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Convex sets appear in various mathematical theories, and are used to define notions such as convex functions and hulls. As an abstraction from the usual definition of convex sets in vector spaces, we formalize in Coq an intrinsic…

Knowledge graphs can be used in many areas related to data semantics such as question-answering systems, knowledge based systems. However, the currently constructed knowledge graphs need to be complemented for better knowledge in terms of…

Complex Query Answering (CQA) is a challenge task of Knowledge Graph (KG). Due to the incompleteness of KGs, query embedding (QE) methods have been proposed to encode queries and entities into the same embedding space, and treat logical…

In recent years, we have witnessed the proliferation of knowledge graphs (KG) in various domains, aiming to support applications like question answering, recommendations, etc. A frequent task when integrating knowledge from different KGs is…

Geospatial Knowledge Graphs (GeoKGs) model geoentities (e.g., places and natural features) and spatial relationships in an interconnected manner, providing strong knowledge support for geographic applications, including data retrieval,…

Knowledge graph embedding aims to learn distributed representations for entities and relations, and is proven to be effective in many applications. Crossover interactions --- bi-directional effects between entities and relations --- help…

A cardinal obstacle to performing quantum-mechanical simulations of strongly-correlated matter is that, with the theoretical tools presently available, sufficiently-accurate computations are often too expensive to be ever feasible. Here we…

Representation learning-based recommendation models play a dominant role among recommendation techniques. However, most of the existing methods assume both historical interactions and embedding dimensions are independent of each other, and…

Entity alignment is to find identical entities in different knowledge graphs (KGs) that refer to the same real-world object. Embedding-based entity alignment techniques have been drawing a lot of attention recently because they can help…

Knowledge graph embedding has been an active research topic for knowledge base completion (KGC), with progressive improvement from the initial TransE, TransH, RotatE et al to the current state-of-the-art QuatE. However, QuatE ignores the…

Concept embeddings offer a practical and efficient mechanism for injecting commonsense knowledge into downstream tasks. Their core purpose is often not to predict the commonsense properties of concepts themselves, but rather to identify…

We investigate the problem of multiplex graph embedding, that is, graphs in which nodes interact through multiple types of relations (dimensions). In recent years, several methods have been developed to address this problem. However, the…

Conventional representation learning algorithms for knowledge graphs (KG) map each entity to a unique embedding vector. Such a shallow lookup results in a linear growth of memory consumption for storing the embedding matrix and incurs high…

The holographic entropy cone (HEC) is a polyhedral cone first introduced in the study of a class of quantum entropy inequalities. It admits a graph-theoretic description in terms of minimum cuts in weighted graphs, a characterization which…

Lying at the interface between Network Science and Machine Learning, node embedding algorithms take a graph as input and encode its structure onto output vectors that represent nodes in an abstract geometric space, enabling various…

Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…

We study the problem of embedding-based entity alignment between knowledge graphs (KGs). Previous works mainly focus on the relational structure of entities. Some further incorporate another type of features, such as attributes, for…

Knowledge graph embeddings (KGEs) were originally developed to infer true but missing facts in incomplete knowledge repositories. In this paper, we link knowledge graph completion and counterfactual reasoning via our new task CFKGR. We…

Knowledge graph embedding (KGE) models typically represent each relation as an operator on entity embeddings. In this work, we identify three structural axioms that any principled relation operator must satisfy, linearity, trace…

Inference on a large-scale knowledge graph (KG) is of great importance for KG applications like question answering. The path-based reasoning models can leverage much information over paths other than pure triples in the KG, which face…