Topic outline

  • Representing Hierarchies in Hyperbolic Geometry

    The course will be conducted physically on campus. The lectures and other events will not be recorded and will not be available online.

    The goal of this seminar is to get acquainted with hyperbolic geometry and its undiscovered potential in computing. In the beginning, the participants will choose research papers  to study and present to the group after some introductory lectures. Each participant presentation will be followed by a discussion led by the presenter. Depending on the number of particpants, we will have one or two presentaitons per session.

    Course description: 

    Hyperbolic geometry is one of three natural geometries (Euclidean, elliptic/spherical, and hyperbolic), which has been intensively studied in mathematics since its inception in the early 19th century. Recently, it has been gaining more and more traction in computer science and machine learning as it is  better suited for representing hierarchical data than Euclidean geometry.
    The seminar will begin with a short introduction to hyperbolic geometry, as well as a short overview of machine learning techniques in Euclidean spaces; these will build both our intuition and technical skills. The presentations will cover topics including nearest neighbor search, embeddings (especially of trees), Gromov hyperbolicity, hyperbolic dimension reduction, as well as optimization and learning of representations.

    Teaching staff:  Sándor Kisfaludi-Bak and Vikas Garg

    Kickoff: September 16, 2022, 1pm in T4

    Seminars and introductory lectures: Every Friday 1-3 pm in T4, until December 2, except October 21

    Prerequisites: Mathematical maturity and knowledge in algorithms. Familiarity with synthetic and computational geometry is an asset, but not required.

    Intended learning outcome: 

    Students have a basic understanding of hyperbolic geometry and its various models. They understand the most important properties and how these are useful for representing hierarchical structures.

    Grading:

    Students are expected to attend in person. Points will come from:

    • Presentation (70 points): This includes the quality and technical content of the slides, as well as how the presentation is delivered. 

    • Leading the discussion after your talk (10 point): You should prepare a few questions about the topic of your paper to get a discussion started.

    • Participating in discussions of the other talks (20 points): Being around and absorbing the material presented requires active participation in the discussions.

    Resources:
    Introduction to hyperbolic geometry by Cannon et al.

    List of (still) available papers: here.