Related papers: Homomorphism Counts for Graph Neural Networks: All…

Graph Neural Networks (GNNs) have achieved significant success in addressing node classification tasks. However, the effectiveness of traditional GNNs degrades on heterophilic graphs, where connected nodes often belong to different labels…

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 Neural Networks (GNNs) have been widely applied to various fields due to their powerful representations of graph-structured data. Despite the success of GNNs, most existing GNNs are designed to learn node representations on the fixed…

Foundation models have emerged as critical components in a variety of artificial intelligence applications, and showcase significant success in natural language processing and several other domains. Meanwhile, the field of graph machine…

This paper looks at the task of network topology inference, where the goal is to learn an unknown graph from nodal observations. One of the novelties of the approach put forth is the consideration of prior information about the density of…

Hypergraphs, as a generalization of traditional graphs, naturally capture high-order relationships. In recent years, hypergraph neural networks (HNNs) have been widely used to capture complex high-order relationships. However, most existing…

The number of homomorphisms from a finite graph $F$ to the complete graph $K_n$ is the evaluation of the chromatic polynomial of $F$ at $n$. Suitably scaled, this is the Tutte polynomial evaluation $T(F;1-n,0)$ and an invariant of the cycle…

This work focuses on training graph foundation models (GFMs) that have strong generalization ability in graph-level tasks such as graph classification. Effective GFM training requires capturing information consistent across different…

Graph Neural Networks (GNNs) have emerged as a powerful tool to capture intricate network patterns, achieving success across different domains. However, existing GNNs require careful domain-specific architecture designs and training from…

The notion of homomorphism indistinguishability offers a combinatorial framework for characterizing equivalence relations of graphs, in particular equivalences in counting logics within finite model theory. That is, for certain graph…

Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by additionally making use of graph structure based on the relational inductive bias (edge bias), rather than treating the nodes as collections of independent and identically…

Persistent homology is a mathematical tool used for studying the shape of data by extracting its topological features. It has gained popularity in network science due to its applicability in various network mining problems, including…

Neural networks efficiently encode learned information within their parameters. Consequently, many tasks can be unified by treating neural networks themselves as input data. When doing so, recent studies demonstrated the importance of…

Graph homophily refers to the phenomenon that connected nodes tend to share similar characteristics. Understanding this concept and its related metrics is crucial for designing effective Graph Neural Networks (GNNs). The most widely used…

Graph-matching metrics such as Smatch are the de facto standard for evaluating neural semantic parsers, yet they capture surface overlap rather than logical equivalence. We reassess evaluation by pairing graph-matching with automated…

Graph signals are functions of the underlying graph. When the edge-weight between a pair of nodes is high, the corresponding signals generally have a higher correlation. As a result, the signals can be represented in terms of a graph-based…

Graph Neural Networks (GNNs) have attracted increasing attention in recent years and have achieved excellent performance in semi-supervised node classification tasks. The success of most GNNs relies on one fundamental assumption, i.e., the…

Graph Neural Networks (GNNs) have achieved much success on graph-structured data. In light of this, there have been increasing interests in studying their expressive power. One line of work studies the capability of GNNs to approximate…

The goal of this work is to give precise bounds on the counting complexity of a family of generalized coloring problems (list homomorphisms) on bounded-treewidth graphs. Given graphs $G$, $H$, and lists $L(v)\subseteq V(H)$ for every $v\in…

Graph neural networks are prominent models for representation learning over graphs, where the idea is to iteratively compute representations of nodes of an input graph through a series of transformations in such a way that the learned graph…