Knowledge Graph Embeddings
How representing entities and relations as vectors turns completion into a scoring problem, what each scoring function can and cannot express, and why evaluation in this area has been unreliable.
A knowledge graph is incomplete by construction, and predicting missing triples is the central task. Embedding methods represent each entity and relation as a vector and define a scoring function whose value indicates how plausible a triple is, converting completion into learning representations under which true triples score highly.
The scoring functions and what they express
TransE models a relation as a translation: \(h + r \approx t\). It is simple, interpretable, and structurally incapable of representing one-to-many relations, since if \((h, r, t_1)\) and \((h, r, t_2)\) are both true, both tails must equal \(h + r\) and therefore each other. It also cannot represent symmetric relations without collapsing them to the zero vector.
DistMult scores by a trilinear product, which handles one-to-many and is symmetric by construction, so it cannot distinguish parentOf from childOf. Half the relations in a typical graph are asymmetric, which is a severe limitation stated plainly.
ComplEx places embeddings in complex space and takes the real part of a Hermitian product, which breaks the symmetry while keeping the tractability, and can express symmetric, antisymmetric and inverse relations.
RotatE models relations as rotations in complex space, which naturally expresses symmetry as a rotation by \(\pi\), inversion as the conjugate rotation, and composition as the product of rotations. This is the cleanest correspondence between algebraic structure and relational semantics in the family.
The lesson is that the scoring function is a statement about which relational patterns are representable, and choosing one is choosing what the model can express rather than tuning for accuracy.
Why evaluation has been unreliable
Reported results in this area proved to be strongly dependent on training details rather than on model design. Systematic re-evaluations found that older models, retrained with modern optimisers, better negative sampling, appropriate loss functions and adequate hyperparameter search, match or exceed much of the newer literature, and that many claimed architectural improvements did not survive a fair comparison.
The practical consequence is that a reported improvement in this field needs the training configuration before it means anything, and that a well-tuned simple model is a serious baseline rather than a formality.
When it breaks
Embeddings do not generalise to unseen entities. An entity absent from training has no vector, so a purely embedding-based model cannot score any triple involving it. Inductive methods that embed from features or from local structure are needed for a graph that grows.
Textual and structural signals are complementary and often not combined. Entity names and descriptions carry information the graph structure does not, and models using only structure discard it. Combining them consistently outperforms either alone and is less commonly done than it should be.
The evaluation protocol dominates the numbers. Filtered versus unfiltered ranking, the candidate set, and the handling of ties all move results substantially, and papers differ on all three.
Benchmark leakage is documented. Widely used benchmarks have contained inverse relations that make many test triples trivially inferable from training ones, which inflated results for years before corrected versions were introduced. The dataset version matters as much as the model.
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