{"type":"ScholarlyArticle","title":"A Unification Framework for Euclidean and Hyperbolic Graph Neural Networks","authors":[{"name":"Mehrdad Khatir","slug":"mehrdad-khatir","given":"Mehrdad","family":"Khatir","affiliation":"Department of Computer Science , Virginia Tech , Arlington , VA , USA"},{"name":"Nurendra Choudhary","slug":"nurendra-choudhary","given":"Nurendra","family":"Choudhary","affiliation":"Department of Computer Science , Virginia Tech , Arlington , VA , USA"},{"name":"Sutanay Choudhury","slug":"sutanay-choudhury","given":"Sutanay","family":"Choudhury","affiliation":"Pacific Northwest National Laboratory , Richland , WA , USA"},{"name":"Khushbu Agarwal","slug":"khushbu-agarwal","given":"Khushbu","family":"Agarwal","affiliation":"Pacific Northwest National Laboratory , Richland , WA , USA"},{"name":"Chandan K. Reddy","slug":"chandan-k-reddy","given":"Chandan K.","family":"Reddy","affiliation":"Department of Computer Science , Virginia Tech , Arlington , VA , USA"}],"abstract":"Hyperbolic neural networks can effectively capture the inherent hierarchy of graph datasets, and consequently a powerful choice of GNNs. However, they entangle multiple incongruent (gyro-)vector spaces within a layer, which makes them limited in terms of generalization and scalability. \r\n\r\nIn this work, we propose the Poincaré disk model as our search space, and apply all approximations on the disk (as if the disk is a tangent space derived from the origin), thus getting rid of all inter-space transformations. Such an approach enables us to propose a hyperbolic normalization layer and to further simplify the entire hyperbolic model to a Euclidean model cascaded with our hyperbolic normalization layer. We applied our proposed nonlinear hyperbolic normalization to the current state-of-the-art homogeneous and multi-relational graph networks. We demonstrate that our model not only leverages the power of Euclidean networks such as interpretability and efficient execution of various model components, but also outperforms both Euclidean and hyperbolic counterparts on various benchmarks. Our code is made publicly available at https://github.com/oom-debugger/ijcai23.","doi":"10.24963/ijcai.2023/431","url":"https://ijcai.org/proceedings/2023/431","pdf":"https://ijcai.org/proceedings/2023/0431.pdf","markdown":"https://ijcai.org/proceedings/2023/431.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/431","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Machine Learning","track":"Main Track","number":431,"pages":{"first":3875,"last":3883},"keywords":["Machine Learning: ML: Representation learning","Machine Learning: ML: Sequence and graph learning"],"videos":[],"references":[{"position":1,"raw":"[Anderson and May, 1992] Roy M Anderson and Robert M May. 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