Related papers: GSF-locality is not sufficient for proximity-obliv…
Several graph properties are characterized as the class of graphs that admit an orientation avoiding finitely many oriented structures. For instance, if $F_k$ is the set of homomorphic images of the directed path on $k+1$ vertices, then a…
Modern machine learning models are highly expressive but notoriously difficult to analyze statistically. In particular, while black-box predictors can achieve strong empirical performance, they rarely provide valid hypothesis tests or…
In local certification, vertices of a $n$-vertex graph perform a local verification to check if a given property is satisfied by the graph. This verification is performed thanks to certificates, which are pieces of information that are…
We investigate under which circumstances there exists nonzero {\it{projective}} smooth $\field[G]$-modules, where $\field$ is a field of characteristic $p$ and $G$ is a locally pro-$p$ group. We prove the non-existence of (non-trivial)…
Hamiltonian cycles in graphs were first studied in the 1850s. Since then, an impressive amount of research has been dedicated to identifying classes of graphs that allow Hamiltonian cycles, and to related questions. The corresponding…
We study the power of local test for bipartite quantum states. Our central result is that, for properties of bipartite pure states, unitary invariance on one part implies an optimal (over all global testers) local tester acting only on the…
Towards the challenging problem of semi-supervised node classification, there have been extensive studies. As a frontier, Graph Neural Networks (GNNs) have aroused great interest recently, which update the representation of each node by…
The notions of bounded expansion and nowhere denseness not only offer robust and general definitions of uniform sparseness of graphs, they also describe the tractability boundary for several important algorithmic questions. In this paper we…
We consider the task of testing properties of Boolean functions that are invariant under linear transformations of the Boolean cube. Previous work in property testing, including the linearity test and the test for Reed-Muller codes, has…
GNN prompting aims to adapt models across tasks and graphs without requiring extensive retraining. However, most existing graph prompt methods still require task-specific parameter updates and face the issue of generalizing across graphs,…
Proximity graphs are used in several areas in which a neighborliness relationship for input data sets is a useful tool in their analysis, and have also received substantial attention from the graph drawing community, as they are a natural…
Homophily, the tendency of nodes from the same class to connect, is a fundamental property of real-world graphs, underpinning structural and semantic patterns in domains such as citation networks and social networks. Existing methods…
Rubinfeld & Vasilyan recently introduced the framework of testable learning as an extension of the classical agnostic model. It relaxes distributional assumptions which are difficult to verify by conditions that can be checked efficiently…
Graph Neural Networks (GNNs) are deep learning methods which provide the current state of the art performance in node classification tasks. GNNs often assume homophily -- neighboring nodes having similar features and labels--, and therefore…
We discuss the importance of measuring $\rho= ReF/ImF$ at LHC to test the forward dispersion relations and local QFT. It is pointed out that at LHC we can reach a short distance domain that has not been pre-explored by QED. This is in…
Using the fact that some depth functions characterize certain family of distribution functions, and under some mild conditions, distribution of the depth is continuous, we have constructed several new multivariate goodness of fit tests…
We investigate numerically and analytically Potts models on ``thin'' random graphs -- generic Feynman diagrams, using the idea that such models may be expressed as the N --> 1 limit of a matrix model. The thin random graphs in this limit…
Graph attention networks (GATs) are powerful tools for analyzing graph data from various real-world scenarios. To learn representations for downstream tasks, GATs generally attend to all neighbors of the central node when aggregating the…
Graph Neural Networks (GNNs) achieve strong performance on node classification tasks but remain difficult to interpret, particularly with respect to which input features drive their predictions. Existing global GNN explainers operate at the…
Graph Neural Networks (GNNs) are proposed without considering the agnostic distribution shifts between training and testing graphs, inducing the degeneration of the generalization ability of GNNs on Out-Of-Distribution (OOD) settings. The…