Knowledge Sheaves: A Sheaf-Theoretic Framework for Knowledge Graph Embedding

Thomas Gebhart, Jakob Hansen, Paul Schrater
Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, PMLR 206:9094-9116, 2023.

Abstract

Knowledge graph embedding involves learning representations of entities—the vertices of the graph—and relations—the edges of the graph—such that the resulting representations encode the known factual information represented by the knowledge graph and can be used in the inference of new relations. We show that knowledge graph embedding is naturally expressed in the topological and categorical language of cellular sheaves: a knowledge graph embedding can be described as an approximate global section of an appropriate knowledge sheaf over the graph, with consistency constraints induced by the knowledge graph’s schema. This approach provides a generalized framework for reasoning about knowledge graph embedding models and allows for the expression of a wide range of prior constraints on embeddings. Further, the resulting embeddings can be easily adapted for reasoning over composite relations without special training. We implement these ideas to highlight the benefits of the extensions inspired by this new perspective.

Cite this Paper

BibTeX
@InProceedings{pmlr-v206-gebhart23a, title = {Knowledge Sheaves: A Sheaf-Theoretic Framework for Knowledge Graph Embedding}, author = {Gebhart, Thomas and Hansen, Jakob and Schrater, Paul}, booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics}, pages = {9094--9116}, year = {2023}, editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem}, volume = {206}, series = {Proceedings of Machine Learning Research}, month = {25--27 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v206/gebhart23a/gebhart23a.pdf}, url = {https://proceedings.mlr.press/v206/gebhart23a.html}, abstract = {Knowledge graph embedding involves learning representations of entities—the vertices of the graph—and relations—the edges of the graph—such that the resulting representations encode the known factual information represented by the knowledge graph and can be used in the inference of new relations. We show that knowledge graph embedding is naturally expressed in the topological and categorical language of cellular sheaves: a knowledge graph embedding can be described as an approximate global section of an appropriate knowledge sheaf over the graph, with consistency constraints induced by the knowledge graph’s schema. This approach provides a generalized framework for reasoning about knowledge graph embedding models and allows for the expression of a wide range of prior constraints on embeddings. Further, the resulting embeddings can be easily adapted for reasoning over composite relations without special training. We implement these ideas to highlight the benefits of the extensions inspired by this new perspective.} }
Endnote
%0 Conference Paper %T Knowledge Sheaves: A Sheaf-Theoretic Framework for Knowledge Graph Embedding %A Thomas Gebhart %A Jakob Hansen %A Paul Schrater %B Proceedings of The 26th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2023 %E Francisco Ruiz %E Jennifer Dy %E Jan-Willem van de Meent %F pmlr-v206-gebhart23a %I PMLR %P 9094--9116 %U https://proceedings.mlr.press/v206/gebhart23a.html %V 206 %X Knowledge graph embedding involves learning representations of entities—the vertices of the graph—and relations—the edges of the graph—such that the resulting representations encode the known factual information represented by the knowledge graph and can be used in the inference of new relations. We show that knowledge graph embedding is naturally expressed in the topological and categorical language of cellular sheaves: a knowledge graph embedding can be described as an approximate global section of an appropriate knowledge sheaf over the graph, with consistency constraints induced by the knowledge graph’s schema. This approach provides a generalized framework for reasoning about knowledge graph embedding models and allows for the expression of a wide range of prior constraints on embeddings. Further, the resulting embeddings can be easily adapted for reasoning over composite relations without special training. We implement these ideas to highlight the benefits of the extensions inspired by this new perspective.
APA
Gebhart, T., Hansen, J. & Schrater, P.. (2023). Knowledge Sheaves: A Sheaf-Theoretic Framework for Knowledge Graph Embedding. Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 206:9094-9116 Available from https://proceedings.mlr.press/v206/gebhart23a.html.

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