ConE: Cone Embeddings for Multi-Hop Reasoning over Knowledge Graphs

TL;DR

ConE introduces a novel geometric embedding model using cones for multi-hop reasoning over knowledge graphs, effectively handling all first-order logic operations including negation, and significantly improves performance on benchmarks.

Contribution

This paper presents the first geometry-based query embedding model capable of modeling negation alongside conjunction and disjunction in knowledge graphs.

Findings

ConE outperforms existing models on benchmark datasets.

It effectively models negation using geometric complement operators.

ConE accurately captures complex logical relationships in knowledge graphs.

Abstract

Query embedding (QE) -- which aims to embed entities and first-order logical (FOL) queries in low-dimensional spaces -- has shown great power in multi-hop reasoning over knowledge graphs. Recently, embedding entities and queries with geometric shapes becomes a promising direction, as geometric shapes can naturally represent answer sets of queries and logical relationships among them. However, existing geometry-based models have difficulty in modeling queries with negation, which significantly limits their applicability. To address this challenge, we propose a novel query embedding model, namely Cone Embeddings (ConE), which is the first geometry-based QE model that can handle all the FOL operations, including conjunction, disjunction, and negation. Specifically, ConE represents entities and queries as Cartesian products of two-dimensional cones, where the intersection and union of cones naturally model the conjunction and disjunction operations. By further noticing that the closure of complement of cones remains cones, we design geometric complement operators in the embedding space for the negation operations. Experiments demonstrate that ConE significantly outperforms existing state-of-the-art methods on benchmark datasets.