Topological Data Analysis


The following were presented in the seminar of the Topological Machine Learning group of the Universitat de Barcelona. These slides contain an introduction to the theory of quiver representation for neural networks. The slides are based on the paper The Representation Theory of Neural Networks, by Marco Antonio Armenta and Pierre-Marc Jodoin.

Quiver representations of neural networks. (28-11-22).


The following slides were presented in the seminar of the Topological Machine Learning research group of the Universitat of Barcelona. In this seminar, I presented computational graphs and I defined neural networks as a particular case. Also, I introduced the basic tools of our work to use TDA to predict generalization gaps without using a training set.

The topology of neural networks: How topology helps us to understand generalization and future challenges. (25-02-22).

The seminar was recorded and can be accessed here:

Recorded seminar in youtube. (25-02-22).


The following slides were presented at a talk in the course related with “Advanced mathematics for scientific challenges”, in the MSc. in Advanced Mathematics of the University of Barcelona. They provide a brief introduction to TDA libraries/packages and an introductory tutorial in Python on how to use Giotto-TDA and Ripser. Also they introduce one of the methods for obtaining confidence sets of persistence diagrams published in the paper Brittany Terese Fasy, Fabrizio Lecci, Alessandro Rinaldo, Larry Wasserman, Sivaraman Balakrishnan, AartiSingh. “Confidence sets for persistence diagrams.” The Annals of Statistics, 42(6) 2301-2339 December 2014.

Introduction to applied TDA slides. (11-11-21).

Python notebook associated to the slides. (11-11-21).