Generalization performance of reservoir computing implemented by asynchronously tuned elementary cellular automaton on parity task

Due to the advantages of low‐voltage operation and memory characteristics, electrolyte‐gated transistors (EGTs) have been proposed as building blocks for neuromorphic systems. Recently, reservoir computing (RC) is attracting interests because RC utilize nonlinear system to enrich the input source into a higher dimension, whereas traditional neural network prefers linear system. RC also has the advantages of low energy consumption and fast response speed because it only trains at the readout layer. EGT is a promising candidate for RC due to tunable output current depending on input pulse voltage using its nonlinear system. Herein, we proposed poly (vinylidene fluoride‐hexafluoropropylene) (PVDF‐HFP) interlayered EGT for RC. Semicrystalline and porous morphology of PVDF‐HFP interlayer induced ion‐trapping at the interface between amorphous and crystalline regions resulted in long retention. Also, the thickness variation of the PVDF‐HFP interlayer modulates the filling capacity of trap sites, balancing ion‐transport for near‐linear weight update. We integrated near‐linear and asymmetric long‐term potentiation and depression curves into RC to elucidate the intensity difference between five frames of spatiotemporal events in dynamic vision sensor (DVS) gestures. Classification of 11 distinct gestures was successfully demonstrated using the RC framework. This work highlights compelling synergy between material‐level device physics and algorithmic architectures of neuromorphic computing.

Reservoir computing is an effective model for learning and predicting nonlinear and chaotic dynamical systems; however, there remains a challenge in achieving a more dependable evolution for such systems. Based on the foundation of Koopman operator theory, considering the effectiveness of the sparse identification of nonlinear dynamics algorithm to construct candidate nonlinear libraries in the application of nonlinear data, an alternative reservoir computing method is proposed, which creates the linear Hilbert space of the nonlinear system by including nonlinear terms in the optimization process of reservoir computing, allowing for the application of linear optimization. We introduce an implementation that incorporates a polynomial transformation of arbitrary order when fitting the readout matrix. Constructing polynomial libraries with reservoir-state vectors as elements enhances the nonlinear representation of reservoir states and more easily captures the complexity of nonlinear systems. The Lorenz-63 system, the Lorenz-96 system, and the Kuramoto-Sivashinsky equation are used to validate the effectiveness of constructing polynomial libraries for reservoir states in the field of state-evolution prediction of nonlinear and chaotic dynamical systems. This study not only promotes the theoretical study of reservoir computing, but also provides a theoretical and practical method for the prediction of nonlinear and chaotic dynamical system evolution.

For many years, Evolutionary Algorithms (EAs) have been applied to improve Neural Networks (NNs) architectures. They have been used for solving different problems, such as training the networks (adjusting the weights), designing network topology, optimizing global parameters, and selecting features. Here, we provide a systematic brief survey about applications of the EAs on the specific domain of the recurrent NNs named Reservoir Computing (RC). At the beginning of the 2000s, the RC paradigm appeared as a good option for employing recurrent NNs without dealing with the inconveniences of the training algorithms. RC models use a nonlinear dynamic system, with fixed recurrent neural network named the reservoir, and learning process is restricted to adjusting a linear parametric function. However, an RC model has several hyper-parameters, therefore EAs are helpful tools to figure out optimal RC architectures. We provide an overview of the results on the area, discuss novel advances, and we present our vision regarding the new trends and still open questions.

Reservoir Computing is a novel computing paradigm that uses a nonlinear recurrent dynamical system to carry out information processing. Recent electronic and optoelectronic Reservoir Computers based on an architecture with a single nonlinear node and a delay loop have shown performance on standardized tasks comparable to state-of-the-art digital implementations. Here we report an all-optical implementation of a Reservoir Computer, made of off-the-shelf components for optical telecommunications. It uses the saturation of a semiconductor optical amplifier as nonlinearity. The present work shows that, within the Reservoir Computing paradigm, all-optical computing with state-of-the-art performance is possible.

There is a wave of interest in using physics-informed neural networks for solving differential equations. Most of the existing methods are based on feed-forward networks, while recurrent neural networks solvers have not been extensively explored. We introduce a reservoir computing (RC) architecture, an echo-state recurrent neural network capable of discovering approximate solutions that satisfy ordinary differential equations (ODEs). We suggest an approach to calculate time derivatives of recurrent neural network outputs without using back-propagation. The internal weights of an RC are fixed, while only a linear output layer is trained, yielding efficient training. However, RC performance strongly depends on finding the optimal hyper-parameters, which is a computationally expensive process. We use Bayesian optimization to discover optimal sets in a high-dimensional hyper-parameter space efficiently and numerically show that one set is robust and can be transferred to solve an ODE for different initial conditions and time ranges. A closed-form formula for the optimal output weights is derived to solve first-order linear equations in a one-shot backpropagation-free learning process. We extend the RC approach by solving nonlinear systems of ODEs using a hybrid optimization method consisting of gradient descent and Bayesian optimization. Evaluation of linear and nonlinear systems of equations demonstrates the efficiency of the RC ODE solver.

In this paper, we investigate online learning-based MIMO-OFDM symbol detection strategies focusing on a special recurrent neural network (RNN) - reservoir computing (RC). We first introduce the Time-Frequency RC to take advantage of the structural information inherent in OFDM signals. Using the time domain RC and the time-frequency RC as building blocks, we provide two extensions of the shallow RC to RCNet: 1) Stacking multiple time domain RCs; 2) Stacking multiple time-frequency RCs into a deep structure. The combination of RNN dynamics, the time-frequency structure of MIMO-OFDM signals, and the deep network enables RCNet to handle the interference and nonlinear distortion of MIMO-OFDM signals to outperform existing methods. Unlike most existing NN-based detection strategies, RCNet is also shown to provide a good generalization performance even with a limited online training set (i.e, similar amount of reference signals/training as standard model-based approaches). Numerical experiments demonstrate that the introduced RCNet can offer a faster learning convergence and as much as 20% gain in bit error rate over a shallow RC structure by compensating for the nonlinear distortion of the MIMO-OFDM signal, such as due to power amplifier compression in the transmitter or due to finite quantization resolution in the receiver.

Reservoir computer (RC) is an attractive neural computing framework that can well predict the dynamics of nonlinear systems, which is promissing to address the nonlinear nature of climatic time series. While in dynamical systems theory, estimating recurrent analog (RA) trajectory in state space is as a reliable method to fit and predict the nonlinear time series. Here we would present an investigation on comparing performances of the RC and RA in predicting climatic time series. We find that the RC outperforms the RA in case of the complete observations for a dynamical system, and a combination between the RC and RA can significantly improve their ability to predict the system in case of partial observation. Additionally, we extend their comparision to the framework of inferring causality from the time series, i.e., a RC-based causality detection framework proposed by us, and the convergent cross mapping causality method based on the RA. The results demonstrate that, in terms of accuracy, computation efficiency and robustness to the noise, the causality method based on the RC outperforms that on the RA. These results could provide indications for future developments and applications of the RC in addressing climatic time series. 

Reservoir computing is a machine learning approach that enables us to use recurrent neural networks without involving the complexity of training algorithms and make hardware implementation possible. We present a novel photonic architecture of a reservoir computer that employs a nonlinear node and a resonator to implement a virtual recurrent neural network. This resonator behaves as an echo generator component that substitutes the delay line in delay-based reservoir computers available in the literature. The virtual neural network formed in our implementation is fundamentally different from the delay-based reservoir computers. Different virtual architectures based on the FSR and the Finesse of the resonator are investigated to provide higher performance depending on the task. We test the performance of our proposed reservoir by 3 benchmark tasks, signal classification, nonlinear channel equalization, and memory capacity. Our system enhances the memory capacity of the reservoir compared to the delay-based systems and shows reliable results in signal classification and nonlinear channel equalization.

Echo state networks (ESN), a type of reservoir computing (RC) architecture, are efficient and accurate artificial neural systems for time series processing and learning. An ESN consists of a core of recurrent neural networks, called a reservoir, with a small number of tunable parameters to generate a high-dimensional representation of an input, and a readout layer which is easily trained using regression to produce a desired output from the reservoir states. Certain computational tasks involve real-time calculation of high-order time correlations, which requires nonlinear transformation either in the reservoir or the readout layer. Traditional ESN employs a reservoir with sigmoid or tanh function neurons. In contrast, some types of biological neurons obey response curves that can be described as a product unit rather than a sum and threshold. Inspired by this class of neurons, we introduce a RC architecture with a reservoir of product nodes for time series computation. We find that the product RC shows many properties of standard ESN such as short-term memory and nonlinear capacity. On standard benchmarks for chaotic prediction tasks, the product RC maintains the performance of a standard nonlinear ESN while being more amenable to mathematical analysis. Our study provides evidence that such networks are powerful in highly nonlinear tasks owing to high-order statistics generated by the recurrent product node reservoir.

Reservoir computing (RC) is considered as a suitable alternative for descending gradient methods in recursive neural networks (RNNs) training. The echo state network (ESN) is a platform for RC and nonlinear system simulation in the cloud environment with many external users. In the past researches, the highest eigenvalue of reservoir connection weight (spectral radius) was used to predict reservoir dynamics. Some researchers have illustrated; the characteristics of scale-free and small-world can improve the approximation capability in echo state networks; however, recent studies have shown importance of the infrastructures such as clusters and the stability criteria of these reservoirs as altered. In this research, we suggest a high clustered ESN called HCESN that its internal neurons are interconnected in form of clusters. Each of the clusters contains one backbone and a number of local nodes. We implemented a classical clustering algorithm, called K-means, and three optimization algorithms including genetic algorithm (GA), differential evolution (DE), and particle swarm optimization (PSO) to improve the clustering efficiency of the new reservoir and compared them with each other. For investigating the spectral radius and predictive power of the resulting reservoirs, we also applied them to the laser time series and the Mackey-Glass dynamical system. It is demonstrated that new clustered reservoirs have some specifications of biologic neural systems and complex networks like average short path length, high clustering coefficient, and power-law distribution. The empirical results illustrated that the ESN based on PSO could strikingly enhance echo state property (ESP) and obtains less chaotic time series prediction error compared with other works and the original version of ESN. Therefore, it can approximate nonlinear dynamical systems and predict the chaotic time series.

Reservoir computing (RC) is a promising machine learning paradigm that processes input data using a fixed random network. However, implementing both reservoir and readout layers typically requires multiple devices and additional fabrication steps. To overcome this, we introduce a fully integrated RC system based on a vertically stacked Ta/Ta2O5/HfO2/W and TiN vertical-resistive random-access memory (VRRAM) structure, which can select short-term and long-term memory in VRRAM structure with different bottom electrodes. The volatile VRRAM serves as a physical reservoir, utilizing its fading memory and nonlinearity to capture temporal dependencies, while the nonvolatile VRRAM functions as a readout network with multi-level storage capability and high linearity. Neuromorphic simulations show that using conductance variations as synaptic weights enables pattern recognition accuracy above 93.14%, successfully replicating biological synaptic behaviors. Finally, the proposed Cyclic RC structure effectively processes temporal patterns, achieving strong performance with an NRMSE of 0.2123 for waveform classification and 0.2377 for Hénon map prediction. These findings underscore the potential of hardware-efficient, short-term memory-based architectures for forecasting nonlinear dynamical systems and advancing neuromorphic computing applications.

Replicating the chaotic characteristics inherent in nonlinear dynamical systems via machine learning (ML) is a key challenge in this rapidly advancing interdisciplinary field. In this work, we explore the potential of variational quantum circuits (VQC) for learning the stochastic properties of classical nonlinear dynamical systems. Specifically, we focus on the one- and two-dimensional Logistic maps, which, while simple, remain under-explored in the context of learning dynamical characteristics. Our findings reveal that, even for such simple dynamical systems, accurately replicating long-term characteristics is hindered by a pronounced sensitivity to overfitting. While increasing the parameter complexity of the ML model typically enhances short-term prediction accuracy, it also leads to a degradation in the model’s ability to replicate long-term characteristics, primarily due to the detrimental effects of overfitting on generalization power. By comparing the VQC with two widely recognized classical ML techniques, which are long short-term memory (LSTM) networks for time-series processing and reservoir computing, we demonstrate that VQC outperforms these methods in terms of replicating long-term characteristics. Our results suggest that for the ML of dynamics, it is demanded to develop more compact and efficient models (such as VQC) rather than more complicated and large-scale ones.

Reservoir computing is a temporal information processing system that exploits artificial or physical dissipative dynamics to learn a dynamical system and generate the target time-series. This paper proposes the use of real superconducting quantum computing devices as the reservoir, where the dissipative property is served by the natural noise added to the quantum bits. The performance of this natural quantum reservoir is demonstrated in a benchmark time-series regression problem and a practical problem classifying different objects based on temporal sensor data. In both cases the proposed reservoir computer shows a higher performance than a linear regression or classification model. The results indicate that a noisy quantum device potentially functions as a reservoir computer, and notably, the quantum noise, which is undesirable in the conventional quantum computation, can be used as a rich computation resource.

The design of accurate trajectory prediction algorithms is crucial to implement adequate countermeasures against drones with anomalous performances. Wrong predictions may cause high-false-positives that compromise safety in national infrastructures. In this article, a physics informed reservoir computing (PIRC) scheme for drone trajectory prediction is proposed. The approach is comprised of two main complementary learning algorithms that enhance the prediction and generalization capabilities: 1) a standard reservoir computing scheme for high-dimensional encoding exploitation and 2) a nonlinear control scheme that gives a physical feedback to the reservoir weights to ensure the prediction error is minimized. The nonlinear control scheme is modeled by the prediction error dynamics and a feedback linearization controller. Two different PIRC schemes are proposed which preserve the reservoir properties and enhance the prediction robustness. Lyapunov stability theory is used to verify the boundedness and convergence of the proposed algorithms. Simulation studies and comparisons are given to verify the proposed approach.

The Reservoir Computing (RC) paradigm is a supervised machine learning approach that makes use of the inherent processing capacity of dynamical systems. Using the system's transient response to an external input, delayed chaotic systems offer rich dynamics for information processing, and have therefore been recognised as ideal systems for reservoir computing. A distinctive feature of delay-line reservoirs is their single-input/single-output structure, which makes them efficient for physical implementation. However, this also presents a significant limitation to multi-input tasks, as the sequence of information in the time-multiplexed input stream is not obvious. Here, we propose enhancing the input masking process used in delay-feedback RCs to mix multiple inputs in the time domain. We investigate two approaches: ‘interleaved’ and ‘sequential’, of injecting multi-input signals into a delay-line reservoir without modifying its topology. Further, we propose a novel task for RC, which inherently requires multiple inputs, to evaluate our approach: the control of a forced Van der Pol oscillator system. We use the trained reservoir as a controller to regulate the nonlinear dynamics of the Van der Pol system by constraining its trajectory to a circle. We find that, with careful choice of model parameters and offset masking scheme, the ‘sequential’ method outperforms the ‘interleaved’ method on this task.