Quantitative evaluation of the performance of discrete-time reservoir computers in the forecasting, filtering, and reconstruction of stochastic stationary signals

Recurrent neural networks (RNNs) are known to be universal approximators of dynamic systems under fairly mild and general assumptions, making them good tools to process temporal information. However, RNNs usually suffer from the issues of vanishing and exploding gradients in the standard RNN training. Reservoir computing (RC), a special RNN where the recurrent weights are randomized and left untrained, has been introduced to overcome these issues and has demonstrated superior...

Reservoir computing is a machine learning framework where the readouts from a nonlinear system (the reservoir) are trained so that the output from the reservoir, when forced with an input signal, reproduces a desired output signal. A common implementation of reservoir computers is to use a recurrent neural network as the reservoir. The design of this network can have significant effects on the performance of the reservoir computer. In this paper we study the effect of the nod...

The notion of memory capacity, originally introduced for echo state and linear networks with independent inputs, is generalized to nonlinear recurrent networks with stationary but dependent inputs. The presence of dependence in the inputs makes natural the introduction of the network forecasting capacity, that measures the possibility of forecasting time series values using network states. Generic bounds for memory and forecasting capacities are formulated in terms of the num...

Reservoir computers (RCs) and recurrent neural networks (RNNs) can mimic any finite-state automaton in theory, and some workers demonstrated that this can hold in practice. We test the capability of generalized linear models, RCs, and Long Short-Term Memory (LSTM) RNN architectures to predict the stochastic processes generated by a large suite of probabilistic deterministic finite-state automata (PDFA). PDFAs provide an excellent performance benchmark in that they can be syst...

We review attempts that have been made towards understanding the computational properties and mechanisms of input-driven dynamical systems like RNNs, and reservoir computing networks in particular. We provide details on methods that have been developed to give quantitative answers to the questions above. Following this, we show how self-organization may be used to improve reservoirs for better performance, in some cases guided by the measures presented before. We also present...

Reservoir Computing Networks (RCNs) belong to a group of machine learning techniques that project the input space non-linearly into a high-dimensional feature space, where the underlying task can be solved linearly. Popular variants of RCNs are capable of solving complex tasks equivalently to widely used deep neural networks, but with a substantially simpler training paradigm based on linear regression. In this paper, we show how to uniformly describe RCNs with small and clea...

The time-delay-based reservoir computing setup has seen tremendous success in both experiment and simulation. It allows for the construction of large neuromorphic computing systems with only few components. However, until now the interplay of the different timescales has not been investigated thoroughly. In this manuscript, we investigate the effects of a mismatch between the time-delay and the clock cycle for a general model. Typically, these two time scales are considered t...

Reservoir Computing is a relatively new framework created to allow the usage of powerful but complex systems as computational mediums. The basic approach consists in training only a readout layer, exploiting the innate separation and transformation provided by the previous, untrained system. This approach has shown to possess great computational capabilities and is successfully used to achieve many tasks. This review aims to represent the current 'state-of-the-art' of the usa...

Reservoir Computing (RC) is a powerful computational paradigm that allows high versatility with cheap learning. While other artificial intelligence approaches need exhaustive resources to specify their inner workings, RC is based on a reservoir with highly non-linear dynamics that does not require a fine tuning of its parts. These dynamics project input signals into high-dimensional spaces, where training linear readouts to extract input features is vastly simplified. Thus, i...

The reservoir computing scheme is a machine learning mechanism which utilizes the naturally occuring computational capabilities of dynamical systems. One important subset of systems that has proven powerful both in experiments and theory are delay-systems. In this work, we investigate the reservoir computing performance of hybrid network-delay systems systematically by evaluating the NARMA10 and the Sante Fe task.. We construct 'multiplexed networks' that can be seen as inter...