795 citations · 1.3k across the 32 of their papers we have counts for
35 papers
On Hallucinations in Inverse Problems: Fundamental Limits and Provable Assessment Methods
David Iagaru, Nina M. Gottschling, Anders C. Hansen +1
Artificial intelligence (AI) has transformed imaging inverse problems, from medical diagnostics to Earth observation. Yet deep neural networks can produce hallucinations, realistic…
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…
Generalised hardness of approximation and the SCI hierarchy -- On determining the boundaries of training algorithms in AI
Luca Eva Gazdag, Alexander Bastounis, Anders C. Hansen
Generalised hardness of approximation (GHA) is the phenomenon that one can easily compute an -approximation to a solution of a computational problem for , but for $ε…
The extended Smale's 9th problem -- On computational barriers and paradoxes in estimation, regularisation, computer-assisted proofs and learning
Alexander Bastounis, Anders C Hansen, Verner Vlačić
Linear and semidefinite programming (LP, SDP), regularisation through basis pursuit (BP) and Lasso have seen great success in mathematics, statistics, data science, computer-assist…
The mathematics of adversarial attacks in AI -- Why deep learning is unstable despite the existence of stable neural networks
Alexander Bastounis, Anders C Hansen, Verner Vlačić
The unprecedented success of deep learning (DL) makes it unchallenged when it comes to classification problems. However, it is well established that the current DL methodology prod…
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…