Position Paper: Challenges and Opportunities in Topological Deep Learning

Traditional machine learning often assumes that the observed data of interest are supported on a linear vector space Topological deep learning (TDL) is a rapidly and can be described by a set of feature vectors. However, evolving field that uses topological features to understand there is growing awareness that, in many cases, this viewpoint and design deep learning models. This is insufficient to describe several data within the real paper posits that TDL may complement graph representation world. For example, molecules may be described more appropriately learning and geometric deep learning by graphs than feature vectors. Other examples by incorporating topological concepts, and can include three-dimensional objects represented by meshes, thus provide a natural choice for various machine as encountered in computer graphics and geometry processing, learning settings. To this end, this paper discusses or data supported on top of a complex social network open problems in TDL, ranging from practical of interrelated actors. Hence, there has been an increased benefits to theoretical foundations. For each problem, interest in importing concepts from geometry and topology it outlines potential solutions and future research into the usual machine learning pipelines to gain further opportunities.