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On instabilities of deep learning in image reconstruction and the potential costs of AI
TLDR
In this paper, we demonstrate a crucial phenomenon: Deep learning typically yields unstable methods for image reconstruction with potential to change the field. Expand
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The troublesome kernel: why deep learning for inverse problems is typically unstable
TLDR
In this paper we present a comprehensive mathematical analysis explaining the many facets of the instability phenomenon in DL for inverse problems. Expand
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Uniform recovery in infinite-dimensional compressed sensing and applications to structured binary sampling
TLDR
In this paper, we introduce a series of uniform recovery guarantees for infinite-dimensional compressed sensing based on sparsity in levels and so-called multilevel random subsampling. Expand
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Coherence estimates between Hadamard matrices and Daubechies wavelets
Traditionally the compressive sensing theory have been focusing on the three principles of sparsity, incoherence and uniform random subsampling. Recent years research have shown that these principlesExpand
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What do AI algorithms actually learn? - On false structures in deep learning
TLDR
There are two big unsolved mathematical questions in artificial intelligence (AI): (1) Why is deep learning so successful in classification problems and (2) why are neural nets based on deep learning at the same time universally unstable. Expand
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Appreciation to Journal of Mathematics Imaging and Vision Reviewers
Sadiq Abdulhussain Hanno Ackermann Jonas Adler Vaneet Aggarwal Gianluca Agresti Miguel Aleman Flores Tobias Alt Luis Alvarez Habib Ammari Eric Andres Vegard Antun Alexis Arnaudon Anaïs Badoual EgilExpand
Can stable and accurate neural networks be computed? -- On the barriers of deep learning and Smale's 18th problem
TLDR
Deep learning (DL) suffers from a universal phenomenon: instability, despite universal approximating properties that often guarantee the existence of stable neural networks (NNs). Expand