Parallel and deep reservoir computing using semiconductor lasers with optical feedback.

We experimentally investigate delay-based photonic reservoir computing using semiconductor lasers with optical feedback and injection. We apply different types of temporal mask signals, such as digital, chaos, and colored-noise mask signals, as the weights between the input signal and the virtual nodes in the reservoir. We evaluate the performance of reservoir computing by using a time-series prediction task for the different mask signals. The chaos mask signal shows superior performance than that of the digital mask signals. However, similar prediction errors can be achieved for the chaos and colored-noise mask signals. Mask signals with larger amplitudes result in better performance for all mask signals in the range of the amplitude accessible in our experiment. The performance of reservoir computing is strongly dependent on the cut-off frequency of the colored-noise mask signals, which is related to the resonance of the relaxation oscillation frequency of the laser used as the reservoir.

This paper investigates in detail the effects of measurement noise on the performance of reservoir computing. We focus on an application in which reservoir computers are used to learn the relationship between different state variables of a chaotic system. We recognize that noise can affect the training and testing phases differently. We find that the best performance of the reservoir is achieved when the strength of the noise that affects the input signal in the training phase equals the strength of the noise that affects the input signal in the testing phase. For all the cases we examined, we found that a good remedy to noise is to low-pass filter the input and the training/testing signals; this typically preserves the performance of the reservoir, while reducing the undesired effects of noise.

Reservoir computers can be used to predict time series generated by spatio-temporal chaotic systems. Using multiple reservoirs in parallel has shown improved performances for these predictions, by effectively reducing the input dimensionality of each reservoir. Similarly, one may further reduce the dimensionality of the input data by transforming to a lower-dimensional latent space. Combining both approaches, we show that using dimensionality-reduced latent space predictions for parallel reservoir computing not only reduces computational costs, but also leads to better prediction results for small to medium reservoir sizes. In the combined approach we further demonstrate that dimensionality reduction improves small–reservoir predictions regardless of noise contaminating the training data. The benefit of dimensionality–reduced parallel reservoir computing is illustrated and evaluated on the basis of the prediction of the one-dimensional Kuramoto–Sivashinsky equation.

Photonic reservoir computing (RC) is emerging as a competitive candidate for ultra-fast and energy-efficient neuromorphic computing, noted for its physical compatibility and straightforward training process. However, this widely appreciated form of machine learning typically employs only a single hidden layer with a feedback loop (FL), which essentially constrains the capability for complex task processing and poses challenges to integration. Here, we present an integrated deep photonic RC setup based on a distributed feedback laser array. This setup eliminates the dependence of the FL through the pre-processing termed quasi-convolution coding (QC), where the QC-based RC (QRC) significantly reduces the complexity of the network under the ensured performance. In particular, we extend this QRC into an on-chip deep structure, where this deep QRC (DQRC) exhibits remarkable superiority to its shallow counterparts. We demonstrate the augmented capabilities of DQRC through both simulations and experimental comparisons with QRC, extreme learning machine, and time-delay RC in time-dependent tasks. Moreover, the proposed deep configuration also excels in static image processing. We confirm the potential for simplifying the hardware implementations of deep neural networks, revealing a promising solution to satisfy the urgent demand for high-integration brain-inspired systems.

During the last decade reservoir computing (RC) has proven to be a powerful machine learning concept using recurrent networks to process sequential information streams [1]. Lately, the concept of RC was drastically simplified to reduce hardware requirements, thus making machine learning concepts more obtainable to apply in actual physical systems [2]. RC has been implemented in photonic configurations and has efficientiy processed analog optical signals following simple schemes and minimal training overhead. Especially the realization using a semiconductor laser with time-delayed optical feedback has shown the potential of all-optical machine learning, utilizing signals with transient states at the GHz regime [3].

We report on a simple approach of time-delayed reservoir computing (RC) based on a two-element phased laser array for image identification. Here the phased laser array with optical feedback and injection is trained according to the representative characteristics extracted through histograms of oriented gradients. These characteristic vectors are multiplied by a random mask signal to form input data, which are subsequently trained in the reservoir. By optimizing the parameters of the RC, we achieve an identification accuracy of 97.44% on the MNIST dataset and 85.46% on the Fashion-MNIST dataset. These results indicate that our proposed RC indeed allows accurate classification of handwritten digit and fashion production. Moreover, we further forecast an RC scheme based on a larger-scale phased laser array, which is expected to tackle more complex tasks at a high speed. Our work offers a possibility for advanced image processing using highly integrated neuromorphic photonic systems.

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.

We overview recent progress in photonic artificial intelligence. We demonstrate reservoir computing using multiple reservoirs of semiconductor lasers with optical feedback. We perform decision making for solving the multi-armed bandit problem using synchronization of laser network.

A theoretical model for numerical simulation of the nonlinear spin-wave transient processes in magnonic active-ring oscillators (MAROs) with variable gain has been developed. The model employs the formalism of the Landau–Ginzburg equation to describe the nonlinear propagation of spectrally narrow magnonic wave packets in a magnetic film. We show that the model allows one to simulate ring's operation above the self-generation threshold as a magnonic physical reservoir computer for which the control of ring gain is employed as a method of data input into the physical reservoir. Performance of the reservoir computer was evaluated by carrying out numerical simulations using the developed model. To this end, we simulated the completion of the short-term memory and the parity-check tasks by the model. We found that the simulation results are in good agreement with experimental data. This evidences that the constructed model can be used for investigating physics underlying the performance of the MARO as a physical reservoir computer and for reservoir optimization with the final goal of maximizing reservoir performance.

Reservoir computers (RCs) are biology-inspired computational frameworks for signal processing that are typically implemented using recurrent neural networks. Recent work has shown that Boolean networks (BN) can also be used as reservoirs. We analyze the performance of BN RCs, measuring their flexibility and identifying the factors that determine the effective approximation of Boolean functions applied in a sliding-window fashion over a binary signal, both non-recursively and recursively. We train and test BN RCs of different sizes, signal connectivity, and in-degree to approximate three-bit, five-bit, and three-bit recursive binary functions, respectively. We analyze how BN RC parameters and function average sensitivity, which is a measure of function smoothness, affect approximation accuracy as well as the spread of accuracies for a single reservoir. We found that approximation accuracy and reservoir flexibility are highly dependent on RC parameters. Overall, our results indicate that not all reservoirs are equally flexible, and RC instantiation and training can be more efficient if this is taken into account. The optimum range of RC parameters opens up an angle of exploration for understanding how biological systems might be tuned to balance system restraints with processing capacity.

Time series forecasting plays a critical role in decision-making across domains such as energy management, healthcare, meteorology, and finance. This paper presents a comparative study of deep learning architectures (RNN, LSTM, GRU), reservoir computing (Echo State Networks), and quantum-enhanced approaches (QLSTM and LQLSTM). Using heterogeneous datasets-Paris daily temperatures (2017-2024) and Apple Inc. stock prices (2017-2024)-we evaluate model performance under both seasonal and highly volatile conditions. Results indicate that while GRU and LSTM provide strong predictive capabilities, Echo State Networks achieve superior accuracy and efficiency. Quantum-inspired models, particularly the LQLSTM, demonstrate promising improvements in capturing nonlinear dependencies, albeit with higher computational costs. The findings highlight the tradeoffs between interpretability, accuracy, and scalability, offering perspectives on the potential of hybrid quantum-classical models for future forecasting tasks.

In this work, the performance of an optoelectronic time-delay reservoir computing system for performing a handwritten digit recognition task is numerically investigated, and a scheme to improve the recognition speed using multiple parallel reservoirs is proposed. By comparing four image injection methods based on a single time-delay reservoir, we find that when injecting the histograms of oriented gradient (HOG) features of the digit image, the accuracy rate (AR) is relatively high and is less affected by the offset phase. To improve the recognition speed, we construct a parallel time-delay reservoir system including multi-reservoirs, where each reservoir processes part of the HOG features of one image. Based on 6 parallel reservoirs with each reservoir possessing 100 virtual nodes, the AR can reach about 97.8%, and the reservoir processing speed can reach about 1 × 106 digits per second. Meanwhile, the parallel reservoir system shows strong robustness to the parameter mismatch between multi-reservoirs.

We analyze the performance of a reservoir computer based on time-delay feedback and optical injection, which is drawing benefits from the high-speed polarization dynamics of a vertical cavity surface emitting laser. We show that such a system has high computation performance and yields deeper memory than an existing single-mode laser-based reservoir computer. Performance is demonstrated on several benchmarking tasks. In particular, the error rate is an order of magnitude smaller when performing channel equalization.

Nonlinear channel equalization is a key technology for reducing signal distortion and ensuring reliable data transmission. This work presents nonlinear channel equalization using a nanolaser-based delayed optical feedback reservoir computing system. The symbol error rate (SER) is adopted to evaluate the performance of equalization. The results show that maintaining low external perturbation strengths on the nanolaser in the reservoir layer results in a low SER and improved system stability. Higher spontaneous emission enhancement factor and spontaneous emission coupling factor improve perturbation tolerance. However, the minimal SER is achieved with optimally chosen moderate values of spontaneous emission enhancement factor and spontaneous emission coupling factor, which is different from the observations in previous nanolaser-based delayed optical feedback reservoir computing systems.

We numerically investigate the performance of Chinese herbal medicine (CHM) recognition using a time delay reservoir computing (TDRC) system consist of a vertical-cavity surface-emitting laser (VCSEL) subjected to optical feedback. A database of 960 images from 12 CHM categories is used to evaluate the recognition performance, most of which contain many CHM samples and have different backgrounds. The CHM image feature vector is masked and optically injected into the VCSEL, and the VCSEL output in two polarization modes are sampled as the virtual node states for readout. After testing the CHM recognition performance of TDRC under injecting the same information into two polarization modes of the VCSEL, we further test the performance of parallel processing by injecting half of the image information into each of the two polarization modes. By concatenating the virtual node states collected from two modes for readout, the recognition speed is doubled. Meanwhile, the influence of key parameters on recognition performance are investigated and the relationship between system idle state and recognition performance is also examined. The results show that, under parallel processing and orthogonal optical feedback, the TDRC achieves the minimum recognition error of 1.7% at a reservoir processing rate of 2×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">9</sup> images per second.