Louis Mozart Kamdem Teyou

Louis Mozart Kamdem Teyou, Caglar Demir, Axel-Cyrille Ngonga Ngomo

We introduce a novel embedding method diverging from conventional approaches by operating within function spaces of finite dimension rather than finite vector space, thus departing significantly from standard knowledge graph embedding techniques. Initially employing polynomial functions to compute embeddings, we progress to more intricate representations using neural networks with varying layer complexities. We argue that employing functions for embedding computation enhances expressiveness and allows for more degrees of freedom, enabling operations such as composition, derivatives and primitive of entities representation. Additionally, we meticulously outline the step-by-step construction of our approach and provide code for reproducibility, thereby facilitating further exploration and application in the field.

Louis Mozart Kamdem Teyou, Caglar Demir, Axel-Cyrille Ngonga Ngomo

Clifford algebras are a natural generalization of the real numbers, the complex numbers, and the quaternions. So far, solely Clifford algebras of the form $Cl_{p,q}$ (i.e., algebras without nilpotent base vectors) have been studied in the context of knowledge graph embeddings. We propose to consider nilpotent base vectors with a nilpotency index of two. In these spaces, denoted $Cl_{p,q,r}$, allows generalizing over approaches based on dual numbers (which cannot be modelled using $Cl_{p,q}$) and capturing patterns that emanate from the absence of higher-order interactions between real and complex parts of entity embeddings. We design two new models for the discovery of the parameters $p$, $q$, and $r$. The first model uses a greedy search to optimize $p$, $q$, and $r$. The second predicts $(p, q,r)$ based on an embedding of the input knowledge graph computed using neural networks. The results of our evaluation on seven benchmark datasets suggest that nilpotent vectors can help capture embeddings better. Our comparison against the state of the art suggests that our approach generalizes better than other approaches on all datasets w.r.t. the MRR it achieves on validation data. We also show that a greedy search suffices to discover values of $p$, $q$ and $r$ that are close to optimal.

Louis Mozart Kamdem Teyou, Caglar Demir, Axel-Cyrille Ngonga Ngomo

Concept learning is a form of supervised machine learning that operates on knowledge bases in description logics. State-of-the-art concept learners often rely on an iterative search through a countably infinite concept space. In each iteration, they retrieve instances of candidate solutions to select the best concept for the next iteration. While simple learning problems might require a few dozen instance retrieval calls to find a fitting solution, complex learning problems might necessitate thousands of calls. We alleviate the resulting runtime challenge by presenting a semantics-aware caching approach. Our cache is essentially a subsumption-aware map that links concepts to a set of instances via crisp set operations. Our experiments on 5 datasets with 4 symbolic reasoners, a neuro-symbolic reasoner, and 5 popular pagination policies demonstrate that our cache can reduce the runtime of concept retrieval and concept learning by an order of magnitude while being effective for both symbolic and neuro-symbolic reasoners.

Louis Mozart Kamdem Teyou, Luke Friedrichs, N'Dah Jean Kouagou et al.

Concept learning exploits background knowledge in the form of description logic axioms to learn explainable classification models from knowledge bases. Despite recent breakthroughs in neuro-symbolic concept learning, most approaches still cannot be deployed on real-world knowledge bases. This is due to their use of description logic reasoners, which are not robust against inconsistencies nor erroneous data. We address this challenge by presenting a novel neural reasoner dubbed EBR. Our reasoner relies on embeddings to approximate the results of a symbolic reasoner. We show that EBR solely requires retrieving instances for atomic concepts and existential restrictions to retrieve or approximate the set of instances of any concept in the description logic $\mathcal{SHOIQ}$. In our experiments, we compare EBR with state-of-the-art reasoners. Our results suggest that EBR is robust against missing and erroneous data in contrast to existing reasoners.