HIGHER-ORDER GRAPH REPRESENTATION LEARNING NEEDS A ROSETTA STONE FOR PORTABILITY

The last decade has seen a rapid proliferation of non-Euclidean neural network architectures to address so-called higher-order network data exhibiting multi-way interactions. These architectures run the gamut, differing in their choice of higher-order representations (e.g., hypergraphs and simplicial complexes), their mathematical vernacular (algebraic, topological, geometric), and their intended task (e.g., link prediction, node classification, or segmentation). To help navigate this diverse landscape, several detailed surveys on higher-order representations have recently appeared, attempting to categorize and taxonomize these architectures. Yet multiple blindspots remain, obstructing both the utility of higher-order network representation learning and the development of its associated theoretical guarantees. In this position paper, we argue that portability between higher-order architectures is one such critical, largely under-explored area, vital to the future of graph deep learning. Through the lens of this meta-analysis, we present a “Rosetta stone" for higher-order graph representation learning, highlighting the recent progress, connecting the mathematical dots among multiple fragmented frameworks, and offering a synergistic perspective on the open problems and future directions of non-Euclidean abstract representation learning.