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In this paper we developed a hierarchical network model, called Hierarchical Prediction Network (HPNet), to understand how spatiotemporal memories might be learned and encoded in the recurrent circuits in the visual cortical hierarchy for…

Faculty hiring networks-who hires whose graduates as faculty-exhibit steep hierarchies, which can reinforce both social and epistemic inequalities in academia. Understanding the mechanisms driving these patterns would inform efforts to…

Activity in coupled systems is often oscillatory, for example, the firing pattern of neuronal populations. Whereas these oscillations have been studied predominantly in local circuits, here we show how the topology of large-scale networks,…

Hierarchy seems to pervade complexity in both living and artificial systems. Despite its relevance, no general theory that captures all features of hierarchy and its origins has been proposed yet. Here we present a formal approach resulting…

Constraints placed upon the phenotypes of organisms result from their interactions with the environment. Over evolutionary timescales, these constraints feed back onto smaller molecular subnetworks comprising the organism. The evolution of…

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…

One of the main challenges in the study of time-varying networks is the interplay of memory effects with structural heterogeneity. In particular, different nodes and dyads can have very different statistical properties in terms of both link…

Many theories have emerged which investigate how in- variance is generated in hierarchical networks through sim- ple schemes such as max and mean pooling. The restriction to max/mean pooling in theoretical and empirical studies has diverted…

Modularity is designed to measure the strength of division of a network into clusters (known also as communities). Networks with high modularity have dense connections between the vertices within clusters but sparse connections between…

Relationships among time series can be exploited as inductive biases in learning effective forecasting models. In hierarchical time series, relationships among subsets of sequences induce hard constraints (hierarchical inductive biases) on…

Empirical complex systems can be characterized not only by pairwise interactions, but also by higher-order (group) interactions influencing collective phenomena, from metabolic reactions to epidemics. Nevertheless, higher-order networks'…

We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively…

We investigate a model of transportation networks with nonlinear elements which may represent local shortage of resources. Frustrations arise from competition for resources. When the initial resources are uniform, different regimes with…

A large variety of real-world Reinforcement Learning (RL) tasks is characterized by a complex and heterogeneous structure that makes end-to-end (or flat) approaches hardly applicable or even infeasible. Hierarchical Reinforcement Learning…

Higher-order networks, naturally described as hypergraphs, are essential for modeling real-world systems involving interactions among three or more entities. Stochastic block models offer a principled framework for characterizing mesoscale…

Hierarchical networks are attracting a renewal interest for modelling the organization of a number of biological systems and for tackling the complexity of statistical mechanical models beyond mean-field limitations. Here we consider the…

Recently, recommender systems have been able to emit substantially improved recommendations by leveraging user-provided reviews. Existing methods typically merge all reviews of a given user or item into a long document, and then process…

Functional networks provide a topological description of activity patterns in the brain, as they stem from the propagation of neural activity on the underlying anatomical or structural network of synaptic connections. This latter is well…

The Griffiths phase has been proposed to induce a stretched critical regime that facilitates self-organizing of brain networks for optimal function. This phase stems from the intrinsic structural heterogeneity of brain networks, such as the…

Link weight is crucial in weighted complex networks. It provides additional dimension for describing and adjusting the properties of networks. The topological role of weight is studied by the effects of random redistribution of link weights…