Position: Topological Deep Learning is the New Frontier for Relational 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

arXiv · 2402.08871

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

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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.

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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. 2024-08-06. Position: Topological Deep Learning is the New Frontier for Relational Learning. https://arxiv.org/abs/2402.08871

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