Oberseminar "Mathematics of Artificial Intelligence" (Math-of-AI)

The Oberseminar Math-of-AI is organized by Alexander Effland and Illia Karabash, jointly with Anton Bovier and Christian Brennecke.

The seminar takes place several times per semester on 

Mondays from 12:45 to 14:00 in the seminar room 1.008 (Endenicher Allee 60).

 

 

Talks in Summer Semester 2026

 

Talks planned for Winter Semester 2026/2027

Abstracts

18.05.2026, Philipp Grohs (Universität Wien) "Neural Wave Functions for the Electronic Schrödinger Equation: A Mathematical Case Study in Scientific Computing”.
Abstract. Deep learning has attracted considerable attention in scientific computing, from neural-network ansätze for partial differential equations to data-driven surrogate models for complex first-principles simulations. Its impact, however, has been uneven: in many standard settings, classical numerical methods remain difficult to outperform. I will begin with a brief broader perspective on this phenomenon, including complexity-theoretic upper and lower bounds that clarify both the limitations of deep-learning-based methods and the special structures under which they can succeed.
The electronic Schrödinger equation provides a particularly compelling example of such a success. In computational quantum chemistry, deep-learning variational Monte Carlo (VMC) has led to striking empirical progress through highly expressive neural-network wave functions. At the same time, this success raises delicate mathematical questions. I will discuss recent results showing that the nodal geometry of the wave function governs the integrability of the local energy and of VMC gradient estimators, leading naturally to heavy-tailed stochastic optimization problems. Motivated by this analysis, I will present a clipped VMC optimization algorithm and prove its convergence under precisely the weak-moment assumptions identified by the nodal theory. The talk will conclude with open questions at the interface of approximation theory, probability, optimization, and computational quantum chemistry.

20.07.2026, Véronique Gayrard (CNRS & Marseille Institute of Mathematics) “Hopfield models of associative memory".
Abstract. In 1982, condensed matter physicist John Hopfield drew inspiration from the physics of spin glasses in order to devise simple artificial neural networks that could learn and remember. This not only revived the largely abandoned field of neural networks, but also built bridges between the fields of statistical mechanics, computational neuroscience and machine learning. His pioneering work was recognised with the award of the 2024 Nobel Prize in Physics.
In this talk, I will first introduce these models and present a non-technical overview of the most significant known results, covering predictions from theoretical physics and mathematically rigorous results. In the second part, I will discuss recent mathematical progress in understanding how false memories are formed alongside intended memories during the learning process.

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