The architecture of dynamic reservoir in the echo state network

Exploration of a brain-inspired photon reservoir computing network based on quantum-dot spin-VCSELs

Based on small-world network theory, we have developed a brain-inspired photonic reservoir computing (RC) network system utilizing quantum dot spin-vertical-cavity surface-emitting lasers (QD spin-VCSELs) and formulated a comprehensive theoretical model for it. This innovative network system comprises input layers, a reservoir network layer, and output layers. The reservoir network layer features four distinct reservoir modules that are asymmetrically coupled. Each module is represented by a QD spin-VCSEL, characterized by optical feedback and optical injection. Within these modules, four chaotic polarization components, emitted from both the ground and excited states of the QD Spin-VCSEL, form four distinct reservoirs through a process of asymmetric coupling. Moreover, these components, when emitted by the ground and excited states of a driving QD spin-VCSEL within a specific parameter space, act as targets for prediction. Delving further, we investigated the correlation between various system parameters, such as the sampling period, the interval between virtual nodes, the strengths of optical injection and feedback, frequency detuning, and the predictive accuracy of each module's four photonic RCs concerning the four designated predictive targets. We also examined how these parameters influence the memory storage capabilities of the four photonics RCs within each module. Our findings indicate that when a module receives coupling injections from more than two other modules, and an RC within this module is also subject to coupling injections from over two other RCs, the system displays reduced predictive errors and enhanced memory storage capacities when the system parameters are fixed. Namely, the superior performance of the reservoir module in predictive accuracy and memory capacities follows from its complex interaction with multiple light injections and coupling injections, with its three various PCs benefiting from three, two, and one coupling injections respectively. Conversely, variations in optical injection and feedback strength, as well as frequency detuning, introduce only marginal fluctuations in the predictive errors across the four photonics RCs within each module and exert minimal impact on the memory storage capacity of individual photonics RCs within the modules. Our investigated results contribute to the development of photonic reservoir computing towards fast response biological neural networks.

A double-cycle echo state network topology for time series prediction

Echo state network (ESN) has gained wide acceptance in the field of time series prediction, relying on sufficiently complex reservoir connections to remember the historical features of the data and using these features to obtain the outputs by a simple linear readout. However, the randomness of its input and reservoir connections pose negative impacts on the prediction performance and performance stability of the models, the complexity of reservoir connections brings high time consumption during network computing, and the presence of randomness and complexity makes the hardware implementation of the ESN difficult. In response, we propose a double-cycle ESN (DCESN) based on the Li-ESN model, which has fixed weights to improve prediction performance and performance stability and simpler reservoir connections compared to the classical ESN to reduce the time consumption. The existence of both greatly reduces the difficulty of hardware implementation of the ESN and provides many conveniences for the future application of the ESN. Experimental results on many widely used time series datasets show that the DCESN has comparable or even better prediction performance than the ESN and good robustness against noise and parameter fluctuations.

Path integral approach to universal dynamics of reservoir computers

In this work, we give a characterization of the reservoir computer (RC) by the network structure, especially the probability distribution of random coupling constants. First, based on the path integral method, we clarify the universal behavior of the random network dynamics in the thermodynamic limit, which depends only on the asymptotic behavior of the second cumulant generating functions of the network coupling constants. This result enables us to classify the random networks into several universality classes, according to the distribution function of coupling constants chosen for the networks. Interestingly, it is revealed that such a classification has a close relationship with the distribution of eigenvalues of the random coupling matrix. We also comment on the relation between our theory and some practical choices of random connectivity in the RC. Subsequently, we investigate the relationship between the RC's computational power and the network parameters for several universality classes. We perform several numerical simulations to evaluate the phase diagrams of the steady reservoir states, common-signal-induced synchronization, and the computational power in the chaotic time series inference tasks. As a result, we clarify the close relationship between these quantities, especially a remarkable computational performance near the phase transitions, which is realized even near a nonchaotic transition boundary. These results may provide us with a new perspective on the designing principle for the RC.

Echo State Network-Based Content Prediction for Mobile Edge Caching Networks

With the rapid development of internet communication and the wide application of intelligent terminal, moving the cache to the edge of the network is an effective solution to shorten the delay of users accessing content. However, the existing cache work lacks the comprehensive consideration of users and content, resulting in low cache hit ratio and low accuracy of the whole system. In this paper, the authors propose a collaborative caching model that considers both user request content and content prediction, so as to improve the caching performance of the whole network. Firstly, the model uses the clustering algorithm based on Akike information criterion to cluster users. Then, combined with the clustering results, echo state network is used as the machine learning framework to predict the content. Finally, the cache contents are selected according to the prediction results and cached in the cache unit of the small base station. Simulation results show that compared with the existing cache algorithms, the proposed method has obvious improvement in cache hit ratio, accuracy, and recall rate.

SpaRCe: Improved Learning of Reservoir Computing Systems Through Sparse Representations

"Sparse" neural networks, in which relatively few neurons or connections are active, are common in both machine learning and neuroscience. While, in machine learning, "sparsity" is related to a penalty term that leads to some connecting weights becoming small or zero, in biological brains, sparsity is often created when high spiking thresholds prevent neuronal activity. Here, we introduce sparsity into a reservoir computing network via neuron-specific learnable thresholds of activity, allowing neurons with low thresholds to contribute to decision-making but suppressing information from neurons with high thresholds. This approach, which we term "SpaRCe," optimizes the sparsity level of the reservoir without affecting the reservoir dynamics. The read-out weights and the thresholds are learned by an online gradient rule that minimizes an error function on the outputs of the network. Threshold learning occurs by the balance of two opposing forces: reducing interneuronal correlations in the reservoir by deactivating redundant neurons, while increasing the activity of neurons participating in correct decisions. We test SpaRCe on classification problems and find that threshold learning improves performance compared to standard reservoir computing. SpaRCe alleviates the problem of catastrophic forgetting, a problem most evident in standard echo state networks (ESNs) and recurrent neural networks in general, due to increasing the number of task-specialized neurons that are included in the network decisions.

Guiding principle of reservoir computing based on "small-world" network

Reservoir computing is a computational framework of recurrent neural networks and is gaining attentions because of its drastically simplified training process. For a given task to solve, however, the methodology has not yet been established how to construct an optimal reservoir. While, "small-world" network has been known to represent networks in real-world such as biological systems and social community. This network is categorized amongst those that are completely regular and totally disordered, and it is characterized by highly-clustered nodes with a short path length. This study aims at providing a guiding principle of systematic synthesis of desired reservoirs by taking advantage of controllable parameters of the small-world network. We will validate the methodology using two different types of benchmark tests-classification task and prediction task.

Model-free prediction of multistability using echo state network

In the field of complex dynamics, multistable attractors have been gaining significant attention due to their unpredictability in occurrence and extreme sensitivity to initial conditions. Co-existing attractors are abundant in diverse systems ranging from climate to finance and ecological to social systems. In this article, we investigate a data-driven approach to infer different dynamics of a multistable system using an echo state network. We start with a parameter-aware reservoir and predict diverse dynamics for different parameter values. Interestingly, a machine is able to reproduce the dynamics almost perfectly even at distant parameters, which lie considerably far from the parameter values related to the training dynamics. In continuation, we can predict whole bifurcation diagram significant accuracy as well. We extend this study for exploring various dynamics of multistable attractors at an unknown parameter value. While we train the machine with the dynamics of only one attractor at parameter p, it can capture the dynamics of a co-existing attractor at a new parameter value p + Δ p. Continuing the simulation for a multiple set of initial conditions, we can identify the basins for different attractors. We generalize the results by applying the scheme on two distinct multistable systems.

Global optimization of hyper-parameters in reservoir computing

<abstract><p>Reservoir computing has emerged as a powerful and efficient machine learning tool especially in the reconstruction of many complex systems even for chaotic systems only based on the observational data. Though fruitful advances have been extensively studied, how to capture the art of hyper-parameter settings to construct efficient RC is still a long-standing and urgent problem. In contrast to the local manner of many works which aim to optimize one hyper-parameter while keeping others constant, in this work, we propose a global optimization framework using simulated annealing technique to find the optimal architecture of the randomly generated networks for a successful RC. Based on the optimized results, we further study several important properties of some hyper-parameters. Particularly, we find that the globally optimized reservoir network has a largest singular value significantly larger than one, which is contrary to the sufficient condition reported in the literature to guarantee the echo state property. We further reveal the mechanism of this phenomenon with a simplified model and the theory of nonlinear dynamical systems.</p></abstract>

Tailoring Echo State Networks for Optimal Learning

As one of the most important paradigms of recurrent neural networks, the echo state network (ESN) has been applied to a wide range of fields, from robotics to medicine, finance, and language processing. A key feature of the ESN paradigm is its reservoir-a directed and weighted network of neurons that projects the input time series into a high-dimensional space where linear regression or classification can be applied. By analyzing the dynamics of the reservoir we show that the ensemble of eigenvalues of the network contributes to the ESN memory capacity. Moreover, we find that adding short loops to the reservoir network can tailor ESN for specific tasks and optimize learning. We validate our findings by applying ESN to forecast both synthetic and real benchmark time series. Our results provide a simple way to design task-specific ESN and offer deep insights for other recurrent neural networks.

In-Ear EEG Based Attention State Classification Using Echo State Network

It is important to maintain attention when carrying out significant daily-life tasks that require high levels of safety and efficiency. Since degradation of attention can sometimes have dire consequences, various brain activity measurement devices such as electroencephalography (EEG) systems have been used to monitor attention states in individuals. However, conventional EEG instruments have limited utility in daily life because they are uncomfortable to wear. Thus, this study was designed to investigate the possibility of discriminating between the attentive and resting states using in-ear EEG signals for potential application via portable, convenient earphone-shaped EEG instruments. We recorded both on-scalp and in-ear EEG signals from 6 subjects in a state of attentiveness during the performance of a visual vigilance task. We have designed and developed in-ear EEG electrodes customized by modelling both the left and right ear canals of the subjects. We use an echo state network (ESN), a powerful type of machine learning algorithm, to discriminate attention states on the basis of in-ear EEGs. We have found that the maximum average accuracy of the ESN method in discriminating between attentive and resting states is approximately 81.16% with optimal network parameters. This study suggests that portable in-ear EEG devices and an ESN can be used to monitor attention states during significant tasks to enhance safety and efficiency.

Feature Extraction of Surface Electromyography Based on Improved Small-World Leaky Echo State Network

Surface electromyography (sEMG) is an electrophysiological reflection of skeletal muscle contractile activity that can directly reflect neuromuscular activity. It has been a matter of research to investigate feature extraction methods of sEMG signals. In this letter, we propose a feature extraction method of sEMG signals based on the improved small-world leaky echo state network (ISWLESN). The reservoir of leaky echo state network (LESN) is connected by a random network. First, we improved the reservoir of the echo state network (ESN) by these networks and used edge-added probability to improve these networks. That idea enhances the adaptability of the reservoir, the generalization ability, and the stability of ESN. Then we obtained the output weight of the network through training and used it as features. We recorded the sEMG signals during different activities: falling, walking, sitting, squatting, going upstairs, and going downstairs. Afterward, we extracted corresponding features by ISWLESN and used principal component analysis for dimension reduction. At the end, scatter plot, the class separability index, and the Davies-Bouldin index were used to assess the performance of features. The results showed that the ISWLESN clustering performance was better than those of LESN and ESN. By support vector machine, it was also revealed that the performance of ISWLESN for classifying the activities was better than those of ESN and LESN.

Good and bad predictions: Assessing and improving the replication of chaotic attractors by means of reservoir computing

The prediction of complex nonlinear dynamical systems with the help of machine learning techniques has become increasingly popular. In particular, reservoir computing turned out to be a very promising approach especially for the reproduction of the long-term properties of a nonlinear system. Yet, a thorough statistical analysis of the forecast results is missing. Using the Lorenz and Rössler system, we statistically analyze the quality of prediction for different parametrizations-both the exact short-term prediction as well as the reproduction of the long-term properties (the "climate") of the system as estimated by the correlation dimension and largest Lyapunov exponent. We find that both short- and long-term predictions vary significantly among the realizations. Thus, special care must be taken in selecting the good predictions as realizations, which deliver better short-term prediction also tend to better resemble the long-term climate of the system. Instead of only using purely random Erdös-Renyi networks, we also investigate the benefit of alternative network topologies such as small world or scale-free networks and show which effect they have on the prediction quality. Our results suggest that the overall performance with respect to the reproduction of the climate of both the Lorenz and Rössler system is worst for scale-free networks. For the Lorenz system, there seems to be a slight benefit of using small world networks, while for the Rössler system, small world and Erdös-Renyi networks performed equivalently well. In general, the observation is that reservoir computing works for all network topologies investigated here.

Decoding electroencephalographic signals for direction in brain-computer interface using echo state network and Gaussian readouts

BACKGROUND

Noninvasive brain-computer interfaces (BCI) for movement control via an electroencephalogram (EEG) have been extensively investigated. However, most previous studies decoded user intention for movement directions based on sensorimotor rhythms during motor imagery. BCI systems based on mapping imagery movement of body parts (e.g., left or right hands) to movement directions (left or right directional movement of a machine or cursor) are less intuitive and less convenient due to the complex training procedures. Thus, direct decoding methods for detecting user intention about movement directions are urgently needed.

METHODS

Here, we describe a novel direct decoding method for user intention about the movement directions using the echo state network and Gaussian readouts. Importantly parameters in the network were optimized using the genetic algorithm method to achieve better decoding performance. We tested the decoding performance of this method with four healthy subjects and an inexpensive wireless EEG system containing 14 channels and then compared the performance outcome with that of a conventional machine learning method.

RESULTS

We showed that this decoding method successfully classified eight directions of intended movement (approximately 95% of an accuracy).

CONCLUSIONS

We suggest that the echo state network and Gaussian readouts can be a useful decoding method to directly read user intention of movement directions even using an inexpensive and portable EEG system.

Growing Echo-State Network With Multiple Subreservoirs

An echo-state network (ESN) is an effective alternative to gradient methods for training recurrent neural network. However, it is difficult to determine the structure (mainly the reservoir) of the ESN to match with the given application. In this paper, a growing ESN (GESN) is proposed to design the size and topology of the reservoir automatically. First, the GESN makes use of the block matrix theory to add hidden units to the existing reservoir group by group, which leads to a GESN with multiple subreservoirs. Second, every subreservoir weight matrix in the GESN is created with a predefined singular value spectrum, which ensures the echo-sate property of the ESN without posterior scaling of the weights. Third, during the growth of the network, the output weights of the GESN are updated in an incremental way. Moreover, the convergence of the GESN is proved. Finally, the GESN is tested on some artificial and real-world time-series benchmarks. Simulation results show that the proposed GESN has better prediction performance and faster leaning speed than some ESNs with fixed sizes and topologies.