Workshop on Topological Deep Learning

This workshop aims to bring together researchers and practicioners from the fields of topological data analysis and deep learning to foster collaboration and exchange of ideas. Through a combination of plenary talks, focused project work, and interactive sessions, we will explore the latest developments in topological deep learning and identify promising directions for future research. Some themes we hope to cover include, but are not limited, to:

• Datasets and benchmarks: Topological data arises naturally in many real-world applications, such as biomolecular problems or transport networks. However, recent research challenges the capabilities of current benchmark datasets to characterize the power of graph learning methods. This motivates our first driving question: can we devise new benchmark data, intrinsically topological, that are well-suited for evaluating topological methods? In a similar spirit: which application domains can provide problems that are inherently topological?
• The expressivity vs. scalability dilemma: Much of the state-of-the-art AI research leverages higher compute capabilities to improve expressivity and performance. However, these demands of energy and computer resources cannot be satisfied by most users and are highly unsustainable and misaligned with the Sustainable Development Goals of the United Nations. Incorporating topological and geometric biases can significantly reduce model size without sacrificing performance, as demonstrated by equivariant networks (leveraging geometric group theory) and neural k-forms (leveraging differential geometry). We aim to contribute to this line of work by exploring new topological methods for the development of expressive yet scalable models.
• Topological neural networks: Recently, many graph learning methods have been extended to accommodate higher-order domains going beyond pairwise interactions, such as simplicial complexes, hypergraphs, or cell complexes. A third topic of exploration of the workshop concerns these models and characterizing their capabilities. As an example, some of these architectures are based on message passing, and suffer from the same shortcomings already known to exist in graph data, like over-squashing and over-smoothing. A potential question to explore in this setting concerns the development of alternative approaches to message passing to learn from relational data, either graph-like or with higher-order relations.
• Mathematical foundations of AI: Finally, we aim to invite participants of the workshop to explore the use of topology and geometry to better understand specific existing models or fundamental questions in AI that lack clear explanations. In this regard, we hope to identify which areas of deep learning reasearch could benefit more from topological approaches, and devote some time to developing these ideas.