Year: 2023
Type: article
Abstract: Deep neural networks have seen tremendous success over the last years. Since the training is performed on digital hardware, in this paper, we analyze what actually can be computed on current hardware platforms modeled as Turing machines, which would lead to inherent restrictions of deep learning. For this, we focus on the class of inverse problems, which, in particular, encompasses any task to reconstruct data from measurements. We prove that finite-dimensional inverse problems are not Banach-Mazur computable for small relaxation parameters. Even more, our results introduce a lower bound on the accuracy that can be obtained algorithmically.
Authors: Holger Boche, Adalbert Fono, Gitta Kutyniok
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: Hardware-Plattform und Computing-Modell für neuromorphes Rechnen - NeuroCM -, G1289050001, Verbundprojekt: Digitale Transformation und Souveränität künftiger Kommunikationsnetze - 6G-life -, Teilvorhaben: Grundlagen und Systemlösungen für Post Shannon Kommunikation, In-Network Computing, eingebettete Sicherheit und Resilienz, G4792813178, G5273600302, G7472567491
OpenAlex ID: W4387872598