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

PubMed, vol. 235, pp. 39529–39555

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.

Authors 22

1. Theodore Papamarkou

   University of Manchester

   Affiliation as printed

   Department of Mathematics , The University of Manchester , Manchester , UK

   Department of Mathematics, The University of Manchester, Manchester, UK

2. Tolga Birdal

   Imperial College London

   Affiliation as printed

   Department of Computing , Imperial College London , London , UK

   Department of Computing, Imperial College London, London, UK

3. Michael M. Bronstein

   University of Oxford · Science Oxford

   Affiliation as printed

   Department of Computer Science , Uni- versity of Oxford , Oxford , UK

   Department of Computer Science, University of Oxford, Oxford, UK

4. Gunnar Carlsson

   nLIGHT (United States) · Stanford University

   Affiliation as printed

   BlueLightAI Inc , USA

   Department of Mathematics , Stanford University , Stanford , USA

   BlueLightAI Inc, USA

   Department of Mathematics, Stanford University, Stanford, USA

5. Justin Michael Curry

   University at Albany, State University of New York

   Affiliation as printed

   University at Albany , New York , USA

   University at Albany, New York, USA

6. Yue Lin Gao

   Tsinghua University

   Affiliation as printed

   School of Software , Tsinghua University , Beijing , China

   School of Software, Tsinghua University, Beijing, China

7. Mustafa Hajij

   University of San Francisco

   Affiliation as printed

   University of San Francisco , San Francisco , USA

   University of San Francisco, San Francisco, USA

8. Roland Kwitt

   University of Salzburg

   Affiliation as printed

   Department of Artificial Intelligence and Hu- man Interfaces , University of Salzburg , Austria

   Department of Artificial Intelligence and Human Interfaces, University of Salzburg, Austria

9. Píetro Lió

   University of Cambridge

   Affiliation as printed

   Department of Computer Science and Technology, University of Cambridge, Cambridge, UK

10. Paolo Di Lorenzo

    Sapienza University of Rome

    Affiliation as printed

    Department of Information Engineering, Electronics and Telecommunications, Sapienza University of Rome, Rome, Italy

11. Vasileios Maroulas

    University of Tennessee at Knoxville

    Affiliation as printed

    Department of Mathematics , University of Tennessee , Knoxville , USA

    Department of Mathematics, University of Tennessee, Knoxville, USA

12. Nina Miolane

    University of California, Santa Barbara

    Affiliation as printed

    Department of Electrical and Computer Engi- neering , UC Santa Barbara , Santa Barbara , USA

    Department of Electrical and Computer Engineering, UC Santa Barbara, Santa Barbara, USA

13. Farzana Nasrin

    University of Hawaiʻi at Mānoa

    Affiliation as printed

    Department of Mathematics , University of Hawai ' i at Mānoa , Hawai ' i , USA

    Department of Mathematics, University of Hawai'i at Mānoa, Hawai'i, USA

14. Karthikeyan Natesan Ramamurthy

    IBM (United States)

    Affiliation as printed

    IBM Corporation New York , USA

    IBM Corporation New York, USA

15. Bastian Rieck

    Helmholtz Munich · Technical University of Munich

    Affiliation as printed

    Helmholtz Munich , Munich Germany

    Technical University of Munich , Munich Germany

    Helmholtz Munich, Munich Germany

    Technical University of Munich, Munich Germany

16. Simone Scardapane

    Sapienza University of Rome

    Affiliation as printed

    Department of Information Engineering, Electronics and Telecommunications , Sapienza University of Rome , Rome , Italy

    Department of Information Engineering, Electronics and Telecommunications, Sapienza University of Rome, Rome, Italy

17. Michael T. Schaub Aachen

    RWTH Aachen University

    Affiliation as printed

    RWTH Aachen University , Aachen , Germany

    RWTH Aachen University, Aachen, Germany

18. Petar Veličković

    University of Cambridge

    Affiliation as printed

    Department of Computer Science and Technology, University of Cambridge, Cambridge, UK

    Google Deep-Mind

19. Bei Wang

    University of Utah

    Affiliation as printed

    School of Computing , University of Utah , Utah , USA

    School of Computing, University of Utah, Utah, USA

20. Yusu Wang

    University of California San Diego

    Affiliation as printed

    Computer Science and Engineering Department , University of California San Diego , San Diego , USA

    Computer Science and Engineering Department, University of California San Diego, San Diego, USA

21. Guo‐Wei Wei

    Michigan State University

    Affiliation as printed

    Department of Mathe- matics , Michigan State University , East Lansing , Michigan , USA

    Department of Mathematics, Michigan State University, East Lansing, Michigan, USA

22. Ghada Zamzmi

    University of South Florida

    Affiliation as printed

    University of South Florida , Florida , USA

    University of South Florida, Florida, USA