Related papers: Embedding and Approximation Theorems for Echo Stat…

Most contemporary neural learning systems rely on epoch-based optimization and repeated access to historical data, implicitly assuming reversible computation. In contrast, real-world environments often present information as irreversible…

We study the learning ability of linear recurrent neural networks with Gradient Descent. We prove the first theoretical guarantee on linear RNNs to learn any stable linear dynamic system using any a large type of loss functions. For an…

A particular case of Recurrent Neural Network (RNN) was introduced at the beginning of the 2000s under the name of Echo State Networks (ESNs). The ESN model overcomes the limitations during the training of the RNNs while introducing no…

Inspired by recent theoretical arguments, physics-informed echo state network (ESN) is discussed on the attempt to train a reservoir model absolutely in physics-informed manner. As the plainest work on such a purpose, an ODE (ordinary…

This work studies approximation based on single-hidden-layer feedforward and recurrent neural networks with randomly generated internal weights. These methods, in which only the last layer of weights and a few hyperparameters are optimized,…

This article introduces a robust hybrid method for solving supervised learning tasks, which uses the Echo State Network (ESN) model and the Particle Swarm Optimization (PSO) algorithm. An ESN is a Recurrent Neural Network with the…

The prediction of the temporal dynamics of chaotic systems is challenging because infinitesimal perturbations grow exponentially. The analysis of the dynamics of infinitesimal perturbations is the subject of stability analysis. In stability…

Echo state networks are a recently developed type of recurrent neural network where the internal layer is fixed with random weights, and only the output layer is trained on specific data. Echo state networks are increasingly being used to…

Dynamic network embedding methods transform nodes in a dynamic network into low-dimensional vectors while preserving network characteristics, facilitating tasks such as node classification and community detection. Several embedding methods…

Echo state networks are computationally lightweight reservoir models inspired by the random projections observed in cortical circuitry. As interest in reservoir computing has grown, networks have become deeper and more intricate. While…

In the field of complex dynamics, multistable attractors have been gaining a significant attention due to its unpredictability in occurrence and extreme sensitivity to initial conditions. Co-existing attractors are abundant in diverse…

Prediction models that capture and use the structure of state-space dynamics can be very effective. In practice, however, one rarely has access to full information about that structure, and accurate reconstruction of the dynamics from…

Generalized synchronization between coupled dynamical systems is a phenomenon of relevance in applications that range from secure communications to physiological modelling. Here we test the capabilities of reservoir computing and, in…

We first study the generalization error of models that use a fixed feature representation (frozen intermediate layers) followed by a trainable readout layer. This setting encompasses a range of architectures, from deep random-feature models…

Network embeddings learn to represent nodes as low-dimensional vectors to preserve the proximity between nodes and communities of the network for network analysis. The temporal edges (e.g., relationships, contacts, and emails) in dynamic…

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…

Despite the superiority of convolutional neural networks demonstrated in time series modeling and forecasting, it has not been fully explored on the design of the neural network architecture and the tuning of the hyper-parameters. Inspired…

Background/introduction: Cross-Validation (CV) is still uncommon in time series modeling. Echo State Networks (ESNs), as a prime example of Reservoir Computing (RC) models, are known for their fast and precise one-shot learning, that often…

Network Embeddings (NEs) map the nodes of a given network into $d$-dimensional Euclidean space $\mathbb{R}^d$. Ideally, this mapping is such that `similar' nodes are mapped onto nearby points, such that the NE can be used for purposes such…

Understanding how biological constraints shape neural computation is a central goal of computational neuroscience. Spatially embedded recurrent neural networks provide a promising avenue to study how modelled constraints shape the combined…