Limitations of Deep Learning for Inverse Problems on Digital Hardware
This work addresses fundamental computational constraints for researchers and practitioners using deep learning in fields like medical imaging or signal processing, revealing inherent restrictions rather than incremental improvements.
The paper tackles the limitations of deep learning for solving inverse problems on digital hardware, proving that finite-dimensional inverse problems are not Banach-Mazur computable for small relaxation parameters and establishing a lower bound on achievable algorithmic accuracy.
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.