Position Paper: Challenges and Opportunities in Topological Deep
  Learning
Theodore Papamarkou Tolga Birdal Michael Bronstein Gunnar Carlsson Justin Curry Yue Gao Mustafa Hajij Roland Kwitt Pietro Liò Paolo Di Lorenzo Vasileios Maroulas Nina Miolane Farzana Nasrin Karthikeyan Natesan Ramamurthy Bastian Rieck Simone Scardapane Michael T. Schaub Petar Veličković Bei Wang Yusu Wang Guo-Wei Wei Ghada Zamzmi
Topological deep learning (TDL) is a rapidly evolving field that uses
topological features to understand and design deep learning models. This paper
posits that TDL may complement graph representation learning and geometric deep
learning by incorporating topological concepts, and can thus provide a natural
choice for various machine learning settings. To this end, this paper discusses
open problems in TDL, ranging from practical benefits to theoretical
foundations. For each problem, it outlines potential solutions and future
research opportunities. At the same time, this paper serves as an invitation to
the scientific community to actively participate in TDL research to unlock the
potential of this emerging field.