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This paper studies social interactions in a game theoretic model with players in a large social network. We consider observations from one single equilibrium of a large network game with asymmetric information, in which each player chooses…

The lottery ticket hypothesis conjectures the existence of sparse subnetworks of large randomly initialized deep neural networks that can be successfully trained in isolation. Recent work has experimentally observed that some of these…

The aim of this paper is to propose a theoretical construct, smart network field theory, for the characterization, monitoring, and control of smart network systems. Smart network systems are intelligent autonomously-operating networks, a…

We investigate recurrent neural networks with asymmetric interactions and demonstrate that the inclusion of self-couplings or sparse excitatory inter-module connections leads to the emergence of a densely connected manifold of dynamically…

Deep networks, composed of multiple layers of hierarchical distributed representations, tend to learn low-level features in initial layers and transition to high-level features towards final layers. Paradigms such as transfer learning,…

A growing body of evidence suggests that the structure of mitochondrial networks is poised near criticality, an intermediate regime lying in between order and disorder. Such description fits well with the idea that biological systems, in…

We propose a dynamical neural network model with a hierarchical and modular structure. The network architecture can be derived by minimizing an energy function that is originally designed based on two kinds of neurons with quite different…

This paper extends the proof of density of neural networks in the space of continuous (or even measurable) functions on Euclidean spaces to functions on compact sets of probability measures. By doing so the work parallels a more then a…

This paper presents a physics-informed neural network approach for dynamic modeling of saturable synchronous machines, including cases with spatial harmonics. We introduce an architecture that incorporates gradient networks directly into…

Network analysis has played a key role in knowledge discovery and data mining. In many real-world applications in recent years, we are interested in mining multilayer networks, where we have a number of edge sets called layers, which encode…

Deep neural network architectures often consist of repetitive structural elements. We introduce an approach that reveals these patterns and can be broadly applied to the study of deep learning. Similarly to how a power strip helps untangle…

We present a theoretically well-founded deep learning algorithm for nonparametric regression. It uses over-parametrized deep neural networks with logistic activation function, which are fitted to the given data via gradient descent. We…

This work finds the analytical expression of the global minima of a deep linear network with weight decay and stochastic neurons, a fundamental model for understanding the landscape of neural networks. Our result implies that the origin is…

Dynamic networks have intrinsic structural, computational, and multidisciplinary advantages. Link prediction estimates the next relationship in dynamic networks. However, in the current link prediction approaches, only bipartite or…

Networks are universally considered as complex structures of interactions of large multi-component systems. In order to determine the role that each node has inside a complex network, several centrality measures have been developed. Such…

Many important multi-component crystalline solids undergo mechanochemical spinodal decomposition: a phase transformation in which the compositional redistribution is coupled with structural changes of the crystal, resulting in dynamically…

Complex network theory provides a powerful framework to statistically investigate the topology of local and non-local statistical interrelationships, i.e. teleconnections, in the climate system. Climate networks constructed from the same…

Merging the two cultures of deep and statistical learning provides insights into structured high-dimensional data. Traditional statistical modeling is still a dominant strategy for structured tabular data. Deep learning can be viewed…

Textual network embeddings aim to learn a low-dimensional representation for every node in the network so that both the structural and textual information from the networks can be well preserved in the representations. Traditionally, the…

In quantum mechanics, a norm squared wave function can be interpreted as the probability density that describes the likelihood of a particle to be measured in a given position or momentum. This statistical property is at the core of the…