Related papers: From Spectra to Localized Networks: A Reverse Engi…

We develop new theoretical results on matrix perturbation to shed light on the impact of architecture on the performance of a deep network. In particular, we explain analytically what deep learning practitioners have long observed…

Synchronization is critical for system level behaviour in physical, chemical, biological and social systems. Empirical evidence has shown that the network topology strongly impacts the synchronizablity of the system, and the analysis of…

Recurrent neural networks (RNNs) are a widely used tool for modeling sequential data, yet they are often treated as inscrutable black boxes. Given a trained recurrent network, we would like to reverse engineer it--to obtain a quantitative,…

Biological systems are driven by intricate interactions among the complex array of molecules that comprise the cell. Many methods have been developed to reconstruct network models of those interactions. These methods often draw on large…

In living cells, chemical reactions are connected by sharing their products and substrates, and form complex networks, e.g. metabolic pathways. Here we developed a theory to predict the sensitivity, i.e. the responses of concentrations and…

Network-structured data becomes ubiquitous in daily life and is growing at a rapid pace. It presents great challenges to feature engineering due to the high non-linearity and sparsity of the data. The local and global structure of the…

The robustness of complex networks against node failure and malicious attack has been of interest for decades, while most of the research has focused on random attack or hub-targeted attack. In many real-world scenarios, however, attacks…

We study networks constructed from gene expression data obtained from many types of cancers. The networks are constructed by connecting vertices that belong to each others' list of K-nearest-neighbors, with K being an a priori selected…

Representation learning has overcome the often arduous and manual featurization of networks through (unsupervised) feature learning as it results in embeddings that can apply to a variety of downstream learning tasks. The focus of…

Identifying influential nodes and edges in directed networks remains a fundamental challenge across domains from social influence to biological regulation. Most existing centrality measures face a critical limitation: they either discard…

Graph Neural Networks (GNNs) have boosted the performance of many graph related tasks such as node classification and graph classification. Recent researches show that graph neural networks are vulnerable to adversarial attacks, which…

The leading eigenvalue $\lambda$ of the adjacency matrix of a graph exerts much influence on the behavior of dynamical processes on that graph. It is thus relevant to relate notions of the importance (specifically, centrality measures) of…

We regard pre-trained residual networks (ResNets) as nonlinear systems and use linearization, a common method used in the qualitative analysis of nonlinear systems, to understand the behavior of the networks under small perturbations of the…

The largest eigenvalue of the adjacency matrix of the networks is a key quantity determining several important dynamical processes on complex networks. Based on this fact, we present a quantitative, objective characterization of the…

A bredge (bridge-edge) is an edge whose deletion would split the network component on which it resides into two components. Bredges are vulnerable links that play an important role in network collapse processes, which may result from node…

Training of neural networks can be reformulated in spectral space, by allowing eigenvalues and eigenvectors of the network to act as target of the optimization instead of the individual weights. Working in this setting, we show that the…

One of the hallmarks of real networks is their ability to perform increasingly complex tasks as their topology evolves. To explain this, it has been observed that as a network grows certain subsets of the network begin to specialize the…

We explore the spectra and localization properties of the N-site banded one-dimensional non-Hermitian random matrices that arise naturally in sparse neural networks. Approximately equal numbers of random excitatory and inhibitory…

Real-world complex systems exhibit intricate interconnections and dependencies, especially social networks, technological infrastructures, and communication networks. These networks are prone to disconnection due to random failures or…

Results regarding probable bifurcations from fixed points are presented in the context of general dynamical systems (real, random matrices), time-delay dynamical systems (companion matrices), and a set of mappings known for their properties…