Related papers: Towards Understanding the Expressive Power of GNNs…

In recent years, there has been growing interest in understanding the expressive power of graph neural networks (GNNs) by relating them to logical languages. This research has been been initialised by an influential result of Barcel\'o et…

We study the expressive power of graph neural networks (GNNs) with mean as the aggregation function, with the following results. In the non-uniform setting, such GNNs have exactly the same expressive power as ratio modal logic, which has…

The expressivity of Graph Neural Networks (GNNs) can be described via appropriate fragments of the first order logic. Any query of the two variable fragment of graded modal logic (GC2) interpreted over labeled graphs can be expressed using…

In pioneering work from 2019, Barcel\'o and coauthors identified logics that precisely match the expressive power of constant iteration-depth graph neural networks (GNNs) relative to properties definable in first-order logic. In this…

As a powerful framework for graph representation learning, Graph Neural Networks (GNNs) have garnered significant attention in recent years. However, to the best of our knowledge, there has been no formal analysis of the logical…

Graph Neural Networks (GNNs) address two key challenges in applying deep learning to graph-structured data: they handle varying size input graphs and ensure invariance under graph isomorphism. While GNNs have demonstrated broad…

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…

We introduce a logical language for reasoning about quantized aggregate-combine graph neural networks with global readout (ACR-GNNs). We provide a logical characterization and use it to prove that verification tasks for quantized GNNs with…

The expressive limitations of message-passing Graph Neural Networks (GNNs) have motivated a wide range of more powerful graph learning architectures. We advocate Deep Homomorphism Networks (DHNs) as a model particularly well-suited for…

Graph neural networks (GNNs) can effectively model structural information of graphs, making them widely used in knowledge graph (KG) reasoning. However, existing studies on the expressive power of GNNs mainly focuses on simple…

In recent years, the expressive power of various neural architectures -- including graph neural networks (GNNs), transformers, and recurrent neural networks -- has been characterised using tools from logic and formal language theory. As the…

Uniform expressivity guarantees that a Graph Neural Network (GNN) can express a query without the parameters depending on the size of the input graphs. This property is desirable in applications in order to have number of trainable…

It has been recently shown that general policies for many classical planning domains can be expressed and learned in terms of a pool of features defined from the domain predicates using a description logic grammar. At the same time, most…

The expressive power of Graph Neural Networks (GNNs) is often analysed via correspondence to the Weisfeiler-Leman (WL) algorithm and fragments of first-order logic. Standard GNNs are limited to performing aggregation over immediate…

Graph neural networks (GNNs) are effective models for representation learning on relational data. However, standard GNNs are limited in their expressive power, as they cannot distinguish graphs beyond the capability of the Weisfeiler-Leman…

We analyse the power of graph neural networks (GNNs) in terms of Boolean circuit complexity and descriptive complexity. We prove that the graph queries that can be computed by a polynomial-size bounded-depth family of GNNs are exactly those…

Graph neural networks (GNNs) are effective machine learning models for many graph-related applications. Despite their empirical success, many research efforts focus on the theoretical limitations of GNNs, i.e., the GNNs expressive power.…

Graph neural networks (GNN) are deep learning architectures for graphs. Essentially, a GNN is a distributed message passing algorithm, which is controlled by parameters learned from data. It operates on the vertices of a graph: in each…

Despite significant advances in Graph Neural Networks (GNNs), their limited expressivity remains a fundamental challenge. Research on GNN expressivity has produced many expressive architectures, leading to architecture hierarchies with…

The expressivity of Graph Neural Networks (GNNs) is dependent on the aggregation functions they employ. Theoretical works have pointed towards Sum aggregation GNNs subsuming every other GNNs, while certain practical works have observed a…