FAKULTÄTSKOLLOQUIUM

Am Mittwoch, dem 06. August 2025, spricht um 13:30 Uhr im Raum Z 4005

Dr. Yota Maeda (Technische Universität Darmstadt)

zum Thema: "Deep learning and algebraic geometry".

Alle Interessenten sind herzlich eingeladen.

Abstract:

In recent years, the increasing availability of computational resources has led to breakthroughs
in problem-solving across various fields through deep learning. Naturally, this has sparked in-
terest in understanding the underlying theory, that is, the source of its remarkable perfor-
mance, yet a full theoretical explanation remains elusive.

In this talk, I will try to introduce two topics relevant to deep learning from the perspective of
algebraic geometry, my area of expertise, which seek to present them in a way that is accessi-
ble to experts in other fields.

The first topic is singular learning theory, which describes a generalization error of singular
models. It is known that deep learning is a typical singular model that shows a situation con-
tradicting the classical bias-variance trade-off. This phenomenon is called double descent,
which shows the generalization error decreases as the number of model parameters increases
beyond the amount of data. In this talk, I will introduce the classical singular learning theory
and (if time permits) how it is generalized to the analysis of quantum singular models
(https://arxiv.org/abs/2411.16396).

The second topic concerns performance guarantees when solving mathematical problems us-
ing deep-learning methods (https://arxiv.org/abs/2504.12465). In this work, we demonstrated
why Transformers can solve mathematical problems, specifically the learning of Gröbner bases
in terms of the diversity of training datasets. Our results provide a rigorous geometric founda-
tion for Transformers to address a mathematical problem, which is an answer to Lample and
Charton’s idea of training on diverse or representative inputs.