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

We prove minimax optimal learning rates for kernel ridge regression, resp.~support vector machines based on a data dependent partition of the input space, where the dependence of the dimension of the input space is replaced by the fractal…

Recurrent neural networks (RNNs) have become increasingly popular in information processing tasks involving time series and temporal data. A fundamental property of RNNs is their ability to create reliable input/output responses, often…

If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…

We present the discriminative recurrent sparse auto-encoder model, comprising a recurrent encoder of rectified linear units, unrolled for a fixed number of iterations, and connected to two linear decoders that reconstruct the input and…

We consider first and second order consensus algorithms in networks with stochastic disturbances. We quantify the deviation from consensus using the notion of network coherence, which can be expressed as an $H_2$ norm of the stochastic…

Neurons in the brain communicate with spikes, which are discrete events in time and value. Functional network models often employ rate units that are continuously coupled by analog signals. Is there a qualitative difference implied by these…

Fractional-order dynamical networks are increasingly being used to model and describe processes demonstrating long-term memory or complex interlaced dependencies amongst the spatial and temporal components of a wide variety of dynamical…

Reservoir Computing is a machine learning approach that uses the rich repertoire of complex system dynamics for function approximation. Current approaches to reservoir computing use a network of coupled integrating neurons that require a…

Neural networks have greatly boosted performance in computer vision by learning powerful representations of input data. The drawback of end-to-end training for maximal overall performance are black-box models whose hidden representations…

The self-similarity of complex networks is typically investigated through computational algorithms the primary task of which is to cover the structure with a minimal number of boxes. Here we introduce a box-covering algorithm that not only…

In certain situations, neural networks will represent environment states in their hidden activations. Our goal is to visualize what environment states the networks are representing. We experiment with a recurrent neural network (RNN)…

Fractal structure of a system suggests the optimal way in which parts arranged or put together to form a whole. The ideas from fractals have a potential application to the researches on urban sustainable development. To characterize fractal…

A fundamental aspect of limitations in learning any computation in neural architectures is characterizing their optimal capacities. An important, widely-used neural architecture is known as autoencoders where the network reconstructs the…

Fractal-like structures of varying complexity are common in nature, and measure-based dimensions (Minkowski, Hausdorff) supply their basic geometric characterization. However, at the level of fundamental dynamics, which is quantum,…

Fractal image compression has some desirable properties like high quality at high compression ratio, fast decoding, and resolution independence. Therefore it can be used for many applications such as texture mapping and pattern recognition…

Reservoir Computing (RC) refers to a Recurrent Neural Networks (RNNs) framework, frequently used for sequence learning and time series prediction. The RC system consists of a random fixed-weight RNN (the input-hidden reservoir layer) and a…

Encoder-decoder networks using convolutional neural network (CNN) architecture have been extensively used in deep learning literatures thanks to its excellent performance for various inverse problems. However, it is still difficult to…

This work aims at shedding some light on connections between finite state machines (FSMs), and recurrent neural networks (RNNs). Examined connections in this master's thesis is threefold: the extractability of finite state machines from…

This article is a mini-review about electrical current flows in networks from the perspective of statistical physics. We briefly discuss analytical methods to solve the conductance of an arbitrary resistor network. We then turn to basic…

Distributed optimization is fundamental to modern machine learning applications like federated learning, but existing methods often struggle with ill-conditioned problems and face stability-versus-speed tradeoffs. We introduce fractional…