Related papers: Learning low-rank latent mesoscale structures in n…

Networks are fundamental for our understanding of complex systems. Interactions between individual nodes in networks generate network motifs - small recurrent patterns that can be considered the network's building-block components,…

Many real-world networks describe systems in which interactions decay with the distance between nodes. Examples include systems constrained in real space such as transportation and communication networks, as well as systems constrained in…

Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior…

Network motifs can capture basic interaction patterns and inform the functional properties of networks. However, real-world complex systems often have multiple types of relationships, which cannot be represented by a monolayer network. The…

The rank of neural networks measures information flowing across layers. It is an instance of a key structural condition that applies across broad domains of machine learning. In particular, the assumption of low-rank feature representations…

Network science can offer fundamental insights into the structural and functional properties of complex systems. For example, it is widely known that neuronal circuits tend to organize into basic functional topological modules, called…

Multilayer networks allow one to represent diverse and coupled connectivity patterns --- e.g., time-dependence, multiple subsystems, or both --- that arise in many applications and which are difficult or awkward to incorporate into standard…

Recurrent neural networks (RNNs) trained on low-dimensional tasks have been widely used to model functional biological networks. However, the solutions found by learning and the effect of initial connectivity are not well understood. Here,…

Networks are a fundamental model of complex systems throughout the sciences, and network datasets are typically analyzed through lower-order connectivity patterns described at the level of individual nodes and edges. However, higher-order…

Many network systems are composed of interdependent but distinct types of interactions, which cannot be fully understood in isolation. These different types of interactions are often represented as layers, attributes on the edges or as a…

Many real-world networks, including nervous systems, exhibit meso-scale structure. This means that their elements can be grouped into meaningful sub-networks. In general, these sub-networks are unknown ahead of time and must be "discovered"…

Large-scale deep neural networks consume expensive training costs, but the training results in less-interpretable weight matrices constructing the networks. Here, we propose a mode decomposition learning that can interpret the weight…

Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…

Many machine learning applications use latent variable models to explain structure in data, whereby visible variables (= coordinates of the given datapoint) are explained as a probabilistic function of some hidden variables. Finding…

Complex systems are large collections of entities that organize themselves into non-trivial structures that can be represented by networks. A key emergent property of such systems is robustness against random failures or targeted attacks…

Mesoscale structures are an integral part of the abstraction and analysis of complex systems. They reveal a node's function in the network, and facilitate our understanding of the network dynamics. For example, they can represent…

Classical network embeddings create a low dimensional representation of the learned relationships between features across nodes. Such embeddings are important for tasks such as link prediction and node classification. In the current paper,…

The new concept of multilevel network is introduced in order to embody some topological properties of complex systems with structures in the mesoscale which are not completely captured by the classical models. This new model, which…

The analysis of small recurrent substructures, so called network motifs, has become a standard tool of complex network science to unveil the design principles underlying the structure of empirical networks. In many natural systems network…

A deluge of new data on social, technological and biological networked systems suggests that a large number of interactions among system units are not limited to pairs, but rather involve a higher number of nodes. To properly encode such…