In this paper, we propose a new method for knowledge base completion (KBC): instance-based learning (IBL). For example, to answer (Jill Biden, lived city,?

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.

Considering local and bounded-size neighborhoods of knowledge bases renders logical inference and learning tractable, mitigates the problem of over-fitting, and facilitates weight sharing.

A common problem in knowledge representation and related fields is reasoning over a large joint knowledge graph, represented as triples of a relation between two entities. The goal of this paper is to develop a more powerful neural network model suitable for inference over these relationships. Previous models suffer from weak interaction between entities or simple linear projection of the vector space. We address these problems by introducing a neural tensor network (NTN) model which allow the entities and relations to interact multiplicatively. Additionally, we observe that such knowledge base models can be further improved by representing each entity as the average of vectors for the words in the entity name, giving an additional dimension of similarity by which entities can share statistical strength. We assess the model by considering the problem of predicting additional true relations between entities given a partial knowledge base. Our model outperforms previous models and can classify unseen relationships in WordNet and FreeBase with an accuracy of 86.2% and 90.0%, respectively.

Additional Feedback: Please number ALL equations for easy reference, at least in the preliminary submission. L139 Translational bumps are certainly very expressive, but a likely first reaction is that they are too expressive. Perhaps you need a couple sentences right here on how you control their power. L153 "for the sample KG, there are 4 2 potential configurations" There are four entities and two binary relations. For each relation, each slot can be occupied by any one of four entities (assuming selectively reflexive and symmetric relations allowed).

The paper aims to improve knowledge base modelling. In this regards, authors propose a rather ingenious use of box embeddings as the latent representation for the relations. Specifically, each n-ary relation is represented by n boxes and each entity is represented by two vectors. Having a pair of vectors is very powerful, as they allow us to model complex interactions across entities. In particular authors show how their proposed box embeddings can simultaneously handle symmetry, asymmetry, anti-symmetry, and transitivity. No previous framework is claimed to be as flexible nor capable of handling all these patterns.

In this paper, we propose a new method for knowledge base completion (KBC): instance-based learning (IBL). For example, to answer (Jill Biden, lived city,? Through prototype entities, IBL provides interpretability. We develop theories for modeling prototypes and combining IBL with translational models. Experiments on various tasks confirmed the IBL model's effectiveness and interpretability.In addition, IBL shed light on the mechanism of rule-based KBC models.

Integrating large language models (LLMs) with rule-based reasoning offers a powerful solution for improving the flexibility and reliability of Knowledge Base Completion (KBC). Traditional rule-based KBC methods offer verifiable reasoning yet lack flexibility, while LLMs provide strong semantic understanding yet suffer from hallucinations. With the aim of combining LLMs' understanding capability with the logical and rigor of rule-based approaches, we propose a novel framework consisting of a Subgraph Extractor, an LLM Proposer, and a Rule Reasoner. The Subgraph Extractor first samples subgraphs from the KB. Then, the LLM uses these subgraphs to propose diverse and meaningful rules that are helpful for inferring missing facts. To effectively avoid hallucination in LLMs' generations, these proposed rules are further refined by a Rule Reasoner to pinpoint the most significant rules in the KB for Knowledge Base Completion. Our approach offers several key benefits: the utilization of LLMs to enhance the richness and diversity of the proposed rules and the integration with rule-based reasoning to improve reliability. Our method also demonstrates strong performance across diverse KB datasets, highlighting the robustness and generalizability of the proposed framework.

Ontology embeddings map classes, relations, and individuals in ontologies into $\mathbb{R}^n$, and within $\mathbb{R}^n$ similarity between entities can be computed or new axioms inferred. For ontologies in the Description Logic $\mathcal{EL}^{++}$, several embedding methods have been developed that explicitly generate models of an ontology. However, these methods suffer from some limitations; they do not distinguish between statements that are unprovable and provably false, and therefore they may use entailed statements as negatives. Furthermore, they do not utilize the deductive closure of an ontology to identify statements that are inferred but not asserted. We evaluated a set of embedding methods for $\mathcal{EL}^{++}$ ontologies, incorporating several modifications that aim to make use of the ontology deductive closure. In particular, we designed novel negative losses that account both for the deductive closure and different types of negatives and formulated evaluation methods for knowledge base completion. We demonstrate that our embedding methods improve over the baseline ontology embedding in the task of knowledge base or ontology completion.

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.