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

The Echo State Network (ESN) is a class of Recurrent Neural Network with a large number of hidden-hidden weights (in the so-called reservoir). Canonical ESN and its variations have recently received significant attention due to their…

We study the geometric properties of random neural networks by investigating the boundary volumes of their excursion sets for different activation functions, as the depth increases. More specifically, we show that, for activations which are…

This paper introduces a framework to capture previously intractable optimization constraints and transform them to a mixed-integer linear program, through the use of neural networks. We encode the feasible space of optimization problems…

We propose a deep architecture for the classification of multivariate time series. By means of a recurrent and untrained reservoir we generate a vectorial representation that embeds temporal relationships in the data. To improve the…

Echo State Networks (ESNs) are a particular type of untrained Recurrent Neural Networks (RNNs) within the Reservoir Computing (RC) framework, popular for their fast and efficient learning. However, traditional ESNs often struggle with…

In many real complex networks, the fractal and self-similarity properties have been found. The fractal dimension is a useful method to describe fractal property of complex networks. Fractal analysis is inadequate if only taking one fractal…

We analyze the Optimal Channel Network model for river networks using both analytical and numerical approaches. This is a lattice model in which a functional describing the dissipated energy is introduced and minimized in order to find the…

Fractal analysis has been widely used in computer vision, especially in texture image processing and texture analysis. The key concept of fractal-based image model is the fractal dimension, which is invariant to bi-Lipschitz transformation…

In this paper, we study the effective dimension of points in infinite fractal trees generated recursively by a finite tree over some alphabet. Using unequal costs coding, we associate a length function with each such fractal tree and show…

The fractal nature of complex networks has received a great deal of research interest in the last two decades. Similarly to geometric fractals, the fractality of networks can also be defined with the so-called box-covering method. A network…

The goal of this work is to segment the objects in an image that are referred to by a sequence of linguistic descriptions (referring expressions). We propose a deep neural network with recurrent layers that output a sequence of binary…

We propose a new network architecture, the Fractal Pyramid Networks (PFNs) for pixel-wise prediction tasks as an alternative to the widely used encoder-decoder structure. In the encoder-decoder structure, the input is processed by an…

Echo-State Networks (ESNs) distil a key neurobiological insight: richly recurrent but fixed circuitry combined with adaptive linear read-outs can transform temporal streams with remarkable efficiency. Yet fundamental questions about…

Distributed storage systems that deploy erasure codes can provide better features such as lower storage overhead and higher data reliability. In this paper, we focus on fractional repetition (FR) codes, which are a class of storage codes…

Reservoir Computing (RC) is a well-known strategy for designing Recurrent Neural Networks featured by striking efficiency of training. The crucial aspect of RC is to properly instantiate the hidden recurrent layer that serves as dynamical…

This paper introduces a novel algorithmic framework for a deep neural network (DNN), which in a mathematically rigorous manner, allows us to incorporate history (or memory) into the network -- it ensures all layers are connected to one…

Echo state networks (ESNs) are a powerful form of reservoir computing that only require training of linear output weights whilst the internal reservoir is formed of fixed randomly connected neurons. With a correctly scaled connectivity…

Graph Neural Networks (GNNs) have emerged as powerful tools for learning on graph-structured data, but often struggle to balance local and global information. While graph Transformers aim to address this by enabling long-range interactions,…

Fractal image compression is attractive except for its high encoding time requirements. The image is encoded as a set of contractive affine transformations. The image is partitioned into non-overlapping range blocks, and a best matching…

We study random networks of nonlinear resistors, which obey a generalized Ohm's law, $V\sim I^r$. Our renormalized field theory, which thrives on an interpretation of the involved Feynman Diagrams as being resistor networks themselves, is…