Related papers: Equivariant Polynomials for Graph Neural Networks
We propose a novel expressivity framework for Graph Neural Networks (GNNs) grounded in Boolean function theory, enabling a fine-grained analysis of their ability to capture complex subpopulation structures. We introduce the notion of…
Graph Neural Networks (GNNs) have demonstrated superior performance on various graph learning tasks, including recommendation, where they leverage user-item collaborative filtering signals in graphs. However, theoretical formulations of…
In this paper we cast neural networks defined on graphs as message-passing neural networks (MPNNs) in order to study the distinguishing power of different classes of such models. We are interested in whether certain architectures are able…
Graph neural networks (GNNs) are a widely used class of machine learning models for graph-structured data, based on local aggregation over neighbors. GNNs have close connections to logic. In particular, their expressive power is linked to…
Graph neural network architectures aligned with the $k$-dimensional Weisfeiler--Leman ($k$-WL) hierarchy offer theoretically well-understood expressive power. However, these architectures often fail to deliver state-of-the-art predictive…
Research on the theoretical expressiveness of Graph Neural Networks (GNNs) has developed rapidly, and many methods have been proposed to enhance the expressiveness. However, most methods do not have a uniform expressiveness measure except…
Graph Neural Networks (GNNs) have become essential in high-stakes domains such as drug discovery, yet their black-box nature remains a significant barrier to trustworthiness. While self-explainable GNNs attempt to bridge this gap, they…
The expressive power of graph neural network formalisms is commonly measured by their ability to distinguish graphs. For many formalisms, the k-dimensional Weisfeiler-Leman (k-WL) graph isomorphism test is used as a yardstick. In this paper…
Graph neural networks are designed to learn functions on graphs. Typically, the relevant target functions are invariant with respect to actions by permutations. Therefore the design of some graph neural network architectures has been…
We formulate an XAI-based model improvement approach for Graph Neural Networks (GNNs) for node classification, called Explanation Enhanced Graph Learning (EEGL). The goal is to improve predictive performance of GNN using explanations. EEGL…
In this article we present new results about the expressivity of Graph Neural Networks (GNNs). We prove that for any GNN with piecewise polynomial activations, whose architecture size does not grow with the graph input sizes, there exists a…
Graph neural networks (GNNs) are powerful graph-based deep-learning models that have gained significant attention and demonstrated remarkable performance in various domains, including natural language processing, drug discovery, and…
Message passing Graph Neural Networks (GNNs) provide a powerful modeling framework for relational data. However, the expressive power of existing GNNs is upper-bounded by the 1-Weisfeiler-Lehman (1-WL) graph isomorphism test, which means…
Graph neural networks (GNNs) have become a workhorse approach for learning from data defined over irregular domains, typically by implicitly assuming that the data structure is represented by a homophilic graph. However, recent works have…
Graph Neural Networks (GNNs) are widely used to compute representations of node pairs for downstream tasks such as link prediction. Yet, theoretical understanding of their expressive power has focused almost entirely on graph-level…
Equivariant Graph Neural Networks (GNNs) have demonstrated significant success across various applications. To achieve completeness -- that is, the universal approximation property over the space of equivariant functions -- the network must…
Recently, neural network based approaches have achieved significant improvement for solving large, complex, graph-structured problems. However, their bottlenecks still need to be addressed, and the advantages of multi-scale information and…
This paper introduces a new model to learn graph neural networks equivariant to rotations, translations, reflections and permutations called E(n)-Equivariant Graph Neural Networks (EGNNs). In contrast with existing methods, our work does…
Learning representations of sets of nodes in a graph is crucial for applications ranging from node-role discovery to link prediction and molecule classification. Graph Neural Networks (GNNs) have achieved great success in graph…
Graph Neural Networks (GNNs) have emerged as a promising approach for ``learning to branch'' in Mixed-Integer Linear Programming (MILP). While standard Message-Passing GNNs (MPNNs) are efficient, they theoretically lack the expressive power…