Directed Graph Embeddings in Pseudo-Riemannian Manifolds

Aaron Sim, Maciej L Wiatrak, Angus Brayne, Paidi Creed, Saee Paliwal
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:9681-9690, 2021.

Abstract

The inductive biases of graph representation learning algorithms are often encoded in the background geometry of their embedding space. In this paper, we show that general directed graphs can be effectively represented by an embedding model that combines three components: a pseudo-Riemannian metric structure, a non-trivial global topology, and a unique likelihood function that explicitly incorporates a preferred direction in embedding space. We demonstrate the representational capabilities of this method by applying it to the task of link prediction on a series of synthetic and real directed graphs from natural language applications and biology. In particular, we show that low-dimensional cylindrical Minkowski and anti-de Sitter spacetimes can produce equal or better graph representations than curved Riemannian manifolds of higher dimensions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-sim21a, title = {Directed Graph Embeddings in Pseudo-Riemannian Manifolds}, author = {Sim, Aaron and Wiatrak, Maciej L and Brayne, Angus and Creed, Paidi and Paliwal, Saee}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {9681--9690}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/sim21a/sim21a.pdf}, url = {https://proceedings.mlr.press/v139/sim21a.html}, abstract = {The inductive biases of graph representation learning algorithms are often encoded in the background geometry of their embedding space. In this paper, we show that general directed graphs can be effectively represented by an embedding model that combines three components: a pseudo-Riemannian metric structure, a non-trivial global topology, and a unique likelihood function that explicitly incorporates a preferred direction in embedding space. We demonstrate the representational capabilities of this method by applying it to the task of link prediction on a series of synthetic and real directed graphs from natural language applications and biology. In particular, we show that low-dimensional cylindrical Minkowski and anti-de Sitter spacetimes can produce equal or better graph representations than curved Riemannian manifolds of higher dimensions.} }
Endnote
%0 Conference Paper %T Directed Graph Embeddings in Pseudo-Riemannian Manifolds %A Aaron Sim %A Maciej L Wiatrak %A Angus Brayne %A Paidi Creed %A Saee Paliwal %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-sim21a %I PMLR %P 9681--9690 %U https://proceedings.mlr.press/v139/sim21a.html %V 139 %X The inductive biases of graph representation learning algorithms are often encoded in the background geometry of their embedding space. In this paper, we show that general directed graphs can be effectively represented by an embedding model that combines three components: a pseudo-Riemannian metric structure, a non-trivial global topology, and a unique likelihood function that explicitly incorporates a preferred direction in embedding space. We demonstrate the representational capabilities of this method by applying it to the task of link prediction on a series of synthetic and real directed graphs from natural language applications and biology. In particular, we show that low-dimensional cylindrical Minkowski and anti-de Sitter spacetimes can produce equal or better graph representations than curved Riemannian manifolds of higher dimensions.
APA
Sim, A., Wiatrak, M.L., Brayne, A., Creed, P. & Paliwal, S.. (2021). Directed Graph Embeddings in Pseudo-Riemannian Manifolds. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:9681-9690 Available from https://proceedings.mlr.press/v139/sim21a.html.

Related Material