795 citations · 958 across the 9 of their papers we have counts for
9 papers
Achieving Data Efficient Neural Networks with Hybrid Concept-based Models
Tobias A. Opsahl, Vegard Antun
Most datasets used for supervised machine learning consist of a single label per data point. However, in cases where more information than just the class label is available, would…
On the existence of optimal multi-valued decoders and their accuracy bounds for ill-posed inverse problems
Nina Maria Gottschling, Paolo Campodonico, Vegard Antun +1
Ill-posed inverse problems occur everywhere in the sciences including medical imaging, radar, astronomy etc., yielding underdetermined or ill-posed linear (non-linear) reconstructi…
Implicit regularization in AI meets generalized hardness of approximation in optimization -- Sharp results for diagonal linear networks
Johan S. Wind, Vegard Antun, Anders C. Hansen
Understanding the implicit regularization imposed by neural network architectures and gradient based optimization methods is a key challenge in deep learning and AI. In this work w…
Recovering wavelet coefficients from binary samples using fast transforms
Vegard Antun
Recovering a signal (function) from finitely many binary or Fourier samples is one of the core problems in modern medical imaging, and by now there exist a plethora of methods for…
Can stable and accurate neural networks be computed? -- On the barriers of deep learning and Smale's 18th problem
Matthew J. Colbrook, Vegard Antun, Anders C. Hansen
Deep learning (DL) has had unprecedented success and is now entering scientific computing with full force. However, current DL methods typically suffer from instability, even when…
The troublesome kernel -- On hallucinations, no free lunches and the accuracy-stability trade-off in inverse problems
Nina M. Gottschling, Vegard Antun, Anders C. Hansen +1
Methods inspired by Artificial Intelligence (AI) are starting to fundamentally change computational science and engineering through breakthrough performances on challenging problem…
What do AI algorithms actually learn? - On false structures in deep learning
Laura Thesing, Vegard Antun, Anders C. Hansen
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 bas…
Uniform recovery in infinite-dimensional compressed sensing and applications to structured binary sampling
Ben Adcock, Vegard Antun, Anders C. Hansen
Infinite-dimensional compressed sensing deals with the recovery of analog signals (functions) from linear measurements, often in the form of integral transforms such as the Fourier…
On instabilities of deep learning in image reconstruction - Does AI come at a cost?
Vegard Antun, Francesco Renna, Clarice Poon +2
Deep learning, due to its unprecedented success in tasks such as image classification, has emerged as a new tool in image reconstruction with potential to change the field. In this…