BoxE: A Box Embedding Model for Knowledge Base Completion (2007.06267v2)

Abstract: Knowledge base completion (KBC) aims to automatically infer missing facts by exploiting information already present in a knowledge base (KB). A promising approach for KBC is to embed knowledge into latent spaces and make predictions from learned embeddings. However, existing embedding models are subject to at least one of the following limitations: (1) theoretical inexpressivity, (2) lack of support for prominent inference patterns (e.g., hierarchies), (3) lack of support for KBC over higher-arity relations, and (4) lack of support for incorporating logical rules. Here, we propose a spatio-translational embedding model, called BoxE, that simultaneously addresses all these limitations. BoxE embeds entities as points, and relations as a set of hyper-rectangles (or boxes), which spatially characterize basic logical properties. This seemingly simple abstraction yields a fully expressive model offering a natural encoding for many desired logical properties. BoxE can both capture and inject rules from rich classes of rule languages, going well beyond individual inference patterns. By design, BoxE naturally applies to higher-arity KBs. We conduct a detailed experimental analysis, and show that BoxE achieves state-of-the-art performance, both on benchmark knowledge graphs and on more general KBs, and we empirically show the power of integrating logical rules.

Overview of BoxE: A Box Embedding Model for Knowledge Base Completion

The paper under discussion introduces BoxE, a novel embedding model designed for Knowledge Base Completion (KBC). KBC is a critical task as it involves inferring missing information from a knowledge base by utilizing the facts that are already present. Traditional methods in this domain have faced challenges, such as theoretical inexpressivity, inability to manage hierarchical and higher-arity relations, and difficulty integrating logical rules. BoxE addresses these challenges through its innovative spatio-translational embedding approach, which encodes entities as points and relations as hyper-rectangles—referred to as boxes.

Key Contributions and Methodology

BoxE positions itself distinctively by providing a fully expressive model, which is a first for translational models. The architecture of BoxE allows it to model relations as axis-aligned hyper-rectangles in a Euclidean space. These boxes represent logical properties, and the positions of the entities relative to these boxes determine the scoring of facts. One of BoxE’s standout features is its ability to capture and enforce rules from various logical languages and to apply these rules across higher-arity knowledge bases naturally.

The simplicity of using hyper-rectangles provides a compact and natural encoding for many logical properties, overcoming the deficiencies of previous models. The paper proves that BoxE is capable of capturing complex logical patterns beyond individual inference patterns, particularly highlighting its capacity to manage symmetry, hierarchy, and intersection rules effectively. Furthermore, BoxE is able to inject logical rules, reinforcing the model's versatility and its potential for application in more complex knowledge bases.

Experimental Evaluation

The results presented in the paper are compelling, demonstrating BoxE’s prowess across a range of datasets, including benchmark knowledge graphs and more general knowledge bases. On distinct datasets like FB15k-237, WN18RR, and YAGO3-10, BoxE showcases its performance, even achieving state-of-the-art results particularly on YAGO3-10. This is significant given the dataset's size and complexity. The performance on higher-arity tasks using JF17K and FB-AUTO datasets confirms BoxE's robustness and adaptability to various KBC scenarios.

Moreover, when tested for rule injection capabilities with a subset of NELL, BoxE shows significant improvement in predictive performance, illustrating its ability to integrate and benefit from logical rules beyond traditional learning methodologies.

Theoretical and Practical Implications

The theoretical implications of BoxE are profound, as it bridges a critical gap in the expressivity and generalization capabilities of KBC models. By enabling the integration of a rich set of logical rules directly into the embedding space, BoxE sets a new trajectory for how knowledge bases can be intuitively and effectively completed.

Practically, the implications are equally impactful. BoxE’s ability to handle higher-arity relations and its scalability make it well-suited for real-world applications where knowledge bases are becoming increasingly complex and multi-relational. As AI systems continue to expand their reasoning capabilities, models like BoxE will be essential in ensuring knowledge bases can accurately and comprehensively represent required information.

Future Directions

Looking ahead, the research opens numerous pathways for expanding BoxE's capabilities. One potential direction is exploring more intricate logical language classes that can be directly encoded within the model. Another is optimizing the scalability of BoxE in distributed environments to handle even larger and more diverse datasets. The potential for integrating BoxE into broader AI systems where comprehensive knowledge representation and reasoning are critical also presents a significant opportunity for further exploration and development.

In conclusion, BoxE offers a robust and interpretable approach to KBC, providing advancements in logical reasoning capacities and embedding expressivity. Its rigorous theoretical foundation, combined with empirical success, makes it a promising model that could significantly enhance both academic research and industrial applications in AI.