In a similarity-based (or semantic matching) scoring function for knowledge graphs, the plausibility of a fact is measured by matching the latent semantics of entities and relations. This relationship is typically expressed using a bilinear formulation, such as $$h^T M_r \sim t^T$$, where $$h$$ and $$t$$ represent the head and tail entity vectors, and $$M_r$$ represents the relation matrix.

San Jose State University

Google

A scoring function can assign a score to each possible output for a given input, and an inference system can then search for the output that maximizes that score. A common AI design pattern is to learn an approximate scoring function and then apply an approximate maximization algorithm.

Scoring Function

A Survey on Knowledge Graphs: Representation, Acquisition and Applications

A scored inference system may compute a score for each possible output but still need an approximate search algorithm to find a high-scoring output, because exhaustive enumeration can be far too large. These approximate algorithms are not guaranteed to find the output that maximizes the score.

Approximate Search in Scored Inference

In a distance-based scoring function for knowledge graphs, the plausibility of a fact is measured by the distance between entities. This relationship is typically expressed as $$h + r \sim t$$, where $$h$$ represents the head entity, $$r$$ represents the relation, and $$t$$ represents the tail entity.

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