Related papers: Lecture Notes on Verifying Graph Neural Networks

It is unknown whether two graphs can be tested for isomorphism in polynomial time. A classical approach to the Graph Isomorphism Problem is the d-dimensional Weisfeiler-Lehman algorithm. The d-dimensional WL-algorithm can distinguish many…

Finding equitable partitions is closely related to the extraction of graph symmetries and of interest in a variety of applications context such as node role detection, cluster synchronization, consensus dynamics, and network control…

The Weisfeiler-Leman (WL) algorithm is a combinatorial procedure that computes colorings on graphs, which can often be used to detect their (non-)isomorphism. Particularly the 1- and 2-dimensional versions 1-WL and 2-WL have received much…

Graph Neural Networks (GNNs) have demonstrated remarkable performance in a wide range of tasks, such as node classification, link prediction, and graph classification, by exploiting the structural information in graph-structured data.…

Large language models have evolved to process multiple modalities beyond text, such as images and audio, which motivates us to explore how to effectively leverage them for graph reasoning tasks. The key question, therefore, is how to…

This paper addresses the challenging problem of retrieval and matching of graph structured objects, and makes two key contributions. First, we demonstrate how Graph Neural Networks (GNN), which have emerged as an effective model for various…

Robustness in complex systems is of significant engineering and economic importance. However, conventional attack-based a posteriori robustness assessments incur prohibitive computational overhead. Recently, deep learning methods, such as…

The presented material is devoted to the equivalent conversion from the vertex graphs to the edge graphs. We suggest that the proved theorems solve the problem of the isomorphism of graphs, the problem of the graph's enumeration with the…

Most graph kernels are an instance of the class of $\mathcal{R}$-Convolution kernels, which measure the similarity of objects by comparing their substructures. Despite their empirical success, most graph kernels use a naive aggregation of…

We focus on graph classification using a graph neural network (GNN) model that precomputes the node features using a bank of neighborhood aggregation graph operators arranged in parallel. These GNN models have a natural advantage of reduced…

We consider Hoare-style verification for the graph programming language GP 2. In previous work, graph properties were specified by so-called E-conditions which extend nested graph conditions. However, this type of assertions is not easy to…

Graph Neural Networks (GNNs) have emerged as powerful representation learning tools for capturing complex dependencies within diverse graph-structured data. Despite their success in a wide range of graph mining tasks, GNNs have raised…

The graph structure is a commonly used data storage mode, and it turns out that the low-dimensional embedded representation of nodes in the graph is extremely useful in various typical tasks, such as node classification, link prediction ,…

Generalizing to unseen graph tasks without task-pecific supervision remains challenging. Graph Neural Networks (GNNs) are limited by fixed label spaces, while Large Language Models (LLMs) lack structural inductive biases. Recent advances in…

The Weisfeiler-Leman procedure is a widely-used technique for graph isomorphism testing that works by iteratively computing an isomorphism-invariant coloring of vertex tuples. Meanwhile, a fundamental tool in structural graph theory, which…

Table-based fact verification task aims to verify whether the given statement is supported by the given semi-structured table. Symbolic reasoning with logical operations plays a crucial role in this task. Existing methods leverage programs…

This paper presents the Persistent Weisfeiler-Lehman Random walk scheme (abbreviated as PWLR) for graph representations, a novel mathematical framework which produces a collection of explainable low-dimensional representations of graphs…

Graph Neural Networks (GNNs) are a powerful representational tool for solving problems on graph-structured inputs. In almost all cases so far, however, they have been applied to directly recovering a final solution from raw inputs, without…

Graph neural networks (GNNs) have emerged recently as a powerful architecture for learning node and graph representations. Standard GNNs have the same expressive power as the Weisfeiler-Leman test of graph isomorphism in terms of…

Despite the remarkable success of Graph Neural Networks (GNNs), the common belief is that their representation power is limited and that they are at most as expressive as the Weisfeiler-Lehman (WL) algorithm. In this paper, we argue the…