Related papers: Structured Information in Metric Neural Networks

Whatever information a deep neural network has gleaned from training data is encoded in its weights. How this information affects the response of the network to future data remains largely an open question. Indeed, even defining and…

Effective information analysis generally boils down to properly identifying the structure or geometry of the data, which is often represented by a graph. In some applications, this structure may be partly determined by design constraints or…

Graphs representing real world systems may be studied from their underlying community structure. A community in a network is an intuitive idea for which there is no consensus on its objective mathematical definition. The most used metric in…

Models of networks play a major role in explaining and reproducing empirically observed patterns. Suitable models can be used to randomize an observed network while preserving some of its features, or to generate synthetic graphs whose…

Many complex systems in nature and society can be described in terms of networks capturing the intricate web of connections among the units they are made of. A key question is how to interpret the global organization of such networks as the…

Neural networks based on metric recognition methods have a strictly determined architecture. Number of neurons, connections, as well as weights and thresholds values are calculated analytically, based on the initial conditions of tasks:…

Current methods for pattern analysis in time series mainly rely on statistical features or probabilistic learning and inference methods to identify patterns and trends in the data. Such methods do not generalize well when applied to…

Models of street networks underlie research in urban travel behavior, accessibility, design patterns, and morphology. These models are commonly defined as planar, meaning they can be represented in two dimensions without any underpasses or…

There has been increasing interest in the integrated information theory (IIT) ofconsciousness, which hypothesizes that consciousness is integrated information withinneuronal dynamics. However, the current formulation of IIT poses both…

Geometry can be used to explain many properties commonly observed in real networks. It is therefore often assumed that real networks, especially those with high average local clustering, live in an underlying hidden geometric space.…

Infomap clustering finds the community structures that minimize the expected description length of a random walk trajectory; algorithms for infomap clustering run fast in practice for large graphs. In this paper we leverage the…

The detection of weak and rare effects in large amounts of data arises in a number of modern data analysis problems. Known results show that in this situation the potential of statistical inference is severely limited by the large-scale…

Lately, network sampling proved as a promising tool for simplifying large real-world networks and thus providing for their faster and more efficient analysis. Still, understanding the changes of network structure and properties under…

A growing interest in complex networks theory results in an ongoing demand for new analytical tools. We propose a novel measure based on information theory that provides a new perspective for a better understanding of networked systems:…

We show that macro-molecular self-assembly can recognize and classify high-dimensional patterns in the concentrations of $N$ distinct molecular species. Similar to associative neural networks, the recognition here leverages dynamical…

We design and analyze a new paradigm for building supervised learning networks, driven only by local optimization rules without relying on a global error function. Traditional neural networks with a fixed topology are made up of identical…

Discovering and characterizing the large-scale topological features in empirical networks are crucial steps in understanding how complex systems function. However, most existing methods used to obtain the modular structure of networks…

The learned weights of a neural network have often been considered devoid of scrutable internal structure. In this paper, however, we look for structure in the form of clusterability: how well a network can be divided into groups of neurons…

Despite the popularity and success of deep learning, there is limited understanding of when, how, and why neural networks generalize to unseen examples. Since learning can be seen as extracting information from data, we formally study…

We investigate the behavior of extended urban traffic networks within the framework of percolation theory by using real and synthetic traffic data. Our main focus shifts from the statistical properties of the cluster size distribution…