analysis. 280 (2021) 10: 108963.
  ISSN 0022-1236 ; 1096-0783
  10.1016/j.jfa.2021.108963
  (Peer-Review-Journal)
• 

  

  Voigtlaender, Felix ; Petersen, Philipp:
  Optimal learning of high-dimensional classification problems using deep neural networks.
  2021. - 41 S.
  arXiv:2112.12555
• 

  

  Grohs, Philipp ; Voigtlaender, Felix:
  Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces.
  2021. - 42 S.
  arXiv:2104.02746
• 

  Caragea, Andrei ; Lee, Dae Gwan ; Philipp, Friedrich ; Voigtlaender, Felix:
  A quantitative subspace Balian-Low theorem.
  In: Applied and computational harmonic analysis. 55 (2021). - S. 368-404.
  ISSN 1063-5203 ; 1096-603x
  10.1016/j.acha.2021.06.005
  (Peer-Review-Journal)
• 

  

  Holighaus, Nicki ; Voigtlaender, Felix:
  Schur-type Banach modules of integral kernels acting on mixed-norm Lebesgue spaces.
  In: Journal of functional analysis. 281 (2021) 9: 109197.
  ISSN 0022-1236 ; 1096-0783
  10.1016/j.jfa.2021.109197
  (Peer-Review-Journal)
• 

  

  Grohs, Philipp ; Voigtlaender, Felix:
  Sobolev-type embeddings for neural network approximation spaces.
  2021. - 14 S.
  arXiv:2110.15304
• 

  

  Petersen, Philipp ; Raslan, Mones ; Voigtlaender, Felix:
  Topological properties of the set of functions generated by neural networks of fixed size.
  In: Foundations of computational mathematics. 21 (2021). - S. 375-444.
  ISSN 1615-3375 ; 1615-3383
  10.1007/s10208-020-09461-0
  (Peer-Review-Journal)

2020

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  Bytchenkoff, Dimitri ; Voigtlaender, Felix:
  Design and properties of wave packet smoothness spaces.
  In: Journal de mathématiques pures et appliquées. 133 (2020). - S. 185-262.
  ISSN 0021-7824
  10.1016/j.matpur.2019.05.006
  (Peer-Review-Journal)
• 

  

  Petersen, Philipp ; Voigtlaender, Felix:
  Equivalence of approximation by convolutional neural networks and fully-connected networks.
  In: Proceedings of the American Mathematical Society. 148 (2020). - S. 1567-1581.
  ISSN 0002-9939 ; 1088-6826
  10.1090/proc/14789
  (Peer-Review-Journal)
• 

  

  Voigtlaender, Felix:
  The universal approximation theorem for complex-valued neural networks.
  2020. - 29 S.
  arXiv:2012.03351

2019

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  Voigtlaender, Felix ; Petersen, Philipp:
  Approximation in Lp(μ) with deep ReLU neural networks.
  In: Proceedings of International Conference on Sampling Theory and Applications (SampTA), Bordeaux, France, 2019. - Piscataway, NJ : IEEE, 2019
  ISBN 978-1-7281-3741-4
  10.1109/SampTA45681.2019.9030992
  (Begutachteter Beitrag / peer-reviewed paper)
• 

  

  Gribonval, Rémi ; Kutyniok, Gitta ; Nielsen, Morten ; Voigtlaender, Felix:
  Approximation spaces of deep neural networks.
  2019. - 64 S.
  arXiv:1905.01208
• 

  

  Romero, José Luis ; Van Velthoven, Jordy Timo ; Voigtlaender, Felix:
  Invertibility of frame operators on Besov-type decomposition spaces.
  2019. - 54 S.
  arXiv:1905.04934
• 

  

  Sureau, Florent ; Voigtlaender, Felix ; Wust, Malte ; Starck, Jean-Luc ; Kutyniok, Gitta:
  Learning sparse representations on the sphere.
  In: Astronomy & astrophysics. 621 (2019): A73. - 17 S.
  ISSN 1432-0746
  10.1051/0004-6361/201834041
  (Peer-Review-Journal)
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  Dahlke, Stefan ; De Mari, Filippo ; De Vito, Ernesto ; Sawatzki, Lukas ; Steidl, Gabriele ; Teschke, Gerd ; Voigtlaender, Felix:
  On the Atomic Decomposition of Coorbit Spaces with Non-Integrable Kernel.
  In: Boggiatto, Paolo ; Cordero, Elena ; de Gosson, Maurice ; Feichtinger, Hans. G ; Nicola, Fabio ; Oliaro, Alessandro ; Tabacco, Anita (Hrsg.): Landscapes of Time-Frequency Analysis. - Basel : Birkhäuser, 2019. - S. 75-144. - (Applied and Numerical Harmonic Analysis)
  ISBN 978-3-030-05209-6
  10.1007/978-3-030-05210-2_4
  (Begutachteter Beitrag / peer-reviewed paper)
• 

  Caragea, Andrei ; Lee, Dae Gwan ; Philipp, Friedrich ; Voigtlaender, Felix:
  A quantitative Balian-Low theorem for subspaces.
  In: Proceedings of International Conference on Sampling Theory and Applications (SampTA), Bordeaux, France, 2019. - Piscataway, NJ : IEEE, 2019
  ISBN 978-1-7281-3741-4
  10.1109/SampTA45681.2019.9030951
  (Begutachteter Beitrag / peer-reviewed paper)
• 

  

  Caragea, Andrei ; Lee, Dae Gwan ; Philipp, Friedrich ; Voigtlaender, Felix:
  A quantitative subspace Balian-Low theorem.
  2019. - 38 S.
  10.48550/arXiv.1904.12250
• 

  Petersen, Philipp ; Raslan, Mones ; Voigtlaender, Felix:
  The structure of spaces of neural network functions.
  In: Proceedings of the conference SPIE 11138, Wavelets and Sparsity XVIII, 2019, San Diego, California, United States. - s.l. : SPIE, 2019
  10.1117/12.2528313
  (Begutachteter Beitrag / peer-reviewed paper)
• 

  

  Caragea, Andrei ; Lee, Dae Gwan ; Philipp, Friedrich ; Voigtlaender, Felix:
  Time-Frequency Shift Invariance of Gabor Spaces.
  In: Proceedings of International Conference on Sampling Theory and Applications (SampTA), Bordeaux, France, 2019. - Piscataway, NJ : IEEE, 2019
  ISBN 978-1-7281-3741-4
  10.1109/SampTA45681.2019.9030919
  (Begutachteter Beitrag / peer-reviewed paper)
• 

  

  Caragea, Andrei ; Lee, Dae Gwan ; Philipp, Friedrich ; Voigtlaender, Felix:
  Time-frequency shift invariance of Gabor spaces with an S0-generator.
  2019. - 15 S.
  arXiv:1904.12345
• 

  Petersen, Philipp ; Raslan, Mones ; Voigtlaender, Felix:
  Unfavorable structural properties of the set of neural networks with fixed architecture.
  In: Proceedings of International Conference on Sampling Theory and Applications (SampTA), Bordeaux, France, 2019. - Piscataway, NJ : IEEE, 2019
  ISBN 978-1-7281-3741-4
  10.1109/SampTA45681.2019.9030975
  (Begutachteter Beitrag / peer-reviewed paper)

2018

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  Petersen, Philipp ; Voigtlaender, Felix:
  Optimal approximation of piecewise smooth functions using deep ReLU neural networks.
  In: Neural networks. 108 (Dezember 2018). - S. 296-330.
  ISSN 1879-2782 ; 0893-6080
  10.1016/j.neunet.2018.08.019
  (Peer-Review-Journal)
• 

  

  Petersen, Philipp ; Voigtlaender, Felix:
  Equivalence of approximation by convolutional neural networks and fully-connected networks.
  2018. - 13 S.
  arXiv:1809.00973
• 

  

  Petersen, Philipp ; Raslan, Mones ; Voigtlaender, Felix:
  Topological properties of the set of functions generated by neural networks of fixed size.
  2018. - 51 S.
  arXiv:1806.08459

2017

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  Voigtlaender, Felix:
  Understanding X-let sparsity via decomposition spaces.
  2017
  Veranstaltung: 2017 International Conference on Sampling Theory and Applications (SampTA), 3-7 July 2017, Tallinn, Estonia.
  (Veranstaltungsbeitrag: Kongress/Konferenz/Symposium/Tagung, Vortrag)
  10.1109/SAMPTA.2017.8024402
• 

  

  Voigtlaender, Felix ; Pein, Anne:
  Analysis vs. synthesis sparsity for α-shearlets.
  2017. - 101 S.
  arXiv:1702.03559
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  Keiper, Sandra ; Kutyniok, Gitta ; Lee, Dae Gwan ; Pfander, Götz E.:
  Compressed sensing for finite-valued signals.
  In: Linear algebra and its applications. 532 (2017). - S. 570-613.
  ISSN 0024-3795
  10.1016/j.laa.2017.07.006
  (Peer-Review-Journal)
• 

  Feichtinger, Hans Georg ; Voigtlaender, Felix:
  From Frazier-Jawerth characterizations of Besov spaces to Wavelets and Decomposition spaces.
  In: Cwikel, Michael ; Milman, Mario (Hrsg.): Functional analysis, harmonic analysis, and image processing : a collection of papers in honor of Björn Jawerth. - Providence, Rhode Island : American Mathematical Society, 2017. - S. 185-216. - (Contemporary mathematics ; 693)
  ISBN 978-1-4704-2836-5 ; 978-1-4704-4166-1
  (Begutachteter Beitrag / peer-reviewed paper)

2016

• Keiper, Sandra ; Kutyniok, Gitta ; Lee, Dae Gwan ; Pfander, Götz E.:
  Compressed Sensing for Finite-Valued Signals.
  s.l., 2016
  arXiv:1609.09450
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  Voigtlaender, Felix:
  Embedding theorems for decomposition spaces with applications to wavelet coorbit spaces.
  RWTH Aachen University
  Aachen, 2016
  urn:nbn:de:hbz:82-rwth-2015-075066
• 

  

  Voigtlaender, Felix:
  Embeddings of Decomposition Spaces into Sobolev and BV Spaces.
  2016. - 64 S.
  arXiv:1601.02201
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  Böhme, David ; Geimer, Markus ; Arnold, Lukas ; Voigtlaender, Felix ; Wolf, Felix:
  Identifying the Root Causes of Wait States in Large-Scale Parallel Applications.
  In: ACM Transactions on Parallel Computing. 3 (2016) 2: 11. - 24 S.
  ISSN 2329-4949 ; 2329-4957
  10.1145/2934661
  (Peer-Review-Journal)
• 

  Fell, Jonathan ; Führ, Hartmut ; Voigtlaender, Felix:
  Resolution of the wavefront set using general continuous wavelet transforms.
  In: The journal of Fourier analysis and applications. 22 (2016) 5. - S. 997-1058.
  ISSN 1069-5869 ; 1531-5851
  10.1007/s00041-015-9445-7
  (Peer-Review-Journal)

2015

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  Fell, Jonathan ; Führ, Hartmut ; Voigtlaender, Felix:
  Resolution of the wave front set using general wavelet transforms.
  2015
  Veranstaltung: 2015 International Conference on Sampling Theory and Applications (SampTA), 25-29 May 2015, Washington, DC, USA.
  (Veranstaltungsbeitrag: Kongress/Konferenz/Symposium/Tagung, Vortrag)
  10.1109/SAMPTA.2015.7148907
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  Führ, Hartmut ; Voigtlaender, Felix:
  Wavelet coorbit spaces viewed as decomposition spaces.
  In: Journal of functional analysis. 269 (2015) 1. - S. 80-154.
  ISSN 0022-1236 ; 1096-0783
  10.1016/j.jfa.2015.03.019
  (Peer-Review-Journal)