Anders C. Hansen

37 papers Journal 36Unranked 1

Year	Rank	Type	Title / Venue / Authors
2025	J	`jnl`	The Troublesome Kernel: On Hallucinations, No Free Lunches, and the Accuracy-Stability Tradeoff in Inverse Problems. SIAM Rev. Nina Maria Gottschling, Vegard Antun, Anders C. Hansen, Ben Adcock
2025	J	`jnl`	Trustworthy AI in numerics: On verification algorithms for neural network-based PDE solvers. CoRR Emil Haugen, Alexei Stepanenko, Anders C. Hansen
2024	J	`jnl`	Do stable neural networks exist for classification problems? - A new view on stability in AI. CoRR Zhen Ning David Liu, Anders C. Hansen
2024	J	`jnl`	On the consistent reasoning paradox of intelligence and optimal trust in AI: The power of 'I don't know'. CoRR Alexander Bastounis, Paolo Campodonico, Mihaela van der Schaar, Ben Adcock, Anders C. Hansen
2023	J	`jnl`	Implicit regularization in AI meets generalized hardness of approximation in optimization - Sharp results for diagonal linear networks. CoRR Johan S. Wind, Vegard Antun, Anders C. Hansen
2023	—	`conf`	The Boundaries of Verifiable Accuracy, Robustness, and Generalisation in Deep Learning. ICANN (1) Alexander Bastounis, Alexander N. Gorban, Anders C. Hansen, Desmond J. Higham, Danil V. Prokhorov, Oliver J. Sutton, Ivan Yu. Tyukin, Qinghua Zhou
2023	J	`jnl`	The Boundaries of Verifiable Accuracy, Robustness, and Generalisation in Deep Learning. CoRR Alexander Bastounis, Alexander N. Gorban, Anders C. Hansen, Desmond J. Higham, Danil V. Prokhorov, Oliver J. Sutton, Ivan Yu. Tyukin, Qinghua Zhou
2023	J	`jnl`	When can you trust feature selection? - I: A condition-based analysis of LASSO and generalised hardness of approximation. CoRR Alexander Bastounis, Felipe Cucker, Anders C. Hansen
2022	J	`jnl`	Stratified Sampling Based Compressed Sensing for Structured Signals. IEEE Trans. Signal Process. Theresa Loss, Matthew J. Colbrook, Anders C. Hansen
2021	J	`jnl`	Can stable and accurate neural networks be computed? - On the barriers of deep learning and Smale's 18th problem. CoRR Vegard Antun, Matthew J. Colbrook, Anders C. Hansen
2021	J	`jnl`	The mathematics of adversarial attacks in AI - Why deep learning is unstable despite the existence of stable neural networks. CoRR Alexander Bastounis, Anders C. Hansen, Verner Vlacic
2020	J	`jnl`	On the infinite-dimensional QR algorithm. CoRR Matthew J. Colbrook, Anders C. Hansen
2020	J	`jnl`	The troublesome kernel: why deep learning for inverse problems is typically unstable. CoRR Nina Maria Gottschling, Vegard Antun, Ben Adcock, Anders C. Hansen
2019	J	`jnl`	On instabilities of deep learning in image reconstruction - Does AI come at a cost? CoRR Vegard Antun, Francesco Renna, Clarice Poon, Ben Adcock, Anders C. Hansen
2019	J	`jnl`	On the infinite-dimensional QR algorithm. Numerische Mathematik Matthew J. Colbrook, Anders C. Hansen
2019	J	`jnl`	Uniform recovery in infinite-dimensional compressed sensing and applications to structured binary sampling. CoRR Ben Adcock, Vegard Antun, Anders C. Hansen
2019	J	`jnl`	What do AI algorithms actually learn? - On false structures in deep learning. CoRR Laura Thesing, Vegard Antun, Anders C. Hansen
2017	J	`jnl`	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. Alexander Bastounis, Anders C. Hansen
2016	J	`jnl`	A Note on Compressed Sensing of Structured Sparse Wavelet Coefficients From Subsampled Fourier Measurements. IEEE Signal Process. Lett. Ben Adcock, Anders C. Hansen, Bogdan Roman
2016	J	`jnl`	Analyzing the structure of multidimensional compressed sensing problems through coherence. CoRR Alexander Daniel Jones, Ben Adcock, Anders C. Hansen
2016	J	`jnl`	Generalized Sampling and Infinite-Dimensional Compressed Sensing. Found. Comput. Math. Ben Adcock, Anders C. Hansen
2016	J	`jnl`	On Asymptotic Incoherence and Its Implications for Compressed Sensing of Inverse Problems. IEEE Trans. Inf. Theory Alexander Daniel Jones, Ben Adcock, Anders C. Hansen
2015	J	`jnl`	Can everything be computed? - On the Solvability Complexity Index and Towers of Algorithms. CoRR Jonathan Ben-Artzi, Anders C. Hansen, Olavi Nevanlinna, Markus Seidel
2015	J	`jnl`	Generalized sampling and the stable and accurate reconstruction of piecewise analytic functions from their Fourier coefficients. Math. Comput. Ben Adcock, Anders C. Hansen
2015	J	`jnl`	Linear Stable Sampling Rate: Optimality of 2D Wavelet Reconstructions from Fourier Measurements. SIAM J. Math. Anal. Ben Adcock, Anders C. Hansen, Gitta Kutyniok, Jackie Ma
2014	J	`jnl`	A Stability Barrier for Reconstructions from Fourier Samples. SIAM J. Numer. Anal. Ben Adcock, Anders C. Hansen, Alexei Shadrin
2014	J	`jnl`	On Asymptotic Incoherence and its Implications for Compressed Sensing of Inverse Problems. CoRR Alexander Daniel Jones, Ben Adcock, Anders C. Hansen
2014	J	`jnl`	On Stable Reconstructions from Nonuniform Fourier Measurements. SIAM J. Imaging Sci. Ben Adcock, Milana Gataric, Anders C. Hansen
2014	J	`jnl`	On asymptotic structure in compressed sensing. CoRR Bogdan Roman, Anders C. Hansen, Ben Adcock
2014	J	`jnl`	On the absence of the RIP in real-world applications of compressed sensing and the RIP in levels. CoRR Alexander Bastounis, Anders C. Hansen
2014	J	`jnl`	The quest for optimal sampling: Computationally efficient, structure-exploiting measurements for compressed sensing. CoRR Ben Adcock, Anders C. Hansen, Bogdan Roman
2013	J	`jnl`	Beyond Consistent Reconstructions: Optimality and Sharp Bounds for Generalized Sampling, and Application to the Uniform Resampling Problem. SIAM J. Math. Anal. Ben Adcock, Anders C. Hansen, Clarice Poon
2013	J	`jnl`	Beyond consistent reconstructions: optimality and sharp bounds for generalized sampling, and application to the uniform resampling problem CoRR Ben Adcock, Anders C. Hansen, Clarice Poon
2013	J	`jnl`	Breaking the coherence barrier: asymptotic incoherence and asymptotic sparsity in compressed sensing CoRR Ben Adcock, Anders C. Hansen, Clarice Poon, Bogdan Roman
2013	J	`jnl`	Generalized sampling: stable reconstructions, inverse problems and compressed sensing over the continuum. CoRR Ben Adcock, Anders C. Hansen, Bogdan Roman, Gerd Teschke
2012	J	`jnl`	On optimal wavelet reconstructions from Fourier samples: linearity and universality of the stable sampling rate CoRR Ben Adcock, Anders C. Hansen, Clarice Poon
2010	J	`jnl`	A Generalized Sampling Theorem for Reconstructions in Arbitrary Bases CoRR Ben Adcock, Anders C. Hansen