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The model theory based notion of the first order convergence unifies the notions of the left-convergence for dense structures and the Benjamini-Schramm convergence for sparse structures. It is known that every first order convergent…

In a quest to thoroughly understand the first-order transduction hierarchy of hereditary graph classes, some questions in particular stand out; such as, what properties hold for graph classes that are first-order transductions of planar…

We propose a distributional theory of how hypernymy -- the ``is-a'' relation between general and specific concepts -- is encoded geometrically in language representations. Starting from the empirically verified assumption that words closer…

This paper introduces a novel approach to learn visually grounded meaning representations of words as low-dimensional node embeddings on an underlying graph hierarchy. The lower level of the hierarchy models modality-specific word…

Word-representable graphs, which are the same as semi-transitively orientable graphs, generalize several fundamental classes of graphs. In this paper we propose a novel approach to study word-representability of graphs using a technique of…

With the rising interest in graph representation learning, a variety of approaches have been proposed to effectively capture a graph's properties. While these approaches have improved performance in graph machine learning tasks compared to…

Many topological data analysis (TDA) pipelines compute large collections of persistence diagrams, yet vectorizations and kernel methods discard the rank-induced implication relations among persistence intervals that are essential for…

Graph representation learning aims to effectively encode high-dimensional sparse graph-structured data into low-dimensional dense vectors, which is a fundamental task that has been widely studied in a range of fields, including machine…

We investigate novel random graph embeddings that can be computed in expected polynomial time and that are able to distinguish all non-isomorphic graphs in expectation. Previous graph embeddings have limited expressiveness and either cannot…

Graph representation learning is a fast-growing field where one of the main objectives is to generate meaningful representations of graphs in lower-dimensional spaces. The learned embeddings have been successfully applied to perform various…

Representation learning models for graphs are a successful family of techniques that project nodes into feature spaces that can be exploited by other machine learning algorithms. Since many real-world networks are inherently dynamic, with…

Research on graph representation learning has received a lot of attention in recent years since many data in real-world applications come in form of graphs. High-dimensional graph data are often in irregular form, which makes them more…

Relational representation learning transforms relational data into continuous and low-dimensional vector representations. However, vector-based representations fall short in capturing crucial properties of relational data that are complex…

In this work, we study the utility of graph embeddings to generate latent user representations for trust-based collaborative filtering. In a cold-start setting, on three publicly available datasets, we evaluate approaches from four method…

In this paper, we discuss a method of constructing separable representations of the $C^*$-algebras associated to strongly connected row-finite $k$-graphs $\Lambda$. We begin by giving an alternative characterization of the…

Many real-world phenomena are naturally modeled by graphs and networks. However, classical graph models are often limited to pairwise interactions and may not adequately capture the richer structures that arise in practice. Higher-order…

As an efficient model for knowledge organization, the knowledge graph has been widely adopted in several fields, e.g., biomedicine, sociology, and education. And there is a steady trend of learning embedding representations of knowledge…

Word-representable graphs, characterized by the existence of a semi-transitive orientation, form a well-studied class of graphs. Comparability graphs form another well-studied class and constitute a subclass of word-representable graphs.…

This work provides the first unifying theoretical framework for node (positional) embeddings and structural graph representations, bridging methods like matrix factorization and graph neural networks. Using invariant theory, we show that…

Patterns stored within pre-trained deep neural networks compose large and powerful descriptive languages that can be used for many different purposes. Typically, deep network representations are implemented within vector embedding spaces,…