Related papers: Weisfeiler-Lehman meets Gromov-Wasserstein
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…
Our starting point is the observation that if graphs in a class C have low descriptive complexity in first order logic, then the isomorphism problem for C is solvable by a fast parallel algorithm (essentially, by a simple combinatorial…
The Wasserstein distance is a powerful metric based on the theory of optimal transport. It gives a natural measure of the distance between two distributions with a wide range of applications. In contrast to a number of the common…
Malware analysis techniques are divided into static and dynamic analysis. Both techniques can be bypassed by circumvention techniques such as obfuscation. In a series of works, the authors have promoted the use of symbolic executions…
The ability of graph neural networks (GNNs) to count certain graph substructures, especially cycles, is important for the success of GNNs on a wide range of tasks. It has been recently used as a popular metric for evaluating the expressive…
In these lecture notes, we first recall the connection between graph neural networks, Weisfeiler-Lehman tests and logics such as first-order logic and graded modal logic. We then present a modal logic in which counting modalities appear in…
From the perspective of expressive power, this work compares multi-layer Graph Neural Networks (GNNs) with a simplified alternative that we call Graph-Augmented Multi-Layer Perceptrons (GA-MLPs), which first augments node features with…
We develop a kernel projected Wasserstein distance for the two-sample test, an essential building block in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. This method…
We revisit a simple model class for machine learning on graphs, where a random walk on a graph produces a machine-readable record, and this record is processed by a deep neural network to directly make vertex-level or graph-level…
Comparing probability distributions is at the crux of many machine learning algorithms. Maximum Mean Discrepancies (MMD) and Wasserstein distances are two classes of distances between probability distributions that have attracted abundant…
Graph Neural Networks (GNNs) have emerged as prominent models for representation learning on graph structured data. GNNs follow an approach of message passing analogous to 1-dimensional Weisfeiler Lehman (1-WL) test for graph isomorphism…
Comparing structured objects such as graphs is a fundamental operation involved in many learning tasks. To this end, the Gromov-Wasserstein (GW) distance, based on Optimal Transport (OT), has proven to be successful in handling the specific…
Identifying similar network structures is key to capture graph isomorphisms and learn representations that exploit structural information encoded in graph data. This work shows that ego-networks can produce a structural encoding scheme for…
Within many real-world networks the links between pairs of nodes change over time. Thus, there has been a recent boom in studying temporal graphs. Recognizing patterns in temporal graphs requires a proximity measure to compare different…
Inspired by the Kantorovich formulation of optimal transport distance between probability measures on a metric space, Gromov-Wasserstein (GW) distances comprise a family of metrics on the space of isomorphism classes of metric measure…
Let $m$ be a positive integer, $X$ a graph with vertex set $\Omega$, and ${\rm WL}_m(X)$ the coloring of the Cartesian $m$-power $\Omega^m$, obtained by the $m$-dimensional Weisfeiler-Leman algorithm. The ${\rm WL}$-dimension of the graph…
Comparing graphs by means of optimal transport has recently gained significant attention, as the distances induced by optimal transport provide both a principled metric between graphs as well as an interpretable description of the…
Graphs with a simple spectrum admit cubic-time isomorphism testing, yet we prove that for every natural number $k$, the $k$-Weisfeiler-Leman ($k$-WL) test cannot distinguish all non-isomorphic graphs with a simple spectrum. As the WL…
We investigate the relationship between various isomorphism invariants for finite groups. Specifically, we use the Weisfeiler-Leman dimension (WL) to characterize, compare and quantify the effectiveness and complexity of invariants for…
Gromov-Hausdorff distances measure shape difference between the objects representable as compact metric spaces, e.g. point clouds, manifolds, or graphs. Computing any Gromov-Hausdorff distance is equivalent to solving an NP-Hard…