Related papers: Generalised Synchronisations, Embeddings, and Appr…

We prove that a generic reservoir system admits a generalized synchronization that is a topological embedding of the input system's attractor. We also prove that for sufficiently high reservoir dimension (given by Nash's embedding theorem)…

A reservoir computer is a special type of neural network, where most of the weights are randomly fixed and only a subset are trained. In this thesis we prove results about reservoir computers trained on deterministic dynamical systems, and…

This paper explores the conditions under which global contraction manifests in the leaky continuous time reservoirs, thus guaranteeing generalized synchronization. Results on continuous time reservoirs make use of the logarithmic norm of…

In recent years, the machine learning community has seen a continuous growing interest in research aimed at investigating dynamical aspects of both training procedures and machine learning models. Of particular interest among recurrent…

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…

Reservoir computing (RC), a particular form of recurrent neural network, is under explosive development due to its exceptional efficacy and high performance in reconstruction or/and prediction of complex physical systems. However, the…

This paper shows that the celebrated Embedding Theorem of Takens is a particular case of a much more general statement according to which, randomly generated linear state-space representations of generic observations of an invertible…

Reservoir computing is a machine learning framework that exploits nonlinear dynamics, exhibiting significant computational capabilities. One of the defining characteristics of reservoir computing is its low cost and straightforward training…

Reservoir computers (RC) are a form of recurrent neural network (RNN) used for forecasting timeseries data. As with all RNNs, selecting the hyperparameters presents a challenge when training onnew inputs. We present a method based on…

Echo State Networks (ESNs) are a class of single layer recurrent neural networks that have enjoyed recent attention. In this paper we prove that a suitable ESN, trained on a series of measurements of an invertible dynamical system, induces…

We show that recurrent quantum reservoir computers (QRCs) and their recurrence-free architectures (RF-QRCs) are robust tools for learning and forecasting chaotic dynamics from time-series data. First, we formulate and interpret quantum…

We prove a general finite convergence theorem for "upward-guarded" fixpoint expressions over a well-quasi-ordered set. This has immediate applications in regular model checking of well-structured systems, where a main issue is the eventual…

In this paper we briefly report some recent developments on generalized synchronization. We discuss different methods of detecting generalized synchronization. We first consider two unidirectionally coupled systems and then two mutually…

The universal approximation properties with respect to $L ^p $-type criteria of three important families of reservoir computers with stochastic discrete-time semi-infinite inputs is shown. First, it is proved that linear reservoir systems…

Reservoir computers (RC) are a form of recurrent neural network (RNN) used for forecasting time series data. As with all RNNs, selecting the hyperparameters presents a challenge when training on new inputs. We present a method based on…

Reservoir computing is a form of machine learning that utilizes nonlinear dynamical systems to perform complex tasks in a cost-effective manner when compared to typical neural networks. Many recent advancements in reservoir computing, in…

The celebrated Takens' embedding theorem provides a theoretical foundation for reconstructing the full state of a dynamical system from partial observations. However, the classical theorem assumes that the underlying system is deterministic…

We present an adaptive reservoir computing framework for the CTF-4-Science Lorenz benchmark, which evaluates machine learning models across twelve distinct tasks spanning five qualitatively different scenarios: baseline forecasting, noisy…

We report on partial and global generalized synchronization in exemplar bidirectionally coupled non-identical chaotic systems with multiple time delays. We derive conditions for such synchronization regimes. The general approach is applied…

Word embedding models offer continuous vector representations that can capture rich contextual semantics based on their word co-occurrence patterns. While these word vectors can provide very effective features used in many NLP tasks such as…