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Graphs & geometric deep learning are cool, but what's next? Our latest work leverages topology to model higher order relationships beyond graphs, covering domains like meshes, sets & their mixtures naturally. Learn more: arxiv.org/abs/2206.00606 #TopologicalDeepLearning #TDL 
So what's a #HigherOrderRelationship? Essentially, it's a relation between relations. Graphs only consider node-to-node relations (via so called edges). Yet, relations between edges or edges & faces, encode interesting patterns, leading to a full hierarchy of relationships.
At the core of our work, lies a new, unifying data structure, we call 'combinatorial complex' (CC), equipped with set-type relations and their hierarchies. Graphs, simplicial complexes and cell complexes are all special cases of CCs, making CCs useful in summarizing complex data.
