Related papers: A Unified Characterization of Private Learnability…
To each finite frame $\varphi$ in an inner product space $\mathcal{H}$ we associate a simple graph $G(\varphi)$, called {\it frame graph}, with the vectors of the frame as vertices and there is an edge between vertices $f$ and $g$ provided…
Natural Language Processing (NLP) provides highly effective tools for interpreting and handling human language, offering a broad spectrum of applications. In this paper, we address a classic combinatorial problem -- finding graph partitions…
The graph with complex annotations is the most potent data type, whose constantly evolving motivates further exploration of the unsupervised dynamic graph representation. One of the representative paradigms is graph contrastive learning. It…
The exact distance $t$-power of a graph $G$, $G^{[\sharp t]}$, is a graph which has the same vertex set as $G$, with two vertices adjacent in $G^{[\sharp t]}$ if and only if they are at distance exactly $t$ in the original graph $G$. We…
Density matrices of graphs are combinatorial laplacians normalized to have trace one (Braunstein \emph{et al.} \emph{Phys. Rev. A,} \textbf{73}:1, 012320 (2006)). If the vertices of a graph are arranged as an array, then its density matrix…
We construct several pairwise-incomparable bounds on the projective dimensions of edge ideals. Our bounds use combinatorial properties of the associated graphs; in particular we draw heavily from the topic of dominating sets. Through…
Recent advances in neural algorithmic reasoning with graph neural networks (GNNs) are propped up by the notion of algorithmic alignment. Broadly, a neural network will be better at learning to execute a reasoning task (in terms of sample…
The connectivity of a graph is an important parameter to evaluate its reliability. $k$-restricted connectivity (resp. $R^h$-restricted connectivity) of a graph $G$ is the minimum cardinality of a set $S$ of vertices in $G$, if exists, whose…
Bir\'{o} et al. (1992) introduced $H$-graphs, intersection graphs of connected subgraphs of a subdivision of a graph $H$. They are related to many classes of geometric intersection graphs, e.g., interval graphs, circular-arc graphs, split…
For a graph class $\mathcal G$ and a graph $H$, the four $\mathcal G$-covering numbers of $H$, namely global ${\rm cn}_{g}^{\mathcal{G}}(H)$, union ${\rm cn}_{u}^{\mathcal{G}}(H)$, local ${\rm cn}_{l}^{\mathcal{G}}(H)$, and folded ${\rm…
Semi-supervised learning (SSL) is effectively used for numerous classification problems, thanks to its ability to make use of abundant unlabeled data. The main assumption of various SSL algorithms is that the nearby points on the data…
Graph embedding has become a powerful tool for learning latent representations of nodes in a graph. Despite its superior performance in various graph-based machine learning tasks, serious privacy concerns arise when the graph data contains…
Graph Contrastive Learning (GCL) is a widely adopted approach in self-supervised graph representation learning, applying contrastive objectives to produce effective representations. However, current GCL methods primarily focus on capturing…
A graph $G$ is called well-covered if all maximal independent sets of vertices have the same cardinality. A simplicial complex $\Delta$ is called pure if all of its facets have the same cardinality. Let $\mathcal G$ be the class of graphs…
Traditional Graph Neural Network (GNN), as a graph representation learning method, is constrained by label information. However, Graph Contrastive Learning (GCL) methods, which tackle the label problem effectively, mainly focus on the…
Label differential privacy (DP) is a framework that protects the privacy of labels in training datasets, while the feature vectors are public. Existing approaches protect the privacy of labels by flipping them randomly, and then train a…
Knowledge graphs (KGs) have gained prominence for their ability to learn representations for uni-relational facts. Recently, research has focused on modeling hyper-relational facts, which move beyond the restriction of uni-relational facts…
In document classification, graph-based models effectively capture document structure, overcoming sequence length limitations and enhancing contextual understanding. However, most existing graph document representations rely on heuristics,…
This work derives an upper bound on the maximum cardinality of a family of graphs on a fixed number of vertices, in which the intersection of every two graphs in that family contains a subgraph that is isomorphic to a specified graph H.…
Graph representation learning (GRL) makes considerable progress recently, which encodes graphs with topological structures into low-dimensional embeddings. Meanwhile, the time-consuming and costly process of annotating graph labels manually…