The choice of geometric space for knowledge graph (KG) embeddings can have significant effects on the performance of KG completion tasks. The hyperbolic geometry has been shown to capture the hierarchical patterns due to its tree-like metrics, which addressed the limitations of the Euclidean embedding models. Recent explorations of the complex hyperbolic geometry further improved the hyperbolic embeddings for capturing a variety of hierarchical structures. However, the performance of the hyperbolic KG embedding models for non-transitive relations is still unpromising, while the complex hyperbolic embeddings do not deal with multi-relations. This paper aims to utilize the representation capacity of the complex hyperbolic geometry in multi-relational KG embeddings. To apply the geometric transformations which account for different relations and the attention mechanism in the complex hyperbolic space, we propose to use the fast Fourier transform (FFT) as the conversion between the real and complex hyperbolic space. Constructing the attention-based transformations in the complex space is very challenging, while the proposed Fourier transform-based complex hyperbolic approaches provide a simple and effective solution. Experimental results show that our methods outperform the baselines, including the Euclidean and the real hyperbolic embedding models.

In recent years, knowledge graph embedding becomes a pretty hot research topic of artificial intelligence and plays increasingly vital roles in various downstream applications, such as recommendation and question answering. However, existing methods for knowledge graph embedding can not make a proper trade-off between the model complexity and the model expressiveness, which makes them still far from satisfactory. To mitigate this problem, we propose a lightweight modeling framework that can achieve highly competitive relational expressiveness without increasing the model complexity. Our framework focuses on the design of scoring functions and highlights two critical characteristics: 1) facilitating sufficient feature interactions; 2) preserving both symmetry and antisymmetry properties of relations. It is noteworthy that owing to the general and elegant design of scoring functions, our framework can incorporate many famous existing methods as special cases. Moreover, extensive experiments on public benchmarks demonstrate the efficiency and effectiveness of our framework. Source codes and data can be found at \url{https://github.com/Wentao-Xu/SEEK}.

Most of the research in Automated Planning relies on the evaluation of different techniques over a set of benchmarks. The generation of planning tasks for these benchmarks is done using generators coded ad-hoc. Instead, we propose an approach for generating planning problems automatically given the domain definition and some declarative semantics-related information provided by the user. The approach consists of modelling the task of generating planning problems also as a planning problem. The main contribution of this work is that the generation of planning problems is partially handled in a domain-independent way, which leads to a saving of time and effort for researchers. Additionally, the declarative input to the generator facilitates the modification of its behavior. This is a feature of interest for generating different problem distributions.

When general purpose software agents fail, it's often because they're brittle and need more background commonsense knowledge. In this paper we present relation properties as a valuable type of commonsense knowledge that can be automatically inferred at scale by reading the Web. People base many commonsense inferences on their knowledge of relation properties such as functionality, transitivity, and others. For example, all people know that bornIn(Year) satisfies the functionality property, meaning that each person can be born in exactly one year. Thus inferences like "Obama was born in 1961, so he was not born in 2008", which computers do not know, are obvious even to children. We demonstrate scalable heuristics for learning relation functionality from noisy Web text that outperform existing approaches to detecting functionality. The heuristics we use address Web NLP challenges that are also common to learning other relation properties, and can be easily transferred. Each relation property we learn for a Web-scale set of relations will enable computers to solve real tasks, and the data from learning many such properties will be a useful addition to general commonsense knowledge bases.