Related papers: Generic and Isometric Embeddings in Reservoir Comp…
We establish conditions under which a continuous time reservoir computer, such as a leaky integrator echo state network, admits a generalised synchronisation $f$ between between the source dynamics and reservoir dynamics. We show that…
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…
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 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 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…
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…
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…
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…
Approximation capability of reservoir systems whose reservoir is a recurrent neural network (RNN) is discussed. We show what we call uniform strong universality of RNN reservoir systems for a certain class of dynamical systems. This means…
A natural hypothesis for the success of reservoir computing in generic tasks is the ability of the untrained reservoir to map different input time series to separable reservoir states - a property we term separation capacity. We provide a…
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…
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…
A new explanation of geometric nature of the reservoir computing phenomenon is presented. Reservoir computing is understood in the literature as the possibility of approximating input/output systems with randomly chosen recurrent neural…
Reservoir computing can embed attractors into random neural networks (RNNs), generating a ``mirror'' of a target attractor because of its inherent symmetrical constraints. In these RNNs, we report that an attractor-merging crisis…
Reservoir computing typically relies on large, randomly generated reservoirs, enabling simple, often linear readouts. Over the past two decades, most constructions have exploited the freedom to select the reservoir, constrained primarily by…
This note is about a little extension of Nash's embedding theorem in the case of complete manifolds.
A physical neural network (PNN) has both the strong potential to solve machine learning tasks and intrinsic physical properties, such as high-speed computation and energy efficiency. Reservoir computing (RC) is an excellent framework for…
It is common for researchers to record long, multiple time series from experiments or calculations. But sometimes there are no good models for the systems or no applicable mathematical theorems that can tell us when there are basic…
We introduce a novel concept of generalized synchronization, able to encompass the setting of collective synchronized behavior for mutually coupled systems and networking systems featuring complex topologies in their connections. The onset…