A Unified Framework for Reservoir Computing and Extreme Learning Machines based on a Single Time-delayed Neuron

Ortín, Silvia; Soriano, Miguel C.; Pesquera, L.; Brunner, Daniel; San-Martín, Daniel; Fischer, Ingo; Mirasso, Claudio R.; Gutiérrez, José Manuel

doi:10.1038/srep14945

Cited by 150 publications

(98 citation statements)

References 21 publications

(44 reference statements)

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“…The proof of Section 4 shows a network is an ESN even if the largest eigenvalue of the recurrent connectivity matrix is equal to 1 and if the transfer function is either Equation (15) or (16). The proof is also extensible to other transfer functions.…”

Section: Summary Discussion and Outlookmentioning

confidence: 82%

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Echo State Condition at the Critical Point

Mayer

2016

Entropy

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Recurrent networks with transfer functions that fulfil the Lipschitz continuity with K = 1 may be echo state networks if certain limitations on the recurrent connectivity are applied. It has been shown that it is sufficient if the largest singular value of the recurrent connectivity is smaller than 1. The main achievement of this paper is a proof under which conditions the network is an echo state network even if the largest singular value is one. It turns out that in this critical case the exact shape of the transfer function plays a decisive role in determining whether the network still fulfills the echo state condition. In addition, several examples with one-neuron networks are outlined to illustrate effects of critical connectivity. Moreover, within the manuscript a mathematical definition for a critical echo state network is suggested.

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Section: Summary Discussion and Outlookmentioning

confidence: 82%

“…Single neuron reservoirs have been studied in other researches [15,16]. Here the intention is to illustrate the principle benefits and other features of critical ESNs.…”

Section: Examples Using a Single Neuron As A Reservoirmentioning

confidence: 99%

Echo State Condition at the Critical Point

Mayer

2016

Entropy

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“…a reservoir without internal connectivity, in which the input layer is randomly mapped to the hidden layer [64]. In Ortín et al [57], it has been shown that the optoelectronic implementation of ELM yields comparable results to RC as long as past inputs are explicitly included in the input layer. A more powerful approach is that of implementing general machine learning models on a hardware device [65].…”

Section: Optoelectronic Delay-based Reservoir Computingmentioning

confidence: 98%

“…A number of classification, prediction, and system modelling tasks have been performed with state-of-the-art results. To name a few, excellent performance has been obtained for speech recognition [21,22,55], chaotic time series prediction [22,56,57], nonlinear channel equalization [21,[57][58][59], and radar signal forecasting [58,59]. A summary of the results obtained for each task is given in Table 1.…”

Section: Optoelectronic Delay-based Reservoir Computingmentioning

confidence: 99%

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Advances in photonic reservoir computing

2017

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Abstract:We review a novel paradigm that has emerged in analogue neuromorphic optical computing. The goal is to implement a reservoir computer in optics, where information is encoded in the intensity and phase of the optical field. Reservoir computing is a bio-inspired approach especially suited for processing time-dependent information. The reservoir's complex and high-dimensional transient response to the input signal is capable of universal computation. The reservoir does not need to be trained, which makes it very well suited for optics. As such, much of the promise of photonic reservoirs lies in their minimal hardware requirements, a tremendous advantage over other hardware-intensive neural network models. We review the two main approaches to optical reservoir computing: networks implemented with multiple discrete optical nodes and the continuous system of a single nonlinear device coupled to delayed feedback.

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Opportunities in Quantum Reservoir Computing and Extreme Learning Machines

et al. 2021

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Quantum reservoir computing and quantum extreme learning machines are two emerging approaches that have demonstrated their potential both in classical and quantum machine learning tasks. They exploit the quantumness of physical systems combined with an easy training strategy, achieving an excellent performance. The increasing interest in these unconventional computing approaches is fueled by the availability of diverse quantum platforms suitable for implementation and the theoretical progresses in the study of complex quantum systems. In this review article, recent proposals and first experiments displaying a broad range of possibilities are reviewed when quantum inputs, quantum physical substrates and quantum tasks are considered. The main focus is the performance of these approaches, on the advantages with respect to classical counterparts and opportunities.

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A Unified Framework for Reservoir Computing and Extreme Learning Machines based on a Single Time-delayed Neuron

Cited by 150 publications

References 21 publications

Echo State Condition at the Critical Point

Echo State Condition at the Critical Point

Advances in photonic reservoir computing

Opportunities in Quantum Reservoir Computing and Extreme Learning Machines

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