Limitations of Deep Learning for Inverse Problems on Digital Hardware

Boche, Holger ; Fono, Adalbert und Kutyniok, Gitta (2023): Limitations of Deep Learning for Inverse Problems on Digital Hardware. In: IEEE Transactions on Information Theory, Vol. 69, No. 12: pp. 7887-7908

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.

• Item Type: Journal article
• Keywords: Computing theory,deep learning,signal processing,turing machine
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Bavarian Chair for Mathematical Foundations of Artificial Intelligence
• Subjects: 000 Computer science, information and general works > 000 Computer science, knowledge, and systems
• ISSN: 0018-9448
• Language: English