相关论文: A Unified Characterization of Private Learnability…

In this work, we study the applications of differential privacy (DP) in the context of graph-structured data. We discuss the formulations of DP applicable to the publication of graphs and their associated statistics as well as machine…

The \emph{difference subgroup graph} $D(G)$ of a finite group $G$ is defined as the graph whose vertices are the non-trivial proper subgroups of $G$, with two distinct vertices $H$ and $K$ adjacent if and only if $\langle H, K \rangle = G$…

We study the contradiction graphs associated with binary concept classes. For a class $H \subseteq \{0,1\}^X$, the order-$m$ contradiction graph $G_m(H)$ has as vertices the $H$-realizable labeled sequences of length $m$, with two vertices…

The simplex graph $S(G)$ of a graph $G$ is defined as the graph whose vertices are the cliques of $G$ (including the empty set), with two vertices being adjacent if, as cliques of $G$, they differ in exactly one vertex. Simplex graphs form…

For a given graph $H$, its subdivisions carry the same topological structure. The existence of $H$-subdivisions within a graph $G$ has deep connections with topological, structural and extremal properties of $G$. One prominent example of…

Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying…

Clique-width is an important graph parameter due to its algorithmic and structural properties. A graph class is hereditary if it can be characterized by a (not necessarily finite) set ${\cal H}$ of forbidden induced subgraphs. We initiate a…

We propose Graph Contrastive Learning (GraphCL), a general framework for learning node representations in a self supervised manner. GraphCL learns node embeddings by maximizing the similarity between the representations of two randomly…

Deep neural networks have been applied to a wide range of problems across different application domains with great success. Recently, research into combinatorial optimization problems in particular has generated much interest in the machine…

We study PAC and online learnability of hypothesis classes formed by copies of a countably infinite graph G, where each copy is induced by permuting G's vertices. This corresponds to learning a graph's labeling, knowing its structure and…

Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. It is well known that structured graph learning from observed samples is an NP-hard combinatorial problem. In…

Learning generalizable self-supervised graph representations for downstream tasks is challenging. To this end, Contrastive Learning (CL) has emerged as a leading approach. The embeddings of CL are arranged on a hypersphere where similarity…

Graph contrastive learning (GCL) has emerged as an effective tool for learning unsupervised representations of graphs. The key idea is to maximize the agreement between two augmented views of each graph via data augmentation. Existing GCL…

Currently, graph learning models are indispensable tools to help researchers explore graph-structured data. In academia, using sufficient training data to optimize a graph model on a single device is a typical approach for training a…

Monadically stable and monadically NIP classes of structures were initially studied in the context of model theory and defined in logical terms. They have recently attracted attention in the area of structural graph theory, as they…

Graph neural networks have become the default choice by practitioners for graph learning tasks such as graph classification and node classification. Nevertheless, popular graph neural network models still struggle to capture higher-order…

Heterogeneous graphs (HGs) are composed of multiple types of nodes and edges, making it more effective in capturing the complex relational structures inherent in the real world. However, in real-world scenarios, labeled data is often…

We study the structure learning problem for $H$-colorings, an important class of Markov random fields that capture key combinatorial structures on graphs, including proper colorings and independent sets, as well as spin systems from…

The boxicity of a graph $G$ is the minimum dimension $d$ that admits a representation of $G$ as the intersection graph of a family of axis-parallel boxes in $\mathbb{R}^d$. Computing boxicity is an NP-hard problem, and there are few known…

We study self-supervised learning on graphs using contrastive methods. A general scheme of prior methods is to optimize two-view representations of input graphs. In many studies, a single graph-level representation is computed as one of the…