Position: Topological Deep Learning is the New Frontier for Relational Learning

TL;DR

This paper introduces topological deep learning as a promising new approach for relational learning, emphasizing its potential to complement existing graph and geometric methods through topological insights.

Contribution

It highlights open problems, discusses potential solutions, and encourages research participation in the emerging field of topological deep learning.

Findings

TDL can enhance relational learning models.

Open problems include theoretical foundations and practical applications.

Future research directions are outlined for TDL development.

Abstract

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 is the new frontier for relational learning. 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.