Topological Deep Learning

Mustafa Hajij (Santa Clara University)

In this work, we introduce topological deep learning, a formalism that is aimed at two goals (1) introducing topological language to deep learning for the purpose of utilizing the minimal mathematical structures to formalize problems that arise in a generic deep learning problem and (2) augment, enhance and create novel deep learning models utilizing tools available in topology. To this end, we define and study the classification problem in machine learning in a topological setting. Using this topological framework, we show that the classification problem in machine learning is always solvable under very mild conditions. Furthermore, we show that a softmax classification network acts on an input topological space by a finite sequence of topological moves to achieve the classification task.  To demonstrate these results, we provide example datasets and show how they are acted upon by neural nets from this topological perspective.


Mustafa Hajij, Kyle Istvan, “A topological framework for deep learning”,

Mustafa Hajij, Kyle Istvan, Ghada Zamzmi, “Cell complex neural networks”,

One thought on “Topological Deep Learning

  1. Thank you, Mustafa, for a wonderful talk! If anyone would like to leave a question for our speaker, please reply to this comment below.

Leave a Reply

Your email address will not be published. Required fields are marked *