Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Limitations of Deep Learning for Inverse Problems on Digital Hardware   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. In fact, our result even holds for Borel-Turing
computability., i.e., there does not exist an algorithm which performs the
training of a neural network on digital hardware for any given accuracy. This
establishes a conceptual barrier on the capabilities of neural networks for
finite-dimensional inverse problems given that the computations are performed
on digital hardware.

25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin