Hyperbolic geometry and data science

In recent years there has been a surprising flow of ideas from the mathematical branch of differential geometry and topology towards applications in the natural sciences. Within an exploratory project of STRUCTURES we started to discuss about recent applications of hyperbolic geometry in machine learning, in particular to reveal underlying hierarchical structures in data sets. The goal of this seminar is to bring together researchers from various Heidelberg institutions interested in these topics from the mathematics side and the application side. We meet bi-weekly on tuesdays 13:00 to 14:00 via zoom. Interested people are encouraged to send me (vdisarlo@mathi.uni-heidelberg.de) an email to be added to our mailing list and receive the zoom link.

Link to the references

Date Speaker(s) Affiliation Talk title Abstract
13/05/2020 Organizational meeting
26/05/2020 Federico Lopez HITS The Shortest History of Geometric Deep Learning slides, video. In this talk, I will provide a high-level description of Deep Learning, for the purpose of clarifying vocabulary and general concepts. Then I will revisit some of the main mathematical novelties in Geometric Deep Learning, with applications on graphs and Natural Language Processing. Most of the tools will be based on hyperbolic and spherical geometry.
09/06/2020 Clemens Fruboese Universitaet Heidelberg Towards Graph Embedding in Symmetric Spaces slides, video. This talk deals with graph embeddings into spaces of non-constant curvature. I will at first review applications of graph embeddings, their advantages and flaws. These comprise in particular dealing with structures of non-hierarchical fashion, i.e. structures which do not fit in spaces of constant curvature. Without delving into Mathematical detail, I will point out the benefits which symmetric spaces provide. I will then present some experimental results which originate in my masters thesis. These results show obstacles, which I will then discuss.
23/05/2020 Ilia Kats, Luca Marconato DKFZ Geometrical and statistical approaches in data science for single-cell biology slides, video. Single-cell biology is a new and rapidly evolving field concerned with characterizing biological features of individual cells, as opposed to bulk samples. A plethora of experimental methods exist and new assays are constantly being developed, driving the need for tailored analysis techniques. Single-cell data presents several challenges: It is typically characterized by high fractions of missing values, non-Gaussian likelihoods, and lack of ground truth. In this talk we will attempt to give an overview of the field aimed at non-biologists, with a focus on how by considering topological aspects and low-dimensional embeddings one can extract biological insights.
07/07/2020 Valentina Disarlo Universitaet Heidelberg A crash introduction to Gromov hyperbolic spaces slides, video. A hyperbolic metric space is a metric space satisfying certain metric relations (depending quantitatively on a nonnegative real number d) between points. This concept was introduced by Mikhael Gromov in order to generalize the metric properties of classical hyperbolic geometry and trees. We will review some basic properties of Gromov hyperbolic spaces and define their boundaries.
21/07/2020 Jan Daldrop Smart Steel Technologies Tackling the last efficiency frontier in steel manufacturing through artificial intelligence slides video available upon request High quality requirements and increasing cost pressure represent an enormous challenge for the steel industry. Smart Steel Technologies offers ready-to-use artificial intelligence software solutions for optimizing productivity and quality in steel production and processing. With the company's deep-learning-based classifiers, surface defects are identified much more accurately than with the classic image recognition algorithms typically used in the steel industry. Data from various process steps are combined with surface inspection results, which allows to directly estimate the effects of relevant process parameters on product quality. Optimal parameter ranges are identified to improve the product quality substantially. By live predictions of the temperature behavior of liquid steel the process stability is increased and the overall temperature levels are lowered, which saves energy costs. Smart Steel Technologies has practical project experience covering the processes of BOF, EAF, LF, RH, VD, CCM, Hot Rolling, Pickling, Cold Rolling, and Hot-Dip Galvanizing.