## No full-text available

To read the full-text of this research,

you can request a copy directly from the authors.

We formulate, using the discrete nonlinear Schrödinger equation (DNLS), a general approach to encode and process information based on reservoir computing. Reservoir computing is a promising avenue for realizing neuromorphic computing devices. In such computing systems, training is performed only at the output level by adjusting the output from the reservoir with respect to a target signal. In our formulation, the reservoir can be an arbitrary physical system, driven out of thermal equilibrium by an external driving. The DNLS is a general oscillator model with broad application in physics, and we argue that our approach is completely general and does not depend on the physical realization of the reservoir. The driving, which encodes the object to be recognized, acts as a thermodynamic force, one for each node in the reservoir. Currents associated with these thermodynamic forces in turn encode the output signal from the reservoir. As an example, we consider numerically the problem of supervised learning for pattern recognition, using as a reservoir a network of nonlinear oscillators.

To read the full-text of this research,

you can request a copy directly from the authors.

... Alternatively, a Ridge regression with Tikhonov regularization can also be employed, a method that has the advantage of being faster to compute numerically, and the ability to penalize large matrix entries, allowing to prevent overfitting that typically occurs in the pseudo-inverse technique [23]. Concerning classification tasks, even though the previous methods are still applicable (by selecting the class with highest forecast value), the use of logistic regression on the output data was reported in recent works yielding promising results [24,25]. Put in this way, it is clear that the versatility of RC paradigm resides in the freedom of choice of the reservoir, making that role accessible to any nonlinear physical system. ...

... To our best knowledge, this work presents the first time that a soliton-based system is considered to deploy a reservoir computer, a fact that in our opinion may inspire future research in two directions. On one hand, the versatility, tunability, and robustness of the system may inspire the development of all-optical computing technologies, not only restricted to propagation geometries and continuous-wave beams but also with temporal optical pulses [24,28], possibly bypassing the obstacle of the absence of periodic conditions in real-world setups by establishing a Newton's cradle-like configuration [26,29,36]. On the other hand, considering the universality of the soliton solutions in nonlinear science, not only in optical systems [19] but also in fluids [37], plasmas [20] and quantum gases [21,22], just to name a few, the present work establishes a general blueprint that can easily be extended towards computing solutions with a great variety of physical systems. ...

Reservoir computing is a promising framework that facilitates the approach to physical neuromorphic hardware by enabling a given nonlinear physical system to act as a computing platform. In this work, we exploit this paradigm to propose a versatile and robust soliton-based computing system using a discrete soliton chain as a reservoir. By taking advantage of its tunable governing dynamics, we show that sufficiently strong nonlinear dynamics allows our soliton-based solution to perform accurate regression and classification tasks of non-linear separable datasets. At a conceptual level, the results presented pave a way for the physical realization of novel hardware solutions and have the potential to inspire future research on soliton-based computing using various physical platforms, leveraging its ubiquity across multiple fields of science, from nonlinear optical media to quantum systems.

... Many nonlinear dynamic systems have been considered as reservoir computers. These include soft robots [3,4,5,6,7], tensegrity structures [8,9], a discrete nonlinear Schrödinger equation (DNLS) based array of seven coupled oscillators with all-to-all coupling [10], chaotic fluid flow [11], a driven Chua's chaotic circuit [12], a coupled chaotic oscillator system (the Lorenz system) [13], optoelectronic systems [14,15,16,17], and even coupled DNA oscillators [18]. The Hopf oscillator has been shown to complete many benchmark tasks [19], and it was shown that dynamic phenomena, such as Arnold tongues and the Farey sequence, correspond to computational ability [20]. ...

The Duffing oscillator array has been extensively studied in the context of localization phenomena. By using the nonlinear dynamics of a physical system, machine learning can unlock computational ability from these physical systems. The Duffing oscillator array can be used as a reservoir computer, and multiple benchmark tasks were used to quantify its computing ability. However , many of the dynamic phenomena that are observed in the array are also mirrored in the computational ability of the reservoir computer.

... The computation is obtained by mapping the transient dynamics of the nonlinear physical system to a higher dimensional space. Some of the popular applications of RC include logical operations [11][12][13][14][15], spoken and handwritten digit recognition [8,16,17], wireless communications [2], complex and chaotic time-series predictions [2,8,[18][19][20][21], long-term chaotic time-series prediction [22,23], image recognition [24], and morphological computation [25,26]. Due to the echo state network structure, many physical systems have been used as reservoirs, which are commonly known as physical reservoir computers (PRCs). ...

Limit cycle oscillators have the potential to be resourced as reservoir computers due to their rich dynamics. Here, a Hopf oscillator is used as a physical reservoir computer by discarding the delay line and time-multiplexing procedure. A parametric study is used to uncover computational limits imposed by the dynamics of the oscillator using parity and chaotic time-series prediction benchmark tasks. Resonance, frequency ratios from the Farey sequence, and Arnold tongues were found to strongly affect the computation ability of the reservoir. These results provide insights into fabricating physical reservoir computers from limit cycle systems.

... An increasingly popular family of these data-based methods is machine learning (ML). Indeed, exciting recent work has been devoted to the use of ML techniques to study partial differential equations [8,9,10], such as the Schrödinger equation [11], which are at the core of practically all branches of science. ...

In this paper we design and use two Deep Learning models to generate the ground and excited wavefunctions of different Hamiltonians suitable for the study the vibrations of molecular systems. The generated neural networks are trained with Hamiltonians that have analytical solutions, and ask the network to generalize these solutions to more complex Hamiltonian functions. This approach allows to reproduce the excited vibrational wavefunctions of different molecular potentials. All methodologies used here are data-driven, therefore they do not assume any information about the underlying physical model of the system. This makes this approach versatile, and can be used in the study of multiple systems in quantum chemistry.

... Reservoir computing was recently considered theoretically for polariton systems, where relatively high success rates for standard benchmark tasks such as character recognition were predicted (95% success rate for recognition of the MNIST set of hand-written digits) [19]. Generally, systems described by discrete nonlinear Schrödinger equation are good candidates for reservoir computing [41]. ...

We show theoretically that neural networks based on disordered exciton-polariton systems allow the realization of Toffoli gates. Noise in input signals is self-corrected by the networks, such that the obtained Toffoli gates are in principle cascadable, where their universality would allow for arbitrary circuits without the need of additional error-correcting codes. We further find that the exciton-polariton reservoir computers can directly simulate composite circuits, such that they are a highly efficient platform allowing circuits to operate in a single step, minimizing the delay of signal transport between elements and error-correction overhead.

... Entropy 2020, 22, 210 2 of 12 efficient electronics, where heat flows can be used to control information [10,11]. However, in magnonic devices, especially arrays of nano disks and spin-transfer nano oscillators [12], the sample-to-sample variability and the noise from the environment are deleterious for the synchronization and transport performance. ...

Transport phenomena are ubiquitous in physics, and it is generally understood that the environmental disorder and noise deteriorates the transfer of excitations. There are, however, cases in which transport can be enhanced by fluctuations. In the present work, we show, by means of micromagnetics simulations, that transport efficiency in a chain of classical macrospins can be greatly increased by an optimal level of dephasing noise. We also demonstrate the same effect in a simplified model, the dissipative Discrete Nonlinear Schrödinger equation, subject to phase noise. Our results point towards the realization of a large class of magnonics and spintronics devices, where disorder and noise can be used to enhance spin-dependent transport efficiency.

... Spin-caloritronics [7][8][9] concerns precisely the coupled spin/heat transport in systems with non-uniform temperature. The wide interest in these types of setups is due to their potential for energy efficient electronics, where heat flows can be used to control information [10,11]. However, in magnonic devices, especially arrays of nano disks and spin-transfer nano oscillators [12], the sample-to-sample variability and the noise from the environment are deleterious for the synchronisation and transport performance. ...

Transport phenomena are ubiquitous in physics, and it is generally understood that the environmental disorder and noise deteriorates the transfer of excitations. There are however cases in which transport can be enhanced by fluctuations. In the present work we show, by means of micromagnetics simulations, that transport efficiency in a chain of classical macrospins can be greatly increased by an optimal level of dephasing noise. We demonstrate also the same effect in a simplified model, the dissipative Discrete Nonlinear Schr\"odinger equation subject to phase noise. Our results point towards the realisation of a large class of magnonics and spintronics devices, where disorder and noise can be used to enhance spin-dependent transport efficiency.

Predicting future evolution based on incomplete information of the past is still a challenge even though data-driven machine learning approaches have been successfully applied to forecast complex nonlinear dynamics. The widely adopted reservoir computing (RC) can hardly deal with this since it usually requires complete observations of the past. In this paper, a scheme of RC with (D+1)-dimension input and output (I/O) vectors is proposed to solve this problem, i.e., the incomplete input time series or dynamical trajectories of a system, in which certain portion of states are randomly removed. In this scheme, the I/O vectors coupled to the reservoir are changed to (D+1)-dimension, where the first D dimensions store the state vector as in the conventional RC, and the additional dimension is the corresponding time interval. We have successfully applied this approach to predict the future evolution of the logistic map and Lorenz, Rössler, and Kuramoto-Sivashinsky systems, where the inputs are the dynamical trajectories with missing data. The dropoff rate dependence of the valid prediction time (VPT) is analyzed. The results show that it can make forecasting with much longer VPT when the dropoff rate θ is lower. The reason for the failure at high θ is analyzed. The predictability of our RC is determined by the complexity of the dynamical systems involved. The more complex they are, the more difficult they are to predict. Perfect reconstructions of chaotic attractors are observed. This scheme is a pretty good generalization to RC and can treat input time series with regular and irregular time intervals. It is easy to use since it does not change the basic architecture of conventional RC. Furthermore, it can make multistep-ahead prediction just by changing the time interval in the output vector into a desired value, which is superior to conventional RC that can only do one-step-ahead forecasting based on complete regular input data.

Nonlinear differential-difference equations appear in optics, condensed matter physics, plasma physics and other fields. In this paper, we investigate a nonlinear differential-difference hierarchy relevant, in the case of θ=0, to the Ablowitz-Ladik equation, where θ=0,1. That hierarchy is obtained via a discrete spectral problem and the associated discrete spectral problem. When θ=1, Lax pair of the first nonlinear differential-difference system in that hierarchy is obtained. When θ=1, conservation laws and N-fold Darboux transformation of the first nonlinear differential-difference system in that hierarchy are derived with the aid of that Lax pair, where N is a positive integer. When θ=1, explicit exact solutions of that system are determined via that N-fold Darboux transformation. Discrete one soliton and interaction between the discrete one soliton and one breather-like wave are graphically depicted.

Physical reservoir computing utilizes a physical system as a computational resource. This nontraditional computing technique can be computationally powerful, without the need of costly training. Here, a Hopf oscillator is implemented as a reservoir computer by using a node-based architecture; however, this implementation does not use delayed feedback lines. This reservoir computer is still powerful, but it is considerably simpler and cheaper to implement as a physical Hopf oscillator. A non-periodic stochastic masking procedure is applied for this reservoir computer following the time multiplexing method. Due to the presence of noise, the Euler–Maruyama method is used to simulate the resulting stochastic differential equations that represent this reservoir computer. An analog electrical circuit is built to implement this Hopf oscillator reservoir computer experimentally. The information processing capability was tested numerically and experimentally by performing logical tasks, emulation tasks, and time series prediction tasks. This reservoir computer has several attractive features, including a simple design that is easy to implement, noise robustness, and a high computational ability for many different benchmark tasks. Since limit cycle oscillators model many physical systems, this architecture could be relatively easily applied in many contexts.

In this paper, we design and use two Deep Learning models to generate the ground and excited wavefunctions of different Hamiltonians suitable for the study of the vibrations of molecular systems. The generated neural networks are trained with Hamiltonians that have analytical solutions and ask the network to generalize these solutions to more complex Hamiltonian functions. Since the Hamiltonians solutions used to train the neural networks are computationally cheap, the training process is fast and efficient. This approach allows to reproduce the excited vibrational wavefunctions of different molecular potentials. All methodologies used here are data-driven, therefore they do not assume any information about the underlying physical model of the system. This makes this approach versatile and can be used in the study of multiple systems in quantum chemistry.

We propose a design for an all-optical logic exclusive-OR (XOR) gate in terms of intensity-modulation or phase-modulation approaches. In this study, the unsupervised optical neuron networks (ONNs) are based on reservoir computing (RC) and the echo state networks (ESNs). Thanks to the optical interfering effect in the directional coupler, it provides a nonlinear function for the reservoir computing. By scanning the phase through the phase shifter in our optical neuron networks, we find the optimized results and demonstrate the relationship between the input and output signals. The simulated results match the truth logic table in XOR gate. We also demonstrate the bit error ratio (BER) of the all-optical logic XOR gate. The BER for intensity-modulation approach is 1.55% at 90 degree, and the phase-modulation approach is 1.78% at 91 degree. Thus, the simulated results also indicate that the optical neuron network has potential to achieve an optical integrated circuit. If this idea could be fabricated as an optical logic device, the processing rate in the ONN is in light frequency. It will help us to process the binary data sequence more efficiently.

Typically, nonlinearity is considered to be problematic and sometimes can lead to dire consequences. However, the nonlinearity in a Duffing oscillator array can enhance its ability to be used as a reservoir computer. Machine learning and artificial neural networks, inspired from the biological computing framework, have shown their immense potential, especially in real-time temporal data processing. Here, the efficacy of a Duffing oscillator array is explored as a reservoir computer by using information theory. To do this, a reservoir computer model is studied numerically, which exploits the dynamics of the array. In this system, the complex dynamics stem from the Duffing term in each of the identical oscillators. The effects of various system parameters of the array on the information processing ability is discussed from the perspective of information theory. By varying these parameters, the information metric was found to be topologically mixed. Additionally, the importance of asynchrony in the oscillator array is also discussed in terms of the information metric. Since such nonlinear oscillators are used to model many different physical systems, this research provides insight into how physical nonlinear oscillatory systems can be used for dynamic computation, without significantly modifying or controlling the underlying dynamical system. To the authors' knowledge, this is the first use of Shannon's information rate for quantifying a reservoir computer of this kind, as well as the first comparison between synchronization phenomena and the computing ability of a reservoir.

Networks of weakly coupled oscillators are special cases of Hopfield networks and as such may be used in building physical systems capable of associative memory recall and pattern recognition. However, the existing architectures are not suitable for hardware implementation mainly due to the complexity of required couplings between the oscillators. In this paper, we propose an alternative way of using coupled oscillators in what we call “discriminant circuits” in analogy to the concept of “discriminant functions” in the field of artificial intelligence and machine learning. The main advantage of our system is in the simplicity of its architecture which relies only on local couplings between adjacent oscillators. Using this architecture, we design a network of coupled CMOS oscillators as the core of a physical non-Boolean pattern recognition engine. The simplicity of the proposed circuit makes it readily implementable on any standard CMOS technology.

We investigate numerically the magnetization dynamics of an array of nanodisks interacting through the magnetodipolar coupling. In the presence of a temperature gradient, the chain reaches a nonequilibrium steady state where energy and magnetization currents propagate. This effect can be described as the flow of energy and particle currents in an off-equilibrium discrete nonlinear Schrödinger (DNLS) equation. This model makes transparent the transport properties of the system and allows for a precise definition of temperature and chemical potential for a precessing spin. The present study proposes a setup for the spin-Seebeck effect, and shows that its qualitative features can be captured by a general oscillator-chain model.

A striking difference between brain-inspired neuromorphic processors and
current von Neumann processors architectures is the way in which memory and
processing is organized. As Information and Communication Technologies continue
to address the need for increased computational power through the increase of
cores within a digital processor, neuromorphic engineers and scientists can
complement this need by building processor architectures where memory is
distributed with the processing. In this paper we present a survey of
brain-inspired processor architectures that support models of cortical networks
and deep neural networks. These architectures range from serial clocked
implementations of multi-neuron systems to massively parallel asynchronous ones
and from purely digital systems to mixed analog/digital systems which implement
more biological-like models of neurons and synapses together with a suite of
adaptation and learning mechanisms analogous to the ones found in biological
nervous systems. We describe the advantages of the different approaches being
pursued and present the challenges that need to be addressed for building
artificial neural processing systems that can display the richness of behaviors
seen in biological systems.

Brain-inspired arrays of parallel processing oscillators represent an intriguing alternative to traditional computational methods for data analysis and recognition. This alternative is now becoming more concrete thanks to the advent of emerging oscillators fabrication technologies providing high density packaging and low power consumption. One challenging issue related to oscillator arrays is the large number of system parameters and the lack of efficient computational techniques for array simulation and performance verification. This paper provides a realistic phase-domain modeling and simulation methodology of oscillator arrays which is able to account for the relevant device nonidealities. The model is employed to investigate the associative memory performance of arrays composed of resonant LC oscillators.

The role of noise in the transport properties of quantum excitations is a
topic of great importance in many fields, from organic semiconductors for
technological applications to light-harvesting complexes in photosynthesis. In
this paper we study a semi-classical model where a tight-binding Hamiltonian is
fully coupled to an underlying spatially extended nonlinear chain of atoms. We
show that the transport properties of a quantum excitation are subtly modulated
by (i) the specific type (local vs non-local) of exciton-phonon coupling and by
(ii) nonlinear effects of the underlying lattice. We report a non-monotonic
dependence of the exciton diffusion coefficient on temperature, in agreement
with earlier predictions, as a direct consequence of the lattice-induced
fluctuations in the hopping rates due to long-wavelength vibrational modes. A
standard measure of transport efficiency confirms that both nonlinearity in the
underlying lattice and off-diagonal exciton-phonon coupling promote transport
efficiency at high temperatures, preventing the Zeno-like quench observed in
other models lacking an explicit noise-providing dynamical system.

By means of a simple theoretical model and numerical simulations, we demonstrate the presence of persistent energy currents in a lattice of classical nonlinear oscillators with uniform temperature and chemical potential. In analogy with the well-known Josephson effect, the currents are proportional to the sine of the phase differences between the oscillators. Our results elucidate general aspects of nonequilibrium thermodynamics and point towards a way to practically control transport phenomena in a large class of systems. We apply the model to describe the phase-controlled spin-wave current in a bilayer nanopillar.

Suitable Langevin thermostats are introduced which are able to control both
the temperature and the chemical potential of a one-dimensional lattice of
nonlinear Schr\"odinger oscillators. The resulting non-equilibrium stationary
states are then investigated in two limit cases (low temperatures and large
particle densities), where the dynamics can be mapped onto that of a
coupled-rotor chain with an external torque. As a result, an effective kinetic
definition of temperature can be introduced and compared with the general
microcanonical (global) definition.

We study nonequilibrium steady states of the one-dimensional discrete nonlinear Schrödinger equation. This system can be regarded as a minimal model for the stationary transport of bosonic particles such as photons in layered media or cold atoms in deep optical traps. Due to the presence of two conserved quantities, namely, energy and norm (or number of particles), the model displays coupled transport in the sense of linear irreversible thermodynamics. Monte Carlo thermostats are implemented to impose a given temperature and chemical potential at the chain ends. As a result, we find that the Onsager coefficients are finite in the thermodynamic limit, i.e., transport is normal. Depending on the position in the parameter space, the “Seebeck coefficient” may be either positive or negative. For large differences between the thermostat parameters, density and temperature profiles may display an unusual nonmonotonic shape. This is due to the strong dependence of the Onsager coefficients on the state variables.

We report on a spectroscopic study of the spin-wave eigenmodes inside an individual normally magnetized two-layer circular nanopillar (permalloytextbarcoppertextbarpermalloy) by means of a magnetic resonance force microscope. We demonstrate that the observed spin-wave spectrum critically depends on the method of excitation. While the spatially uniform radio-frequency (rf) magnetic field excites only the axially symmetric modes having azimuthal index l=0, the rf current flowing through the nanopillar, creating a circular rf Oersted field, excites only the modes having azimuthal index l=+1. Breaking the axial symmetry of the nanopillar, either by tilting the bias magnetic field or by making the pillar shape elliptical, mixes different l-index symmetries, which can be excited simultaneously by the rf current. Experimental spectra are compared to theoretical prediction using both analytical and numerical calculations. An analysis of the influence of the static and dynamic dipolar coupling between the nanopillar magnetic layers on the mode spectrum is performed.

Novel methods for information processing are highly desired in our information-driven society. Inspired by the brain's ability to process information, the recently introduced paradigm known as 'reservoir computing' shows that complex networks can efficiently perform computation. Here we introduce a novel architecture that reduces the usually required large number of elements to a single nonlinear node with delayed feedback. Through an electronic implementation, we experimentally and numerically demonstrate excellent performance in a speech recognition benchmark. Complementary numerical studies also show excellent performance for a time series prediction benchmark. These results prove that delay-dynamical systems, even in their simplest manifestation, can perform efficient information processing. This finding paves the way to feasible and resource-efficient technological implementations of reservoir computing.

A nanoscale magnetic device that mimics the behaviour of neurons has been used to recognize audio signals. Such a device could be adapted to tackle tasks with greater efficiency than conventional computers. See Letter p.428

In the brain, hundreds of billions of neurons develop rhythmic activities and interact to process information. Taking inspiration from this behavior to realize high density, low power neuromorphic computing will require huge numbers of nanoscale non-linear oscillators. However, there is no proof of concept today of neuromorphic computing with nano-oscillators. Indeed, nanoscale devices tend to be noisy and to lack the stability required to process data in a reliable way. Here, we show experimentally that a nanoscale spintronic oscillator can achieve spoken digit recognition with accuracies similar to state of the art neural networks. We pinpoint the regime of magnetization dynamics leading to highest performance in the bias conditions space. These results, combined with the exceptional ability of these spintronic oscillators to interact together, their long lifetime, and low energy consumption, open the path to fast, parallel, on-chip computation based on networks of oscillators.

We describe a mechanism to control the energy and magnetization currents in an artificial spin chain, consisting of an array of permalloy nanodisks coupled through a magnetodipolar interaction. The chain is kept out of equilibrium by two thermal baths with different temperatures connected to its ends, which control the current propagation. Transport is enhanced by applying a uniform radio-frequency pump field resonating with some of the spin-wave modes of the chain. Moreover, the two currents can be controlled independently by tuning the static field applied on the chain. Thus we describe two effective means for the independent control of coupled currents and the enhancement of thermal and spin-wave conductivity in a realistic magnonics device, suggesting that similar effects could be observed in a large class of nonlinear oscillating systems.

The operation of an array of coupled oscillators underlying the associative memory function is demonstrated for various interconnection topologies (cross-connect and star-coupled). Three types of nonlinear oscillators (Andronov–Hopf, phase-locked loop, and spin torque) and their synchronization behavior are compared. Frequency-shift keying scheme of encoding input and memorized data is introduced. The speed of synchronization of oscillators and the evolution of the degree of match are studied as a function of device parameters.

In this paper, we show that the dynamics of injection-locked Spin Hall Effect Spin-Torque Oscillator (SHE-STO) cluster can be exploited as a robust primitive computational operator for non-Boolean associative computing. A cluster of SHE-STOs can be locked to a common frequency and phase with an injected ac current signal. DC input to each STO from external stimuli can conditionally unlock some of them. Based on the input dc signal, the degree of synchronization of SHE-STO cluster is detected by CMOS interface circuitry. The degree of synchronization can be used for associative computing/matching. We present a numerical simulation model of SHE-STO devices based on Landau-Lifshitz-Gilbert equation with spin-transfer torque term and Spin Hall Effect. The model is then used to analyze the frequency and phase locking properties of injection-locked SHE-STO cluster. Results show that associative computing based on the injection locked SHE-STO cluster can be energy efficient and relatively immune to device parameter variations and thermal noise.

We show the link between U1 lattice gauge theories and the off-equilibrium
thermodynamics of a large class of nonlinear oscillators networks. The coupling
between the oscillators plays the role of a gauge field, or connection, on the
network. The thermodynamical forces that drive energy flows are expressed in
terms of the curvature of the connection, analogous to a geometric phase. The
model, which holds both close and far from equilibrium, predicts the existence
of persistent energy and particle currents circulating in close loops through
the network. The predictions are confirmed by numerical simulations. Possible
extension of the theory and experimental applications to nanoscale devices are
briefly discussed.

Our study of thalamo-cortical systems suggests a new architecture for a neurocomputer that consists of oscillators having different frequencies and that are connected weakly via a common medium forced by an external input. Even though such oscillators are all interconnected homogeneously, the external input imposes a dynamic connectivity. We use Kuramoto's model to illustrate the idea and to prove that such a neurocomputer has oscillatory associative properties. Then we discuss a general case. The advantage of such a neurocomputer is that it can be built using voltage controlled oscillators, optical oscillators, lasers, microelectromechanical systems, Josephson junctions, macromolecules, or oscillators of other kinds. (Provisional patent 60/108,353)

Echo State Networks and Liquid State Machines introduced a new paradigm in artificial recurrent neural network (RNN) training, where an RNN (the reservoir) is generated randomly and only a readout is trained. The paradigm, becoming known as reservoir computing, greatly facilitated the practical application of RNNs and outperformed classical fully trained RNNs in many tasks. It has lately become a vivid research field with numerous extensions of the basic idea, including reservoir adaptation, thus broadening the initial paradigm to using different methods for training the reservoir and the readout. This review systematically surveys both current ways of generating/adapting the reservoirs and training different types of readouts. It offers a natural conceptual classification of the techniques, which transcends boundaries of the current “brand-names” of reservoir methods, and thus aims to help in unifying the field and providing the reader with a detailed “map” of it.