# Position Paper: Challenges and Opportunities in Topological Deep Learning

**Authors:** 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  
**arXiv:** [2402.08871](https://arxiv.org/abs/2402.08871)  
**Date:** 2024-02-14  
**Summary page:** https://www.summarizepaper.com/en/paper/2402.08871v1/

## Key points

- Topological deep learning (TDL) leverages topological features to enhance deep learning models
- The paper explores TDL's potential in complementing graph representation and geometric deep learning
- Various open problems within TDL are discussed, with potential solutions and future research opportunities identified
- The paper invites the scientific community to engage in TDL research for unlocking its full potential
- Focus on challenges and opportunities in TDL provides valuable insights into integrating topological concepts into machine learning settings

## Summary

Topological deep learning (TDL) is a rapidly evolving field that leverages topological features to enhance the understanding and design of deep learning models. This paper, authored by 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,
and Ghada Zamzmi explores the potential of TDL in complementing graph representation learning and geometric deep learning by incorporating topological concepts. The authors discuss various open problems within TDL that range from practical benefits to theoretical foundations. Each problem is meticulously outlined with potential solutions and future research opportunities identified. The paper serves as an invitation to the scientific community to actively engage in TDL research to unlock the full potential of this emerging field. With a focus on challenges and opportunities in Topological Deep Learning (TDL), this paper provides valuable insights into how topological concepts can be integrated into machine learning settings. By addressing key issues and proposing innovative solutions within TDL, the authors pave the way for further exploration and advancement in this cutting-edge field. Through collaboration and participation from researchers across disciplines, the transformative power of TDL can be fully realized to drive advancements in deep learning methodologies.