Papamarkou Theodore, Birdal Tolga, Bronstein Michael, Carlsson Gunnar, Curry Justin, Gao Yue, Hajij Mustafa, Kwitt Roland, Liò Pietro, Di Lorenzo Paolo, Maroulas Vasileios, Miolane Nina, Nasrin Farzana, Ramamurthy Karthikeyan Natesan, Rieck Bastian, Scardapane Simone, Schaub Michael T, Veličković Petar, Wang Bei, Wang Yusu, Wei Guo-Wei, Zamzmi Ghada
Department of Mathematics, The University of Manchester, Manchester, UK.
Department of Computing, Imperial College London, London, UK.
Proc Mach Learn Res. 2024 Jul;235:39529-39555.
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.
拓扑深度学习（TDL）是一个快速发展的领域，它利用拓扑特征来理解和设计深度学习模型。本文认为TDL是关系学习的新前沿。TDL可以通过纳入拓扑概念来补充图表示学习和几何深度学习，从而为各种机器学习场景提供自然的选择。为此，本文讨论了TDL中的开放问题，从实际益处到理论基础。针对每个问题，本文概述了潜在的解决方案和未来的研究机会。同时，本文邀请科学界积极参与TDL研究，以释放这一新兴领域的潜力。
