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Anders C. Hansen
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2020 – today
- 2024
- [i26]Zhen Ning David Liu, Anders C. Hansen:
Do stable neural networks exist for classification problems? - A new view on stability in AI. CoRR abs/2401.07874 (2024) - [i25]Alexander Bastounis, Paolo Campodonico, Mihaela van der Schaar, Ben Adcock, Anders C. Hansen:
On the consistent reasoning paradox of intelligence and optimal trust in AI: The power of 'I don't know'. CoRR abs/2408.02357 (2024) - 2023
- [c1]Alexander Bastounis
, Alexander N. Gorban
The Boundaries of Verifiable Accuracy, Robustness, and Generalisation in Deep Learning. ICANN (1) 2023: 530-541 - [i24]Johan S. Wind, Vegard Antun, Anders C. Hansen:
Implicit regularization in AI meets generalized hardness of approximation in optimization - Sharp results for diagonal linear networks. CoRR abs/2307.07410 (2023) - [i23]Alexander Bastounis, Alexander N. Gorban, Anders C. Hansen, Desmond J. Higham, Danil V. Prokhorov
The Boundaries of Verifiable Accuracy, Robustness, and Generalisation in Deep Learning. CoRR abs/2309.07072 (2023) - [i22]Alexander Bastounis, Felipe Cucker, Anders C. Hansen:
When can you trust feature selection? - I: A condition-based analysis of LASSO and generalised hardness of approximation. CoRR abs/2312.11425 (2023) - 2022
- [j11]Theresa Loss
Stratified Sampling Based Compressed Sensing for Structured Signals. IEEE Trans. Signal Process. 70: 3530-3539 (2022) - 2021
- [i21]Vegard Antun, Matthew J. Colbrook, Anders C. Hansen:
Can stable and accurate neural networks be computed? - On the barriers of deep learning and Smale's 18th problem. CoRR abs/2101.08286 (2021) - [i20]Alexander Bastounis, Anders C. Hansen, Verner Vlacic:
The mathematics of adversarial attacks in AI - Why deep learning is unstable despite the existence of stable neural networks. CoRR abs/2109.06098 (2021) - 2020
- [i19]Nina M. Gottschling, Vegard Antun, Ben Adcock, Anders C. Hansen:
The troublesome kernel: why deep learning for inverse problems is typically unstable. CoRR abs/2001.01258 (2020) - [i18]Matthew J. Colbrook, Anders C. Hansen:
On the infinite-dimensional QR algorithm. CoRR abs/2011.08172 (2020)
2010 – 2019
- 2019
- [j10]Matthew J. Colbrook
On the infinite-dimensional QR algorithm. Numerische Mathematik 143(1): 17-83 (2019) - [i17]Vegard Antun, Francesco Renna, Clarice Poon, Ben Adcock, Anders C. Hansen:
On instabilities of deep learning in image reconstruction - Does AI come at a cost? CoRR abs/1902.05300 (2019) - [i16]Ben Adcock, Vegard Antun, Anders C. Hansen:
Uniform recovery in infinite-dimensional compressed sensing and applications to structured binary sampling. CoRR abs/1905.00126 (2019) - [i15]Laura Thesing, Vegard Antun, Anders C. Hansen:
What do AI algorithms actually learn? - On false structures in deep learning. CoRR abs/1906.01478 (2019) - [i14]Laura Thesing, Anders Christian Hansen:
Linear reconstructions and the analysis of the stable sampling rate. CoRR abs/1907.12286 (2019) - [i13]Anders Christian Hansen, Laura Thesing:
On the stable sampling rate for binary measurements and wavelet reconstruction. CoRR abs/1908.00185 (2019) - [i12]Laura Thesing, Anders Christian Hansen:
Non-uniform recovery guarantees for binary measurements and infinite-dimensional compressed sensing. CoRR abs/1909.01143 (2019) - 2017
- [j9]Alexander Bastounis
On the Absence of Uniform Recovery in Many Real-World Applications of Compressed Sensing and the Restricted Isometry Property and Nullspace Property in Levels. SIAM J. Imaging Sci. 10(1): 335-371 (2017) - 2016
- [j8]Ben Adcock, Anders C. Hansen:
Generalized Sampling and Infinite-Dimensional Compressed Sensing. Found. Comput. Math. 16(5): 1263-1323 (2016) - [j7]Ben Adcock, Anders C. Hansen, Bogdan Roman:
A Note on Compressed Sensing of Structured Sparse Wavelet Coefficients From Subsampled Fourier Measurements. IEEE Signal Process. Lett. 23(5): 732-736 (2016) - [j6]Alexander Daniel Jones, Ben Adcock, Anders C. Hansen:
On Asymptotic Incoherence and Its Implications for Compressed Sensing of Inverse Problems. IEEE Trans. Inf. Theory 62(2): 1020-1037 (2016) - [i11]Alexander Daniel Jones, Ben Adcock, Anders C. Hansen:
Analyzing the structure of multidimensional compressed sensing problems through coherence. CoRR abs/1610.07497 (2016) - 2015
- [j5]Ben Adcock, Anders C. Hansen:
Generalized sampling and the stable and accurate reconstruction of piecewise analytic functions from their Fourier coefficients. Math. Comput. 84(291): 237-270 (2015) - [j4]Ben Adcock, Anders C. Hansen, Gitta Kutyniok
Linear Stable Sampling Rate: Optimality of 2D Wavelet Reconstructions from Fourier Measurements. SIAM J. Math. Anal. 47(2): 1196-1233 (2015) - [i10]Jonathan Ben-Artzi, Anders C. Hansen, Olavi Nevanlinna, Markus Seidel:
Can everything be computed? - On the Solvability Complexity Index and Towers of Algorithms. CoRR abs/1508.03280 (2015) - 2014
- [j3]Ben Adcock, Milana Gataric
On Stable Reconstructions from Nonuniform Fourier Measurements. SIAM J. Imaging Sci. 7(3): 1690-1723 (2014) - [j2]Ben Adcock, Anders C. Hansen, Alexei Shadrin:
A Stability Barrier for Reconstructions from Fourier Samples. SIAM J. Numer. Anal. 52(1): 125-139 (2014) - [i9]Alexander Daniel Jones, Ben Adcock, Anders C. Hansen:
On Asymptotic Incoherence and its Implications for Compressed Sensing of Inverse Problems. CoRR abs/1402.5324 (2014) - [i8]Ben Adcock, Anders C. Hansen, Bogdan Roman:
The quest for optimal sampling: Computationally efficient, structure-exploiting measurements for compressed sensing. CoRR abs/1403.6540 (2014) - [i7]Bogdan Roman, Anders C. Hansen, Ben Adcock:
On asymptotic structure in compressed sensing. CoRR abs/1406.4178 (2014) - [i6]Alexander Bastounis, Anders C. Hansen:
On the absence of the RIP in real-world applications of compressed sensing and the RIP in levels. CoRR abs/1411.4449 (2014) - 2013
- [j1]Ben Adcock, Anders C. Hansen, Clarice Poon:
Beyond Consistent Reconstructions: Optimality and Sharp Bounds for Generalized Sampling, and Application to the Uniform Resampling Problem. SIAM J. Math. Anal. 45(5): 3132-3167 (2013) - [i5]Ben Adcock, Anders C. Hansen, Clarice Poon:
Beyond consistent reconstructions: optimality and sharp bounds for generalized sampling, and application to the uniform resampling problem. CoRR abs/1301.2831 (2013) - [i4]Ben Adcock, Anders C. Hansen, Clarice Poon, Bogdan Roman:
Breaking the coherence barrier: asymptotic incoherence and asymptotic sparsity in compressed sensing. CoRR abs/1302.0561 (2013) - [i3]Ben Adcock, Anders C. Hansen, Bogdan Roman, Gerd Teschke:
Generalized sampling: stable reconstructions, inverse problems and compressed sensing over the continuum. CoRR abs/1310.1141 (2013) - 2012
- [i2]Ben Adcock, Anders C. Hansen, Clarice Poon:
On optimal wavelet reconstructions from Fourier samples: linearity and universality of the stable sampling rate. CoRR abs/1208.5959 (2012) - 2010
- [i1]Ben Adcock, Anders C. Hansen:
A Generalized Sampling Theorem for Reconstructions in Arbitrary Bases. CoRR abs/1007.1852 (2010)
Coauthor Index
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