Mathematical Algorithm Design for Deep Learning under Societal and
  Judicial Constraints: The Algorithmic Transparency Requirement
Holger Boche Adalbert Fono Gitta Kutyniok
Deep learning still has drawbacks in terms of trustworthiness, which
describes a comprehensible, fair, safe, and reliable method. To mitigate the
potential risk of AI, clear obligations associated to trustworthiness have been
proposed via regulatory guidelines, e.g., in the European AI Act. Therefore, a
central question is to what extent trustworthy deep learning can be realized.
Establishing the described properties constituting trustworthiness requires
that the factors influencing an algorithmic computation can be retraced, i.e.,
the algorithmic implementation is transparent. Motivated by the observation
that the current evolution of deep learning models necessitates a change in
computing technology, we derive a mathematical framework which enables us to
analyze whether a transparent implementation in a computing model is feasible.
We exemplarily apply our trustworthiness framework to analyze deep learning
approaches for inverse problems in digital and analog computing models
represented by Turing and Blum-Shub-Smale Machines, respectively. Based on
previous results, we find that Blum-Shub-Smale Machines have the potential to
establish trustworthy solvers for inverse problems under fairly general
conditions, whereas Turing machines cannot guarantee trustworthiness to the
same degree.