Related papers: Analyzing Echo-state Networks Using Fractal Dimens…

This study reports an unintuitive finding that positional encoding enhances learning of recurrent neural networks (RNNs). Positional encoding is a high-dimensional representation of time indices on input data. Most famously, positional…

The purpose of this paper is to study the fractal phenomena in large data sets and the associated questions of dimension reduction. We examine situations where the classical Principal Component Analysis is not effective in identifying the…

In reservoir computing, an input sequence is processed by a recurrent neural network, the reservoir, which transforms it into a spatial pattern that a shallow readout network can then exploit for tasks such as memorization and time-series…

Fractional repetition (FR) codes are a class of repair efficient erasure codes that can recover a failed storage node with both optimal repair bandwidth and complexity. In this paper, we study the minimum distance of FR codes, which is the…

This paper provides a new model to compute the fractal dimension of a subset on a generalized-fractal space. Recall that fractal structures are a perfect place where a new definition of fractal dimension can be given, so we perform a…

This paper introduces a scale-invariant methodology employing \textit{Fractal Geometry} to analyze and explain the nonlinear dynamics of complex connectionist systems. By leveraging architectural self-similarity in Deep Neural Networks…

Reservoir Computing (RC) is a popular methodology for the efficient design of Recurrent Neural Networks (RNNs). Recently, the advantages of the RC approach have been extended to the context of multi-layered RNNs, with the introduction of…

With an increasing emphasis on network security, much more attention has been attracted to the vulnerability of complex networks. The multi-scale evaluation of vulnerability is widely used since it makes use of combined powers of the links'…

Building upon [1], this study aims to introduce fractal geometry into graph theory, and to establish a potential theoretical foundation for complex networks. Specifically, we employ the method of substitution to create and explore…

Although there is increasing evidence of criticality in the brain, the processes that guide neuronal networks to reach or maintain criticality remain unclear. The present research examines the role of neuronal gain plasticity in time-series…

Fractals are self-similar and scale-invariant patterns found ubiquitously in nature. A lot of evidences implying fractal properties such as 1/f power spectrums have been also observed in resting state fMRI time series. To explain the…

Reservoir computing (RC) represents a class of state-space models (SSMs) characterized by a fixed state transition mechanism (the reservoir) and a flexible readout layer that maps from the state space. It is a paradigm of computational…

Deep convolutional neural networks (DCNNs) have shown remarkable performance in image classification tasks in recent years. Generally, deep neural network architectures are stacks consisting of a large number of convolutional layers, and…

Physical reservoir computing exploits the intrinsic dynamics of physical systems for information processing, while keeping the internal dynamics fixed and training only linear readouts; yet the role of input encoding remains poorly…

The study of deep recurrent neural networks (RNNs) and, in particular, of deep Reservoir Computing (RC) is gaining an increasing research attention in the neural networks community. The recently introduced Deep Echo State Network (DeepESN)…

Fractal scaling--a power-law behavior of the number of boxes needed to tile a given network with respect to the lateral size of the box--is studied. We introduce a new box-covering algorithm that is a modified version of the original…

We explore the concepts of self-similarity, dimensionality, and (multi)scaling in a new family of recursive scale-free nets that yield themselves to exact analysis through renormalization techniques. All nets in this family are self-similar…

Wireless mesh networks (WMNs) depend on the spatial distribution of nodes, which directly influences connectivity, routing efficiency, and overall network performance. Conventional models typically assume uniform or random node placement,…

The extension of deep learning towards temporal data processing is gaining an increasing research interest. In this paper we investigate the properties of state dynamics developed in successive levels of deep recurrent neural networks…

We study algorithmic problems on subsets of Euclidean space of low fractal dimension. These spaces are the subject of intensive study in various branches of mathematics, including geometry, topology, and measure theory. There are several…