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Network reconstruction consists in retrieving the hidden interaction structure of a system from observations. Many reconstruction algorithms have been proposed, although less research has been devoted to describe their theoretical…

Knowledge graph embeddings are now a widely adopted approach to knowledge representation in which entities and relationships are embedded in vector spaces. In this chapter, we introduce the reader to the concept of knowledge graph…

Despite the extreme popularity of deep learning in science and industry, its formal understanding is limited. This thesis puts forth notions of rank as key for developing a theory of deep learning, focusing on the fundamental aspects of…

Textual graphs are ubiquitous in real-world applications, featuring rich text information with complex relationships, which enables advanced research across various fields. Textual graph representation learning aims to generate…

Graph is an important data representation ubiquitously existing in the real world. However, analyzing the graph data is computationally difficult due to its non-Euclidean nature. Graph embedding is a powerful tool to solve the graph…

In recent years, the Graph Model has become increasingly popular, especially in the application domain of social networks. The model has been semantically augmented with properties and labels attached to the graph elements. It is difficult…

Maximizing influences in complex networks is a practically important but computationally challenging task for social network analysis, due to its NP- hard nature. Most current approximation or heuristic methods either require tremendous…

Many problems, especially those with a composite structure, can naturally be expressed in higher order logic. From a KR perspective modeling these problems in an intuitive way is a challenging task. In this paper we study the graph mining…

Recent progress in language modeling has expanded the range of tasks that can be approached through natural language interfaces, including problems that require structured reasoning. However, it remains unclear how effectively…

Interpretability has emerged as a crucial aspect of building trust in machine learning systems, aimed at providing insights into the working of complex neural networks that are otherwise opaque to a user. There are a plethora of existing…

Many real-world and artificial systems and processes can be represented as graphs. Some examples of such systems include social networks, financial transactions, supply chains, and molecular structures. In many of these cases, one needs to…

Graph-structured data arise in a variety of real-world context ranging from sensor and transportation to biological and social networks. As a ubiquitous tool to process graph-structured data, spectral graph filters have been used to solve…

In rank-metric cryptography, a vector from a finite dimensional linear space over a finite field is viewed as the linear space spanned by its entries. The rank decoding problem which is the analogue of the problem of decoding a random…

Statistical analysis of a graph often starts with embedding, the process of representing its nodes as points in space. How to choose the embedding dimension is a nuanced decision in practice, but in theory a notion of true dimension is…

Representation learning is the first step in automating tasks such as research paper recommendation, classification, and retrieval. Due to the accelerating rate of research publication, together with the recognised benefits of…

We introduce a new form of restricted term rewrite system, the graph-embedded term rewrite system. These systems, and thus the name, are inspired by the graph minor relation and are more flexible extensions of the well-known…

There has been a surge of recent interest in learning representations for graph-structured data. Graph representation learning methods have generally fallen into three main categories, based on the availability of labeled data. The first,…

This article aims to study the topological invariant properties encoded in node graph representational embeddings by utilizing tools available in persistent homology. Specifically, given a node embedding representation algorithm, we…

The field of Graph Signal Processing (GSP) has proposed tools to generalize harmonic analysis to complex domains represented through graphs. Among these tools are translations, which are required to define many others. Most works propose to…

Multiplex networks are collections of networks with identical nodes but distinct layers of edges. They are genuine representations for a large variety of real systems whose elements interact in multiple fashions or flavors. However,…