Related papers: Measuring the Hierarchy of Feedforward Networks

What is information, physically, and why does it so reliably emerge in living, cultural, and technological systems? Existing theories quantify uncertainty, cost, or compressibility, but do not identify which physical structures count as…

In social networks, information and influence diffuse among users as cascades. While the importance of studying cascades has been recognized in various applications, it is difficult to observe the complete structure of cascades in practice.…

Many social and biological systems are characterized by enduring hierarchies, including those organized around prestige in academia, dominance in animal groups, and desirability in online dating. Despite their ubiquity, the general…

Many networked systems are governed by non-pairwise interactions between nodes. The resulting higher-order interaction structure can then be encoded by means of a hypernetwork. In this paper we consider dynamical systems on hypernetworks by…

Structural causal models postulate noisy functional relations among a set of interacting variables. The causal structure underlying each such model is naturally represented by a directed graph whose edges indicate for each variable which…

Networks and graphs provide a simple but effective model to a vast set of systems which building blocks interact throughout pairwise interactions. Unfortunately, such models fail to describe all those systems which building blocks interact…

A highly successful approach to route planning in networks (particularly road networks) is to identify a hierarchy in the network that allows faster queries after some preprocessing that basically inserts additional "shortcut"-edges into a…

Many real networks in nature and society share two generic properties: they are scale-free and they display a high degree of clustering. We show that these two features are the consequence of a hierarchical organization, implying that small…

Like natural complex systems such as the Earth's climate or a living cell, semiconductor lithography systems are characterized by nonlinear dynamics across more than a dozen orders of magnitude in space and time. Thousands of sensors…

We consider labelings of a finite regular tree by a finite alphabet subject to restrictions specified by a nonnegative transition matrix, propose an algorithm for determining whether the set of possible configurations on the last row of the…

Hypergraphs, describing networks where interactions take place among any number of units, are a natural tool to model many real-world social and biological systems. In this work we propose a principled framework to model the organization of…

Several real-world and abstract structures and systems are characterized by marked hierarchy to the point of being expressed as trees. Because the study of these entities often involves sampling (or discovering) the tree nodes in a specific…

We started with a knowledge graph of connected entities and descriptive properties of those entities, from which, a hierarchical representation of the knowledge graph is derived. Using a graphical, energy-based neural network, we are able…

Hierarchical neural networks are exponentially more efficient than their corresponding "shallow" counterpart with the same expressive power, but involve huge number of parameters and require tedious amounts of training. Our main idea is to…

The hierarchical Dirichlet process is the cornerstone of Bayesian nonparametric multilevel models. Its generative model can be described through a set of latent variables, commonly referred to as tables within the popular restaurant…

Balance theory explains the forces behind the structure of social systems, which are commonly modeled as static undirected signed networks. We expand this modeling approach to incorporate directionality of edges, and consider three levels…

This paper introduces some tools from graph theory and distributed consensus algorithms to construct an optimal, yet robust, hierarchical information sharing structure for large-scale decision making and control problems. The proposed…

Machine learning is the dominant approach to artificial intelligence, through which computers learn from data and experience. In the framework of supervised learning, a necessity for a computer to learn from data accurately and efficiently…

Hierarchical analysis is considered and a multilevel model is presented in order to explore causality, chance and complexity in financial economics. A coupled system of models is used to describe multilevel interactions, consistent with…

With the great success of networks, it witnesses the increasing demand for the interpretation of the internal network mechanism, especially for the net decision-making logic. To tackle the challenge, the Concept-harmonized HierArchical…