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Mathematical Foundations of Artificial Intelligence

Ludwig-Maximilians-Universität München

Akademiestr. 7

80799 München

+49 89 2180 4401

kutyniok[at]lmu.de

Research Website

Artificial intelligence is transforming science, industry, and society in unprecedented ways. I am eager to contribute to its reliability and sustainability—particularly in terms of energy efficiency—by leveraging innovative analog computing approaches, such as quantum computing, through a mathematical lens.

Description

Research focus: Artificial Intelligence, Computing Theory, Explainability, Generalization, Imaging Sciences, Inverse Problems, Quantum Computing, Sustainable AI

AI systems still struggle with reliability issues, such as non-robustness. We already showed that certain problems, such as inverse problems, are incomputable on digital hardware, making neural networks trained on them inherently unreliable. However, these problems become computable with the Blum-Shub-Smale (BSS) model, a mathematical framework for analog computing—of which quantum computing is a possible realization.
Another pressing issue in AI is lack of sustainability in the sense of its massive energy consumption. Also here, we could show that analog computing might resolve this problem. Additionally, legal requirements for AI, such as those in the EU AI Act, are becoming increasingly relevant. Through formalizing legal requirements and their analysis, it could be proven that compliance with the EU AU Act could also be eased by analog AI-systems.
Within MCQST, I collaborate with experimental physicists and theorists to develop mathematical models of current quantum computers. This serves as a basis for analyzing their suitability for ensuring reliability of AI systems, for instance, by generalization bounds. Hybrid approaches, combining analog quantum computing with digital hardware, will be explored for improved performance. In addition, we evaluate energy efficiency, determing quantum computing’s potential to reduce AI’s environmental footprint. Close collaboration with experimentalists is key to refining these setups for both reliability and sustainability. Finally, our work assesses whether these setups can meet legal requirements like the "Right to Explanation" and "Algorithmic Transparency," which are often unattainable with digital hardware due to computability limits.

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