Related papers: The Weisfeiler-Lehman Distance: Reinterpretation a…
Consider a finite directed graph without cycles in which the arrows are weighted. We present an algorithm for the computation of a new distance, called path-length-weighted distance, which has proven useful for graph analysis in the context…
Graph Neural Networks (GNNs) excel in handling graph-structured data but often underperform in link prediction tasks compared to classical methods, mainly due to the limitations of the commonly used message-passing principle. Notably, their…
Graph Neural Networks (GNNs) have emerged as a powerful tool for data-driven learning on various graph domains. They are usually based on a message-passing mechanism and have gained increasing popularity for their intuitive formulation,…
The $k$-dimensional Weisfeiler-Leman algorithm ($k$-WL) is a very useful combinatorial tool in graph isomorphism testing. We address the applicability of $k$-WL to recognition of graph properties. Let $G$ be an input graph with $n$…
A graph is said to be distance-hereditary if the distance function in every connected induced subgraph is the same as in the graph itself. We prove that the ordinary Weisfeiler-Leman algorithm correctly tests the isomorphism of any two…
We introduce a theoretical framework for performing statistical tasks---including, but not limited to, averaging and principal component analysis---on the space of (possibly asymmetric) matrices with arbitrary entries and sizes. This is…
The expressive power of message passing neural networks (MPNNs) is known to match the expressive power of the 1-dimensional Weisfeiler-Leman graph (1-WL) isomorphism test. To boost the expressive power of MPNNs, a number of graph neural…
The Weisfeiler-Leman (WL) dimension of a graph is a measure for the inherent descriptive complexity of the graph. While originally derived from a combinatorial graph isomorphism test called the Weisfeiler-Leman algorithm, the WL dimension…
We introduce $r$-loopy Weisfeiler-Leman ($r$-$\ell{}$WL), a novel hierarchy of graph isomorphism tests and a corresponding GNN framework, $r$-$\ell{}$MPNN, that can count cycles up to length $r + 2$. Most notably, we show that…
When learning graph neural networks (GNNs) in node-level prediction tasks, most existing loss functions are applied for each node independently, even if node embeddings and their labels are non-i.i.d. because of their graph structures. To…
The pairwise interaction paradigm of graph machine learning has predominantly governed the modelling of relational systems. However, graphs alone cannot capture the multi-level interactions present in many complex systems and the expressive…
Gromov-Wasserstein distances are generalization of Wasserstein distances, which are invariant under distance preserving transformations. Although a simplified version of optimal transport in Wasserstein spaces, called linear optimal…
Graph Neural Networks (GNNs) have emerged as a dominant approach in graph representation learning, yet they often struggle to capture consistent similarity relationships among graphs. While graph kernel methods such as the Weisfeiler-Lehman…
Line graph transformation has been widely studied in graph theory, where each node in a line graph corresponds to an edge in the original graph. This has inspired a series of graph neural networks (GNNs) applied to transformed line graphs,…
Message passing graph neural networks (GNNs) are known to have their expressiveness upper-bounded by 1-dimensional Weisfeiler-Leman (1-WL) algorithm. To achieve more powerful GNNs, existing attempts either require ad hoc features, or…
In this work, we propose a novel generalized Wasserstein-2 distance approach for efficiently training stochastic neural networks to reconstruct random field models, where the target random variable comprises both continuous and categorical…
Graph is an usual representation of relational data, which are ubiquitous in manydomains such as molecules, biological and social networks. A popular approach to learningwith graph structured data is to make use of graph kernels, which…
Recently, subgraph GNNs have emerged as an important direction for developing expressive graph neural networks (GNNs). While numerous architectures have been proposed, so far there is still a limited understanding of how various design…
As a fundamental problem of natural language processing, it is important to measure the distance between different documents. Among the existing methods, the Word Mover's Distance (WMD) has shown remarkable success in document semantic…
In this paper, we study the design and analysis of a class of efficient algorithms for computing the Gromov-Wasserstein (GW) distance tailored to large-scale graph learning tasks. Armed with the Luo-Tseng error bound…