  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.
