Related papers: Weisfeiler-Lehman meets Gromov-Wasserstein
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…
The Weisfeiler-Leman dimension of a graph $G$ is the least number $k$ such that the $k$-dimensional Weisfeiler-Leman algorithm distinguishes $G$ from every other non-isomorphic graph. The dimension is a standard measure of the descriptive…
In recent years, algorithms and neural architectures based on the Weisfeiler--Leman algorithm, a well-known heuristic for the graph isomorphism problem, have emerged as a powerful tool for machine learning with graphs and relational data.…
The Gromov-Wasserstein (GW) distance has gained increasing interest in the machine learning community in recent years, as it allows for the comparison of measures in different metric spaces. To overcome the limitations imposed by the equal…
We give an isomorphism test for graphs of Euler genus $g$ running in time $2^{O(g^4 \log g)}n^{O(1)}$. Our algorithm provides the first explicit upper bound on the dependence on $g$ for an fpt isomorphism test parameterized by the Euler…
For graph learning tasks, many existing methods utilize a message-passing mechanism where vertex features are updated iteratively by aggregation of neighbor information. This strategy provides an efficient means for graph features…
This paper presents a new graph isomorphism invariant, called $\mathfrak{w}$-labeling, that can be used to design a polynomial-time algorithm for solving the graph isomorphism problem for various graph classes. For example, all…
The classical Weisfeiler-Lehman method WL[2] uses edge colors to produce a powerful graph invariant. It is at least as powerful in its ability to distinguish non-isomorphic graphs as the most prominent algebraic graph invariants. It…
We prove that the Weisfeiler-Leman (WL) dimension of the class of all finite planar graphs is at most 3. In particular, every finite planar graph is definable in first-order logic with counting using at most 4 variables. The previously best…
Although recent advances in higher-order Graph Neural Networks (GNNs) improve the theoretical expressiveness and molecular property predictive performance, they often fall short of the empirical performance of models that explicitly use…
Graph Neural Networks (GNNs) have become an essential tool for analyzing graph-structured data, leveraging their ability to capture complex relational information. While the expressivity of GNNs, particularly their equivalence to the…
Twin-width is a graph parameter introduced in the context of first-order model checking, and has since become a central parameter in algorithmic graph theory. While many algorithmic problems become easier on arbitrary classes of bounded…
Graph isomorphism testing is usually approached via the comparison of graph invariants. Two popular alternatives that offer a good trade-off between expressive power and computational efficiency are combinatorial (i.e., obtained via the…
In this paper, we propose a novel graph kernel specifically to address a challenging problem in the field of cyber-security, namely, malware detection. Previous research has revealed the following: (1) Graph representations of programs are…
While numerous methods have been proposed for computing distances between probability distributions in Euclidean space, relatively little attention has been given to computing such distances for distributions on graphs. However, there has…
As a classical approach on graph learning, the propagation-aggregation methodology is widely exploited by many of Graph Neural Networks (GNNs), wherein the representation of a node is updated by aggregating representations from itself and…
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…
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…
This paper provides a graphical characterization of Markov blankets in chain graphs (CGs) under the Lauritzen-Wermuth-Frydenberg (LWF) interpretation. The characterization is different from the well-known one for Bayesian networks and…
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…