Signal Embeddings for Complex Logical Reasoning in Knowledge Graphs

Complex logical reasoning over Knowledge Graph is one of the fundamental tasks of Artificial Intelligence. Traditional approaches suffer from the incompleteness and noise of knowledge graph, making complex logical reasoning a challenging task. Recent methods propose to embed entities and first-order logic (FOL) queries in low-dimensional vector spaces. However, most of the current models cannot deal with logical negation. In addition, many methods utilize neural networks to model relation projections, which require a large number of parameters and computational expense. In this work, we proposes SignalE that simplifies relation projection operations while being able to handle logical negation. We represent entities and queries by signal embeddings, which can be represented in both time domain and frequency domain interchangeably. The logical negation operation is handled by inverting the amplitude in each dimension of the frequency-domain form of the signal embedding. Furthermore, relational projection operations are simplified into translation between entities. Experiments demonstrate that SignalE significantly outperforms existing state-of-the-art methods on benchmark datasets.