Related papers: Laplacian Coarse Graining in Complex Networks
While renormalization groups are fundamental in physics, renormalization of complex networks remains vague in its conceptual definition and methodology. Here, we propose a novel strategy to renormalize complex networks. Rather than…
Laplacian regularized stratified models (LRSM) are models that utilize the explicit or implicit network structure of the sub-problems as defined by the categorical features called strata (e.g., age, region, time, forecast horizon, etc.),…
We explore a systematic approach to studying the dynamics of evolving networks at a coarse-grained, system level. We emphasize the importance of finding good observables (network properties) in terms of which coarse grained models can be…
Can complex engineered and biological networks be coarse-grained into smaller and more understandable versions in which each node represents an entire pattern in the original network? To address this, we define coarse-graining units (CGU)…
Separating relevant and irrelevant information is key to any modeling process or scientific inquiry. Theoretical physics offers a powerful tool for achieving this in the form of the renormalization group (RG). Here we demonstrate a…
Discrete amorphous materials are best described in terms of arbitrary networks which can be embedded in three dimensional space. Investigating the thermodynamic equilibrium as well as non-equilibrium behavior of such materials around second…
We introduce an efficient algorithm for reducing bond dimensions in an arbitrary tensor network without changing its geometry. The method is based on a novel, quantitative understanding of local correlations in a network. Together with a…
In this paper, we focus on the interpretability of deep neural network. Our work is motivated by the renormalization group (RG) in statistical mechanics. RG plays the role of a bridge connecting microscopical properties and macroscopic…
Network synchronization is an emerging phenomenon in complex networks. The spectrum of Laplacian matrix will be immensely helpful for getting the network dynamics information. Especially, network synchronizability is characterized by the…
Networks with a prescribed power-law scaling in the spectrum of the graph Laplacian can be generated by evolutionary optimization. The Laplacian spectrum encodes the dynamical behavior of many important processes. Here, the networks are…
Multilayer graphs are appealing mathematical tools for modeling multiple types of relationship in the data. In this paper, we aim at analyzing multilayer graphs by properly combining the information provided by individual layers, while…
Exploring and understanding topological phases in systems with strong distributed disorder requires developing fundamentally new approaches to replace traditional tools such as topological band theory. Here, we present a general real-space…
Graph Convolutional Network (GCN) is a model that can effectively handle graph data tasks and has been successfully applied. However, for large-scale graph datasets, GCN still faces the challenge of high computational overhead, especially…
We introduce a novel stochastic regularization technique for deep neural networks, which decomposes a layer into multiple branches with different parameters and merges stochastically sampled combinations of the outputs from the branches…
Coarse graining model is a promising way to analyze and visualize large-scale networks. The coarse-grained networks are required to preserve the same statistical properties as well as the dynamic behaviors as the initial networks. Some…
Graph neural network (GNN) is achieving remarkable performances in a variety of application domains. However, GNN is vulnerable to noise and adversarial attacks in input data. Making GNN robust against noises and adversarial attacks is an…
Coarse-graining is a molecular modeling technique in which an atomistic system is represented in a simplified fashion that retains the most significant system features that contribute to a target output, while removing the degrees of…
Recommendation algorithm plays an important role in recommendation system (RS), which predicts users' interests and preferences for some given items based on their known information. Recently, a recommendation algorithm based on the graph…
We consider the properties of vibrational dynamics on random networks, with random masses and spring constants. The localization properties of the eigenstates contrast greatly with the Laplacian case on these networks. We introduce several…
We propose a new concept upon the renormalization group (RG) procedure for an interacting many-electron correlated system in the framework of natural orbitals, and formulate an algorithm for this RG approach. To demonstrate its…