Geometry of Deep Learning

Ph.D. Course

  • Date:

    26 JANUARY
    -
    23 FEBRUARY 2023
     from 15:30 to 18:00

  • Event location: Modena, FIM, via Campi / ZOOM - In presence and online event

  • Type: CaLIGOLA Training School

Timetable:

On Thursdays, h. 3:30 p.m. - 6:00 p.m.

The course will be given in a hybrid mode:

Schedule:

  • Thursday 26 January: Aula M1.7 - [MO 18]
  • Thursday 2 February: Aula M1.6 - [MO 18]
  • Thursday 9 February: Aula M1.7 Disegno - [MO 18]
  • Thursday 16 February: Laboratorio Zironi - [MO 18]
  • Thursday 23 February: Aula M1.7 Disegno - [MO 18]

Slides

Video

Syllabus:

  • Introduction to Deep Learning, basic steps of the algorithm analogies with the human visual systems and its mathematical models.
  • The geometry of the space of data and the space of parameters; KL divergence and its information geometry interpretation.
  • Geometric Deep Learning: the algorithm of Deep Learning on Graphs.
  • Message passing and GATs: a geometrical modelling via heat equation and laplacian on graphs.

This course will be self-contained as much as possible. The necessary differential geometric concepts (manifolds, Frobenius theorem, Cartan formalism) will be introduced and explained. The necessary programming skills will NOT be assumed, but a part of the course will be "hands on" illustrating key examples on colab.

The exam will consist in a brief exposition of some concepts and the students can choose the part of the program they like the most and present a focused exposition on one argument.