Related papers: Dynamical Systems as Temporal Feature Spaces

Recurrent neural networks (RNNs) have drawn interest from machine learning researchers because of their effectiveness at preserving past inputs for time-varying data processing tasks. To understand the success and limitations of RNNs, it is…

This work advances the theoretical foundations of reservoir computing (RC) by providing a unified treatment of fading memory and the echo state property (ESP) in both deterministic and stochastic settings. We investigate state-space…

We investigate the ability of an ensemble reservoir computing approach to predict the long-term behaviour of the phase-space region in which the motion of charged particles in hadron storage rings is bounded, the so-called dynamic aperture.…

As an efficient recurrent neural network (RNN) model, reservoir computing (RC) models, such as Echo State Networks, have attracted widespread attention in the last decade. However, while they have had great success with time series data…

Echo state networks (ESN), a type of reservoir computing (RC) architecture, are efficient and accurate artificial neural systems for time series processing and learning. An ESN consists of a core of recurrent neural networks, called a…

Spiking neural networks (SNNs) support energy-efficient machine intelligence because event-driven computation and sparse activity map naturally to low-power digital hardware. In practical implementations, however, membrane states, synaptic…

State space models (SSMs) have emerged as a powerful framework for modelling long-range dependencies in sequence data. Unlike traditional recurrent neural networks (RNNs) and convolutional neural networks (CNNs), SSMs offer a structured and…

The unprecedented dissemination of edge devices is accompanied by a growing demand for neuromorphic chips that can process time-series data natively without cloud support. Echo state network (ESN) is a class of recurrent neural networks…

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…

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…

The identification of a nonlinear dynamic model is an open topic in control theory, especially from sparse input-output measurements. A fundamental challenge of this problem is that very few to zero prior knowledge is available on both the…

Spatio-temporal data and processes are prevalent across a wide variety of scientific disciplines. These processes are often characterized by nonlinear time dynamics that include interactions across multiple scales of spatial and temporal…

Machine learning methods have shown promise in learning chaotic dynamical systems, enabling model-free short-term prediction and attractor reconstruction. However, when applied to large-scale, spatiotemporally chaotic systems, purely…

This paper studies sequence modeling for prediction tasks with long range dependencies. We propose a new formulation for state space models (SSMs) based on learning linear dynamical systems with the spectral filtering algorithm (Hazan et…

Echo State Networks (ESNs) are time-series processing models working under the Echo State Property (ESP) principle. The ESP is a notion of stability that imposes an asymptotic fading of the memory of the input. On the other hand, the…

State space models (SSMs) have shown remarkable empirical performance on many long sequence modeling tasks, but a theoretical understanding of these models is still lacking. In this work, we study the learning dynamics of linear SSMs to…

Dynamic temporal graphs represent evolving relations between entities, e.g. interactions between social network users or infection spreading. We propose an extension of graph echo state networks for the efficient processing of dynamic…

Echo State Networks (ESNs) are simplified recurrent neural network models composed of a reservoir and a linear, trainable readout layer. The reservoir is tunable by some hyper-parameters that control the network behaviour. ESNs are known to…

In this paper, we elaborate over the well-known interpretability issue in echo state networks. The idea is to investigate the dynamics of reservoir neurons with time-series analysis techniques taken from research on complex systems.…

Study of dynamical systems using partial state observation is an important problem due to its applicability to many real-world systems. We address the problem by studying an echo state network (ESN) framework with partial state input with…