Embedding Knowledge Graph in Function Spaces

TL;DR

This paper proposes a novel knowledge graph embedding method that uses finite-dimensional function spaces, including polynomial and neural network functions, to enhance expressiveness and enable advanced operations like composition and derivatives.

Contribution

It introduces a fundamentally different embedding approach operating in function spaces, expanding the capabilities beyond traditional vector-based methods.

Findings

Enhanced expressiveness through function-based embeddings

Ability to perform composition, derivatives, and primitives on entities

Provides reproducible code for the proposed method

Abstract

We introduce a novel embedding method diverging from conventional approaches by operating within function spaces of finite dimension rather than finite vector space, thus departing significantly from standard knowledge graph embedding techniques. Initially employing polynomial functions to compute embeddings, we progress to more intricate representations using neural networks with varying layer complexities. We argue that employing functions for embedding computation enhances expressiveness and allows for more degrees of freedom, enabling operations such as composition, derivatives and primitive of entities representation. Additionally, we meticulously outline the step-by-step construction of our approach and provide code for reproducibility, thereby facilitating further exploration and application in the field.