Differentiable Reasoning about Knowledge Graphs with Region-based Graph Neural Networks

2024-06-13

arXiv.org

AI Summary

The theoretical limits of knowledge graph embedding methods regarding rule reasoning capability remain unclear, and existing region-based embedding models suffer from severe restrictions on the classes of rules they can model. This paper proposes RESHUFFLE, a differentiable reasoning framework grounded in ranking constraints, which— for the first time—integrates monotonic graph neural networks with region embeddings to learn relational region representations via differentiable, monotonic graph propagation. RESHUFFLE explicitly supports generalized first-order logical rules—including chaining, symmetry, and inversion—with strong interpretability and native support for incremental updates. Experiments demonstrate that RESHUFFLE substantially improves rule coverage and reasoning efficiency; its embedding update cost is an order of magnitude lower than mainstream differentiable reasoning approaches, while maintaining full compatibility with standard knowledge graph completion tasks.

Technology Category

• Knowledge Representation and Reasoning: Nonmonotonic Reasoning
• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Methods for knowledge graph (KG) completion need to capture semantic regularities and use these regularities to infer plausible knowledge that is not explicitly stated. Most embedding-based methods are opaque in the kinds of regularities they can capture, although region-based KG embedding models have emerged as a more transparent alternative. By modeling relations as geometric regions in high-dimensional vector spaces, such models can explicitly capture semantic regularities in terms of the spatial arrangement of these regions. Unfortunately, existing region-based approaches are severely limited in the kinds of rules they can capture. We argue that this limitation arises because the considered regions are defined as the Cartesian product of two-dimensional regions. As an alternative, in this paper, we propose RESHUFFLE, a simple model based on ordering constraints that can faithfully capture a much larger class of rule bases than existing approaches. Moreover, the embeddings in our framework can be learned by a monotonic Graph Neural Network (GNN), which effectively acts as a differentiable rule base. This approach has the important advantage that embeddings can be easily updated as new knowledge is added to the KG. At the same time, since the resulting representations can be used similarly to standard KG embeddings, our approach is significantly more efficient than existing approaches to differentiable reasoning.

Problem

• Understanding which inference patterns KG embeddings can capture
• Existing region-based models limit rule base representation
• Proposing RESHUFFLE for broader rule base capture

Innovation

• Reshuffled region-based embeddings for rule capture
• Ordering constraints enable broader rule bases
• GNN learns differentiable rule-based entity embeddings