[{"_1":2,"_3":-5,"_4":-5},"loaderData",{"_5":6,"_7":8},"actionData","errors","root",{"_28":-5,"_38":-5,"_39":40,"_41":42,"_43":44,"_45":46,"_47":48,"_49":50,"_51":52,"_53":54,"_55":56,"_57":58},"routes/_store+/_readers+/email_author.$slug/route",{"_9":10,"_11":-5},"book",{"_12":13,"_14":15,"_16":17,"_18":19,"_20":21,"_22":23},"currentUser","id","Z2lkOi8vbGVhbnB1Yi9TdG9yZTo6Qm9va1Byb2R1Y3QvODE3Nzg","title","Knowledge Graph Embeddings as Geometric Operators","state","published","contactAuthorMethod","email","aboutText","

Knowledge graph embeddings are often presented as a crowded model zoo: TransE, DistMult, ComplEx, RotatE, QuatE, RESCAL, TuckER and many more, each with its own notation and intuition. Knowledge Graph Embeddings as Geometric Operators replaces that list with a unifying map. It shows that these models can be understood as configurations of a single relation operator built from rotation, stretch and translation. Under this operator view, symmetry, inversion, composition and cardinality become geometric properties that can be imposed, learned and measured.

Beginning with linear algebra and requiring no prior knowledge of geometric algebra, the book develops the mathematics step by step before connecting it to training, expressivity, diagnostics, calibration and computation. A capstone case study demonstrates two-graph geometric binding for anti-money-laundering detection, while the companion PyTorch library and chapter notebooks make the results reproducible and practical. Written for graduate-level data scientists and practitioners who want more than a recipe, the book serves as the mathematical prequel to the KnowlytiX AI Engineering Series—the foundation beneath trustworthy retrieval, structured memory, geometric ground truth and governed agentic AI.

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Kick off your book project, get started with GhostAI, get better at marketing, or spend the day doing all three! Free live workshops on Zoom. Saturday, June 27, 2026.

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