Related papers: The Hierarchical Graphene model
Graph Neural Networks (GNNs) are widely adopted in advanced AI systems due to their capability of representation learning on graph data. Even though GNN explanation is crucial to increase user trust in the systems, it is challenging due to…
Graphane is a two-dimensional system consisting of a single layer of fully saturated (sp$^3$ hybridization) carbon atoms. In an ideal graphane structure C-H bonds exhibit an alternating pattern (up and down with relation to the plane…
Many biological and social systems are naturally represented as edge-weighted directed or undirected hypergraphs since they exhibit group interactions involving three or more system units as opposed to pairwise interactions that can be…
Machine learning methods have a long history of applications in high energy physics (HEP). Recently, there is a growing interest in exploiting these methods to reconstruct particle signatures from raw detector data. In order to benefit from…
In this paper we are interested in decomposing a dihypergraph $\mathcal{H} = (V, \mathcal{E})$ into simpler dihypergraphs, that can be handled more efficiently. We study the properties of dihypergraphs that can be hierarchically decomposed…
Hypergraphs generalize classical graphs by allowing a single edge to connect multiple vertices, providing a natural language for modeling higher-order interactions. Superhypergraphs extend this paradigm further by accommodating nested,…
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…
We propose a novel graph-driven generative model, that unifies multiple heterogeneous learning tasks into the same framework. The proposed model is based on the fact that heterogeneous learning tasks, which correspond to different…
Recently, graph neural networks have been widely used for network embedding because of their prominent performance in pairwise relationship learning. In the real world, a more natural and common situation is the coexistence of pairwise…
The renormalization group flow of an integrable two dimensional quantum field theory which contains unstable particles is investigated. The analysis is carried out for the Virasoro central charge and the conformal dimensions as a function…
Graphs have a superior ability to represent relational data, like chemical compounds, proteins, and social networks. Hence, graph-level learning, which takes a set of graphs as input, has been applied to many tasks including comparison,…
The Hierarchical Reference Theory (HRT) of fluids is a general framework for the description of phase transitions in microscopic models of classical and quantum statistical physics. The foundations of HRT are briefly reviewed in a…
Odd electrons of benzenoid units and correlation of these electrons having different spins are the main concepts of the molecular theory of graphene. In contrast to the theory of aromaticity, the molecular theory is based on the fact that…
Recovering the random graph model from an observed collection of networks is known to present significant challenges in the setting, where the networks do not share a common node set and have different sizes. More specifically, the goal is…
Graph Neural Networks (GNNs) achieve outstanding performance across graph-based tasks but remain difficult to interpret. In this paper, we revisit foundational assumptions underlying model-level explanation methods for GNNs, namely: (1)…
Graph kernels are kernel methods measuring graph similarity and serve as a standard tool for graph classification. However, the use of kernel methods for node classification, which is a related problem to graph representation learning, is…
The thermodynamic entropy of coarse-grained (CG) models stands as one of the most important properties for quantifying the missing information during the CG process and for establishing transferable (or extendible) CG interactions. However,…
Denoising-based models, including diffusion and flow matching, have led to substantial advances in graph generation. Despite this progress, such models remain constrained by two fundamental limitations: a computational cost that scales…
Trophic coherence, a measure of a graph's hierarchical organisation, has been shown to be linked to a graph's structural and dynamical aspects such as cyclicity, stability and normality. Trophic levels of vertices can reveal their…
Many complex systems involve interactions between more than two agents. Hypergraphs capture these higher-order interactions through hyperedges that may link more than two nodes. We consider the problem of embedding a hypergraph into…