Knowledge Graph Embeddings as Geometric Operators

The literature presents knowledge graph embedding models as a catalog of competing methods. TransE, RotatE, ComplEx, and a dozen more, each with its own paper and its own claim.

They are closer than that. This book shows the family can be read as configurations of a single relation operator, built from rotation, stretch and translation — which turns model selection from a bake-off into a question about the geometry your data actually has.

Once the operator is in view, the relational properties follow from it. Symmetry, inversion, composition and cardinality stop being empirical quirks and become geometric properties you can impose deliberately, learn from data, or measure in a trained model.

The book starts at the linear algebra and builds to applied work, with PyTorch implementations throughout and a case study on anti-money-laundering detection. It’s the mathematical groundwork under the rest of the series: the trustworthy systems and geometric reasoning that the Beyond books put into production start here.