Mathematical algorithm design for deep learning under societal and judicial constraints: The algorithmic transparency requirement

Boche, Holger; Fono, Adalbert und Kutyniok, Gitta (2025): Mathematical algorithm design for deep learning under societal and judicial constraints: The algorithmic transparency requirement. In: Applied and Computational Harmonic Analysis, Bd. 77, 101763

Abstract

Deep learning still has drawbacks regarding trustworthiness, which describes a comprehensible, fair, safe, and reliable method. To mitigate the potential risk of AI, clear obligations associated with 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 that enables us to analyze whether a transparent implementation in a computing model is feasible. The core idea is to formalize and subsequently relate the properties of a transparent algorithmic implementation to the mathematical model of the computing platform, thereby establishing verifiable criteria. 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.

• Dokumententyp: Zeitschriftenartikel
• Keywords: Deep learning, Trustworthiness, Algorithmic transparency, Turing machines, Blum-Shub-Smale machines
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Professur für Mathematische Grundlagen des Verständnisses der künstlichen Intelligenz
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 1063-5203
• Sprache: Englisch
• DFG: Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - 441826958