Fully analogue photonic reservoir computer

Photonic next-generation reservoir computer based on distributed feedback in optical fiber

Reservoir computing (RC) is a machine learning paradigm that excels at dynamical systems analysis. Photonic RCs, which perform implicit computation through optical interactions, have attracted increasing attention due to their potential for low latency predictions. However, most existing photonic RCs rely on a nonlinear physical cavity to implement system memory, limiting control over the memory structure and requiring long warm-up times to eliminate transients. In this work, we resolve these issues by demonstrating a photonic next-generation reservoir computer (NG-RC) using a fiber optic platform. Our photonic NG-RC eliminates the need for a cavity by generating feature vectors directly from nonlinear combinations of the input data with varying delays. Our approach uses Rayleigh backscattering to produce output feature vectors by an unconventional nonlinearity resulting from coherent, interferometric mixing followed by a quadratic readout. Performing linear optimization on these feature vectors, our photonic NG-RC demonstrates state-of-the-art performance for the observer (cross-prediction) task applied to the Rössler, Lorenz, and Kuramoto-Sivashinsky systems. In contrast to digital NG-RC implementations, we show that it is possible to scale to high-dimensional systems while maintaining low latency and low power consumption.

Resource-constrained narrowband optoelectronic oscillator-based reservoir computing for classification of modulated signals

We experimentally investigate the performance of narrowband optoelectronic oscillator (OEO) reservoir computers using the standard 10th-order nonlinear autoregressive-moving-average (NARMA10) task. Because comparing results from differently parameterized photonic time-delay systems can be difficult, we introduce a new, to the best of our knowledge, metric that accounts for system size, computational accuracy, and training effort overhead in order to provide an "at-a-glance" method to holistically determine a reservoir computer's performance. We then demonstrate the first experimental effort of narrowband OEO-based reservoir computing for the RADIOML dataset, which consists of recognizing and classifying IQ-modulated radio signals including analog and digital modulations. Our results indicate that narrowband OEOs are capable of achieving reasonable accuracies with exceptionally small training sets, thereby paving the way to real-time machine learning for radio frequency signals.

Magnetization Vector Rotation Reservoir Computing Operated by Redox Mechanism

Physical reservoir computing is a promising way to develop efficient artificial intelligence using physical devices exhibiting nonlinear dynamics. Although magnetic materials have advantages in miniaturization, the need for a magnetic field and large electric current results in high electric power consumption and a complex device structure. To resolve these issues, we propose a redox-based physical reservoir utilizing the planar Hall effect and anisotropic magnetoresistance, which are phenomena described by different nonlinear functions of the magnetization vector that do not need a magnetic field to be applied. The expressive power of this reservoir based on a compact all-solid-state redox transistor is higher than the previous physical reservoir. The normalized mean square error of the reservoir on a second-order nonlinear equation task was 1.69 × 10-3, which is lower than that of a memristor array (3.13 × 10-3) even though the number of reservoir nodes was fewer than half that of the memristor array.

Time delay reservoir computing with a silicon microring resonator and a fiber-based optical feedback loop

Silicon microring resonators serve as critical components in integrated photonic neural network implementations, owing to their compact footprint, compatibility with CMOS technology, and passive nonlinear dynamics. Recent advancements have leveraged their filtering properties as weighting functions, and their nonlinear dynamics as activation functions with spiking capabilities. In this work, we investigate experimentally the linear and nonlinear dynamics of microring resonators for time delay reservoir computing, by introducing an external optical feedback loop. After effectively mitigating the impact of environmental noise on the fiber-based feedback phase dependencies, we evaluate the computational capacity of this system by assessing its performance across various benchmark tasks at a bit rate of few Mbps. We show that the additional memory provided by the optical feedback is necessary to achieve error-free operation in delayed-boolean tasks that require up to 3 bits of memory. In this case the microring was operated in the linear regime and the photodetection was the nonlinear activation function. We also show that the Santa Fe and Mackey Glass prediction tasks are solved when the microring nonlinearities are activated. Notably, our study reveals competitive outcomes even when employing only 7 virtual nodes within our photonic reservoir. Our findings illustrate the silicon microring's versatile performance in the presence of optical feedback, highlighting its ability to be tailored for various computing applications.

Photonic delay reservoir computer based on ring resonator for reconfigurable microwave waveform generator

To achieve an autonomously controlled reconfigurable microwave waveform generator, this study proposes and demonstrates a self-adjusting synthesis method based on a photonic delay reservoir computer with ring resonator. The proposed design exploits the ring resonator to configure the reservoir, facilitating a nonlinear transformation and providing delay space. A theoretical analysis is conducted to explain how this configuration addresses the challenges of microwave waveform generation. Considering the generalization performance of waveform generation, the simulations demonstrate the system's capability to produce six distinct representative waveforms, all exhibiting a highly impressive root mean square error (RMSE) of less than 1%. To further optimize the system's flexibility and accuracy, we explore the application of various artificial intelligence algorithms at the reservoir computer's output layer. Furthermore, our investigation delves deeply into the complexities of system performance, specifically exploring the influence of reservoir neurons and micro-ring resonator parameters on calculation performance. We also delve into the scalability of reservoirs, considering both parallel and cascaded arrangements.

High-speed parallel processing with photonic feedforward reservoir computing

High-speed photonic reservoir computing (RC) has garnered significant interest in neuromorphic computing. However, existing reservoir layer (RL) architectures mostly rely on time-delayed feedback loops and use analog-to-digital converters for offline digital processing in the implementation of the readout layer, posing inherent limitations on their speed and capabilities. In this paper, we propose a non-feedback method that utilizes the pulse broadening effect induced by optical dispersion to implement a RL. By combining the multiplication of the modulator with the summation of the pulse temporal integration of the distributed feedback-laser diode, we successfully achieve the linear regression operation of the optoelectronic analog readout layer. Our proposed fully-analog feed-forward photonic RC (FF-PhRC) system is experimentally demonstrated to be effective in chaotic signal prediction, spoken digit recognition, and MNIST classification. Additionally, using wavelength-division multiplexing, our system manages to complete parallel tasks and improve processing capability up to 10 GHz per wavelength. The present work highlights the potential of FF-PhRC as a high-performance, high-speed computing tool for real-time neuromorphic computing.

Resonant properties of the memory capacity of a laser-based reservoir computer with filtered optoelectronic feedback

We provide a comprehensive analysis of the resonant properties of the memory capacity of a reservoir computer based on a semiconductor laser subjected to time-delayed filtered optoelectronic feedback. Our analysis reveals first how the memory capacity decreases sharply when the input-data clock cycle is slightly time-shifted from the time delay or its multiples. We attribute this effect to the inertial properties of the laser. We also report on the damping of the memory-capacity drop at resonance with a decrease of the virtual-node density and its broadening with the filtering properties of the optoelectronic feedback. These results are interpretated using the eigenspectrum of the reservoir obtained from a linear stability analysis. Then, we unveil an invariance in the minimum value of the memory capacity at resonance with respect to a variation of the number of nodes if the number is big enough and quantify how the filtering properties impact the system memory in and out of resonance.

High speed human action recognition using a photonic reservoir computer

The recognition of human actions in videos is one of the most active research fields in computer vision. The canonical approach consists in a more or less complex preprocessing stages of the raw video data, followed by a relatively simple classification algorithm. Here we address recognition of human actions using the reservoir computing algorithm, which allows us to focus on the classifier stage. We introduce a new training method for the reservoir computer, based on "Timesteps Of Interest", which combines in a simple way short and long time scales. We study the performance of this algorithm using both numerical simulations and a photonic implementation based on a single non-linear node and a delay line on the well known KTH dataset. We solve the task with high accuracy and speed, to the point of allowing for processing multiple video streams in real time. The present work is thus an important step towards developing efficient dedicated hardware for video processing.

Photonic reservoir computing enabled by stimulated Brillouin scattering

Artificial intelligence (AI) drives the creation of future technologies that disrupt the way humans live and work, creating new solutions that change the way we approach tasks and activities, but it requires a lot of data processing, large amounts of data transfer, and computing speed. It has led to a growing interest of research in developing a new type of computing platform which is inspired by the architecture of the brain specifically those that exploit the benefits offered by photonic technologies, fast, low-power, and larger bandwidth. Here, a new computing platform based on the photonic reservoir computing architecture exploiting the non-linear wave-optical dynamics of the stimulated Brillouin scattering is reported. The kernel of the new photonic reservoir computing system is constructed of an entirely passive optical system. Moreover, it is readily suited for use in conjunction with high performance optical multiplexing techniques to enable real-time artificial intelligence. Here, a methodology to optimise the operational condition of the new photonic reservoir computing is described which is found to be strongly dependent on the dynamics of the stimulated Brillouin scattering system. The new architecture described here offers a new way of realising AI-hardware which highlight the application of photonics for AI.

Real-time respiratory motion prediction using photonic reservoir computing

Respiration induced motion is a well-recognized challenge in many clinical practices including upper body imaging, lung tumor motion tracking and radiation therapy. In this work, we present a recurrent neural network algorithm that was implemented in a photonic delay-line reservoir computer (RC) for real-time respiratory motion prediction. The respiratory motion signals are quasi-periodic waveforms subject to a variety of non-linear distortions. In this work, we demonstrated for the first time that RC can be effective in predicting short to medium range of respiratory motions within practical timescales. A double-sliding window technology is explored to enable the real-time establishment of an individually trained model for each patient and the real-time processing of live-streamed respiratory motion data. A breathing dataset from a total of 76 patients with breathing speeds ranging from 3 to 20 breaths per minute (BPM) is studied. Motion prediction of look-ahead times of 66.6, 166.6, and 333 ms are investigated. With a 333 ms look-ahead time, the real-time RC model achieves an average normalized mean square error (NMSE) of 0.025, an average mean absolute error (MAE) of 0.34 mm, an average root mean square error (RMSE) of 0.45 mm, an average therapeutic beam efficiency (TBE) of 94.14% for an absolute error (AE) < 1 mm, and 99.89% for AE < 3 mm. This study demonstrates that real-time RC is an efficient computing framework for high precision respiratory motion prediction.

Enhanced optoelectronic reservoir computation using semiconductor laser with double delay feedbacks

We numerically explored the enhanced performance and physical mechanism of semiconductor laser (SL) based reservoir computation (RC) with double optoelectronic feedback (DOEF). One-step and multistep Santa Fe time series predictions were used as standard test benchmarks in this work. We found that in the optimized parameter region the normalized mean square error (NMSE) of an SL-based RC under DOEF is smaller than an SL-based RC with single optoelectronic feedback (SOEF). In addition, the performance improvement is more obvious for multistep prediction, which is particularly suitable for more complex tasks that requires a higher memory capability (MC). The enriched node states (optical intensity of the virtual nodes for each sample) and the enhanced MC of the proposed DOEF were verified by a comparison to SOEF under the optimized feedback strength. The influence of the feedback strength and the delay difference on the NMSE and the MC was also investigated. Our study should be helpful in the design of a high-performance optoelectronic RC based on an SL.

Impact of filtering on photonic time-delay reservoir computing

We analyze the modification of the computational properties of a time-delay photonic reservoir computer with a change in its feedback bandwidth. For a reservoir computing configuration based on a semiconductor laser subject to filtered optoelectronic feedback, we demonstrate that bandwidth selection can lead to a flat-topped eigenvalue spectrum for which a large number of system frequencies are weakly damped as a result of the attenuation of modulational instability by feedback filtering. This spectral configuration allows for the optimization of the reservoir in terms of its memory capacity, while its computational ability appears to be only weakly affected by the characteristics of the filter.

A Neuromorphic Model With Delay-Based Reservoir for Continuous Ventricular Heartbeat Detection

There is a growing interest in neuromorphic hardware since it offers a more intuitive way to achieve bio-inspired algorithms. This paper presents a neuromorphic model for intelligently processing continuous electrocardiogram (ECG) signal. This model aims to develop a hardware-based signal processing model and avoid employing digitally intensive operations, such as signal segmentation and feature extraction, which are not desired in an analogue neuromorphic system. We apply delay-based reservoir computing as the information processing core, along with a novel training and labelling method. Different from the conventional ECG classification techniques, this computation model is a end-to-end dynamic system that mimics the real-time signal flow in neuromorphic hardware. The input is the raw ECG stream, while the amplitude of the output represents the risk factor of a ventricular ectopic heartbeat. The intrinsic memristive property of the reservoir empowers the system to retain the historical ECG information for high-dimensional mapping. This model was evaluated with the MIT-BIH database under the inter-patient paradigm and yields 81% sensitivity and 98% accuracy. Under this architecture, the minimum size of memory required in the inference process can be as low as 3.1 MegaByte(MB) because the majority of the computation takes place in the analogue domain. Such computational modelling boosts memory efficiency by simplifying the computing procedure and minimizing the required memory for future wearable devices.

Enhanced performance of a reservoir computing system based on a dual-loop optoelectronic oscillator

Time-delayed reservoir computing (RC) is a brain inspired paradigm for processing temporal information, with simplification in the network's architecture using virtual nodes embedded in a temporal delay line. In this work, a novel, to the best of our knowledge, RC system based on a dual-loop optoelectronic oscillator is proposed to enhance the prediction and classification. The hardware is compact and easy to implement, and only a section of fiber compared to the traditional optoelectronic oscillator reservoir is added to conform the dual-loop scheme. Compared with the traditional reservoir, a remarkable performance of the proposed RC system is demonstrated by simulation on three well-known tasks, namely the nonlinear auto regressive moving average (NARMA10) task, signal waveform recognized task, and handwritten numeral recognition. The parameter optimization in the NARMA10 task is presented with influenced factors. The novel RC system finally obtains a normalized mean square error at 0.0493±0.007 in NARMA10 task, 6.172×10^-6 in signal waveform recognized task, and a word error rate at 9% in handwritten numeral recognition with suitable parameters.

Influence of the input signal's phase modulation on the performance of optical delay-based reservoir computing using semiconductor lasers

In photonic reservoir computing, semiconductor lasers with delayed feedback have shown to be suited to efficiently solve difficult and time-consuming problems. The input data in this system is often optically injected into the reservoir. Based on numerical simulations, we show that the performance depends heavily on the way that information is encoded in this optical injection signal. In our simulations we compare different input configurations consisting of Mach-Zehnder modulators and phase modulators for injecting the signal. We observe far better performance on a one-step ahead time-series prediction task when modulating the phase of the injected signal rather than only modulating its amplitude.

Rotating neurons for all-analog implementation of cyclic reservoir computing

Hardware implementation in resource-efficient reservoir computing is of great interest for neuromorphic engineering. Recently, various devices have been explored to implement hardware-based reservoirs. However, most studies were mainly focused on the reservoir layer, whereas an end-to-end reservoir architecture has yet to be developed. Here, we propose a versatile method for implementing cyclic reservoirs using rotating elements integrated with signal-driven dynamic neurons, whose equivalence to standard cyclic reservoir algorithm is mathematically proven. Simulations show that the rotating neuron reservoir achieves record-low errors in a nonlinear system approximation benchmark. Furthermore, a hardware prototype was developed for near-sensor computing, chaotic time-series prediction and handwriting classification. By integrating a memristor array as a fully-connected output layer, the all-analog reservoir computing system achieves 94.0% accuracy, while simulation shows >1000× lower system-level power than prior works. Therefore, our work demonstrates an elegant rotation-based architecture that explores hardware physics as computational resources for high-performance reservoir computing.

Reservoir computing has demonstrated high-level performance, however efficient hardware implementations demand an architecture with minimum system complexity. The authors propose a rotating neuron-based architecture for physically implementing all-analog resource efficient reservoir computing system.

Photonic reinforcement learning based on optoelectronic reservoir computing

Reinforcement learning has been intensively investigated and developed in artificial intelligence in the absence of training data, such as autonomous driving vehicles, robot control, internet advertising, and elastic optical networks. However, the computational cost of reinforcement learning with deep neural networks is extremely high and reducing the learning cost is a challenging issue. We propose a photonic on-line implementation of reinforcement learning using optoelectronic delay-based reservoir computing, both experimentally and numerically. In the proposed scheme, we accelerate reinforcement learning at a rate of several megahertz because there is no required learning process for the internal connection weights in reservoir computing. We perform two benchmark tasks, CartPole-v0 and MountanCar-v0 tasks, to evaluate the proposed scheme. Our results represent the first hardware implementation of reinforcement learning based on photonic reservoir computing and pave the way for fast and efficient reinforcement learning as a novel photonic accelerator.

Reservoir computing with random and optimized time-shifts

We investigate the effects of application of random time-shifts to the readouts of a reservoir computer in terms of both accuracy (training error) and performance (testing error). For different choices of the reservoir parameters and different "tasks," we observe a substantial improvement in both accuracy and performance. We then develop a simple but effective technique to optimize the choice of the time-shifts, which we successfully test in numerical experiments.

Photonic Reservoir Computer with Output Expansion for Unsupervized Parameter Drift Compensation

We present a method to improve the performance of a reservoir computer by keeping the reservoir fixed and increasing the number of output neurons. The additional neurons are nonlinear functions, typically chosen randomly, of the reservoir neurons. We demonstrate the interest of this expanded output layer on an experimental opto-electronic system subject to slow parameter drift which results in loss of performance. We can partially recover the lost performance by using the output layer expansion. The proposed scheme allows for a trade-off between performance gains and system complexity.

Photonic reservoir computer using speckle in multimode waveguide ring resonators

Photonic reservoir computers (RC) come in single mode ring and multimode array geometries. We propose and simulate a photonic RC architecture using speckle in a multimode waveguide ring resonator that requires neither the ultra-high-speed analog-digital conversion nor the spatial light modulator used in other designs. We show that the equations for propagation around a multimode (MM) ring resonator along with an optical nonlinearity, and optical feedback can be cast exactly in the standard RC form with speckle mixing performing the pseudo-random matrix multiplications. The hyperparameters are the outcoupling efficiency, the nonlinearity saturation intensity, the input bias, and the waveguide properties. In particular, the number of waveguide modes is a measure of the number of effective neurons in the RC. Simulations show a ring using a strongly guiding 50-µm planar waveguide gives 206 effective neurons and excellent predictions of Mackey-Glass waveforms for a broad range of the hyperparameters, while a weakly guiding MM 200-µm diameter fiber gives 4,238 effective neurons and excellent predictions of chaotic solutions of the Kuramoto-Sivashinsky equation. We discuss physical realizations for implementing the system with a chip-scale device or with discrete components and a MM optical fiber.

The rise of intelligent matter

Artificial intelligence (AI) is accelerating the development of unconventional computing paradigms inspired by the abilities and energy efficiency of the brain. The human brain excels especially in computationally intensive cognitive tasks, such as pattern recognition and classification. A long-term goal is de-centralized neuromorphic computing, relying on a network of distributed cores to mimic the massive parallelism of the brain, thus rigorously following a nature-inspired approach for information processing. Through the gradual transformation of interconnected computing blocks into continuous computing tissue, the development of advanced forms of matter exhibiting basic features of intelligence can be envisioned, able to learn and process information in a delocalized manner. Such intelligent matter would interact with the environment by receiving and responding to external stimuli, while internally adapting its structure to enable the distribution and storage (as memory) of information. We review progress towards implementations of intelligent matter using molecular systems, soft materials or solid-state materials, with respect to applications in soft robotics, the development of adaptive artificial skins and distributed neuromorphic computing.

Enhancing Performance of Reservoir Computing System Based on Coupled MEMS Resonators

Reservoir computing (RC) is an attractive paradigm of a recurrent neural network (RNN) architecture, owning to the ease of training and existing neuromorphic implementation. Its simulated performance matches other digital algorithms on a series of benchmarking tasks, such as prediction tasks and classification tasks. In this article, we propose a novel RC structure based on the coupled MEMS resonators with the enhanced dynamic richness to optimize the performance of the RC system both on the system level and data set level. Moreover, we first put forward that the dynamic richness of RC comprises linear dynamic richness and nonlinear dynamic richness, which can be enhanced by adding delayed feedbacks and nonlinear nodes, respectively. In order to set forth this point, we compare three typical RC structures, a single-nonlinearity RC structure with single-feedback, a single-nonlinearity RC structure with double-feedbacks, and the couple-nonlinearity RC structure with double-feedbacks. Specifically, four different tasks are enumerated to verify the performance of the three RC structures, and the results show the enhanced dynamic richness by adding delayed feedbacks and nonlinear nodes. These results prove that coupled MEMS resonators offer an interesting platform to implement a complex computing paradigm leveraging their rich dynamical features.

Fast physical repetitive patterns generation for masking in time-delay reservoir computing

Albeit the conceptual simplicity of hardware reservoir computing, the various implementation schemes that have been proposed so far still face versatile challenges. The conceptually simplest implementation uses a time delay approach, where one replaces the ensemble of nonlinear nodes with a unique nonlinear node connected to a delayed feedback loop. This simplification comes at a price in other parts of the implementation; repetitive temporal masking sequences are required to map the input information onto the diverse states of the time delay reservoir. These sequences are commonly introduced by arbitrary waveform generators which is an expensive approach when exploring ultra-fast processing speeds. Here we propose the physical generation of clock-free, sub-nanosecond repetitive patterns, with increased intra-pattern diversity and their use as masking sequences. To that end, we investigate numerically a semiconductor laser with a short optical feedback cavity, a well-studied dynamical system that provides a wide diversity of emitted signals. We focus on those operating conditions that lead to a periodic signal generation, with multiple harmonic frequency tones and sub-nanosecond limit cycle dynamics. By tuning the strength of the different frequency tones in the microwave domain, we access a variety of repetitive patterns and sample them in order to obtain the desired masking sequences. Eventually, we apply them in a time delay reservoir computing approach and test them in a nonlinear time-series prediction task. In a performance comparison with masking sequences that originate from random values, we find that only minor compromises are made while significantly reducing the instrumentation requirements of the time delay reservoir computing system.

Parameters optimization method for the time-delayed reservoir computing with a nonlinear duffing mechanical oscillator

Reservoir computing (RC) is a recently introduced bio-inspired computational framework capable of excellent performances in the temporal data processing, owing to its derivation from the recurrent neural network (RNN). It is well-known for the fast and effective training scheme, as well as the ease of the hardware implementation, but also the problematic sensitivity of its performance to the optimizable architecture parameters. In this article, a particular time-delayed RC with a single clamped-clamped silicon beam resonator that exhibits a classical Duffing nonlinearity is presented and its optimization problem is studied. Specifically, we numerically analyze the nonlinear response of the resonator and find a quasi-linear bifurcation point shift of the driving voltage with the driving frequency sweeping, which is called Bifurcation Point Frequency Modulation (BPFM). Furthermore, we first proposed that this method can be used to find the optimal driving frequency of RC with a Duffing mechanical resonator for a given task, and then put forward a comprehensive optimization process. The high performance of RC presented on four typical tasks proves the feasibility of this optimization method. Finally, we envision the potential application of the method based on the BPFM in our future work to implement the RC with other mechanical oscillators.

Continuous and long-term stabilization of degenerate optical parametric oscillators for large-scale optical hybrid computers

The minimum requirements for an optical reservoir computer, a recent paradigm for computation using simple algorithms, are nonlinearity and internal interactions. A promising optical system satisfying these requirements is a platform based on coupled degenerate optical parametric oscillators (DOPOs) in a fiber ring cavity. We can expect advantages using DOPOs for reservoir computing with respect to scalability and reduction of excess noise; however, the continuous stabilization required for reservoir computing has not yet been demonstrated. Here, we report the continuous and long-term stabilization of an optical system by introducing periodical phase modulation patterns for DOPOs and a local oscillator. We observed that the Allan variance of the optical phase up to 100 ms was suppressed and that the homodyne measurement signal had a relative standard deviation of 1.4% over 62,500 round trips. The proposed methods represent important technical bases for realizing stable computation on large-scale optical hybrid computers.

Nonlinear dynamics in an optoelectronic feedback delay oscillator with piecewise linear transfer functions from the laser diode and photodiode

We investigate the nonlinear dynamics of a recent architecture of an optoelectronic oscillator, where the emitting laser and the receiving diode are connected in a head-to-tail configuration via an optical fiber delay line. The resulting nonlinear transfer function is a piecewise linear profile, and its interplay with the delay leads to many complex behaviors such as relaxation oscillations and deterministic chaos. This system belongs to a recent class of optoelectronic oscillators where the nonlinearity does not originate from the sinusoidal transfer function of an imbalanced interferometer, and, in particular, it is a simple optoelectronic oscillator configuration that is capable of displaying a chaotic behavior. The results of the analytic study are confirmed by numerical simulations and experimental measurements.

Impact of optical coherence on the performance of large-scale spatiotemporal photonic reservoir computing systems

Large-scale spatiotemporal photonic reservoir computer (RC) systems offer remarkable solutions for massively parallel processing of a wide variety of hard real-world tasks. In such systems, neural networks are created by either optical or electronic coupling. Here, we investigate the impact of the optical coherence on the performance of large-scale spatiotemporal photonic RCs by comparing a coherent (optical coupling between the reservoir nodes) and incoherent (digital coupling between the reservoir nodes) RC systems. Although the coherent configuration offers significant reduction on the computational load compared to the incoherent architecture, for image and video classification benchmark tasks, it is found that the incoherent RC configuration outperforms the coherent configuration. Moreover, the incoherent configuration is found to exhibit a larger memory capacity than the coherent scheme. Our results pave the way towards the optimization of implementation of large-scale RC systems.

Study of the effect of the offset phase in time-delay electro-optical systems

We show that the effect of the offset phase on the dynamics of the time-delay optoelectronic oscillators that is observed experimentally can be explained in terms of switching between the subcritical and supercritical Hopf bifurcations. The domains of the offset phase for which the system functions are determined analytically. We also show that the width of these domains exceptionally depends on the interplay between the three time scales of the system. Our theoretical results fit with the experimental measurements.

Dynamical Learning of Dynamics

The ability of humans and animals to quickly adapt to novel tasks is difficult to reconcile with the standard paradigm of learning by slow synaptic weight modification. Here, we show that fixed-weight neural networks can learn to generate required dynamics by imitation. After appropriate weight pretraining, the networks quickly and dynamically adapt to learn new tasks and thereafter continue to achieve them without further teacher feedback. We explain this ability and illustrate it with a variety of target dynamics, ranging from oscillatory trajectories to driven and chaotic dynamical systems.

Delay-based reservoir computing: tackling performance degradation due to system response time

We analyze the degradation of the computational capacity of delay-based reservoir computers due to system response time. We demonstrate that this degradation is reduced when the delay time is greater than the data injection time. Performance improvement is demonstrated on several benchmarking tasks.

Demonstrating delay-based reservoir computing using a compact photonic integrated chip

Photonic delay-based reservoir computing (RC) has gained considerable attention lately, as it allows for simple technological implementations of the RC concept that can operate at high speed. In this paper, we discuss a practical, compact and robust implementation of photonic delay-based RC, by integrating a laser and a 5.4 cm delay line on an InP photonic integrated circuit. We demonstrate the operation of this chip with 23 nodes at a speed of 0.87 GSa/s, showing performances that is similar to previous non-integrated delay-based setups. We also investigate two other post-processing methods to obtain more nodes in the output layer. We show that these methods improve the performance drastically, without compromising the computation speed.

Classification of time-domain waveforms using a speckle-based optical reservoir computer

Reservoir computing is a recurrent machine learning framework that expands the dimensionality of a problem by mapping an input signal into a higher-dimension reservoir space that can capture and predict features of complex, non-linear temporal dynamics. Here, we report on a bulk electro-optical demonstration of a reservoir computer using speckles generated by propagating a laser beam modulated with a spatial light modulator through a multimode waveguide. We demonstrate that the hardware can successfully perform a multivariate audio classification task performed using the Japanese vowel speakers public data set. We perform full wave optical calculations of this architecture implemented in a chip-scale platform using an SiO₂ waveguide and demonstrate that it performs as well as a fully numerical implementation of reservoir computing. As all the optical components used in the experiment can be fabricated using a commercial photonic integrated circuit foundry, our result demonstrates a framework for building a scalable, chip-scale, reservoir computer capable of performing optical signal processing.

Machine learning based on reservoir computing with time-delayed optoelectronic and photonic systems

The concept of reservoir computing emerged from a specific machine learning paradigm characterized by a three-layered architecture (input, reservoir, and output), where only the output layer is trained and optimized for a particular task. In recent years, this approach has been successfully implemented using various hardware platforms based on optoelectronic and photonic systems with time-delayed feedback. In this review, we provide a survey of the latest advances in this field, with some perspectives related to the relationship between reservoir computing, nonlinear dynamics, and network theory.

Task-Independent Computational Abilities of Semiconductor Lasers with Delayed Optical Feedback for Reservoir Computing

Reservoir computing has rekindled neuromorphic computing in photonics. One of the simplest technological implementations of reservoir computing consists of a semiconductor laser with delayed optical feedback. In this delay-based scheme, virtual nodes are distributed in time with a certain node distance and form a time-multiplexed network. The information processing performance of a semiconductor laser-based reservoir computing (RC) system is usually analysed by way of testing the laser-based reservoir computer on specific benchmark tasks. In this work, we will illustrate the optimal performance of the system on a chaotic time-series prediction benchmark. However, the goal is to analyse the reservoir’s performance in a task-independent way. This is done by calculating the computational capacity, a measure for the total number of independent calculations that the system can handle. We focus on the dependence of the computational capacity on the specifics of the masking procedure. We find that the computational capacity depends strongly on the virtual node distance with an optimal node spacing of 30 ps. In addition, we show that the computational capacity can be further increased by allowing for a well chosen mismatch between delay and input data sample time.

Stability analysis of reservoir computers dynamics via Lyapunov functions

A Lyapunov design method is used to analyze the nonlinear stability of a generic reservoir computer for both the cases of continuous-time and discrete-time dynamics. Using this method, for a given nonlinear reservoir computer, a radial region of stability around a fixed point is analytically determined. We see that the training error of the reservoir computer is lower in the region where the analysis predicts global stability but is also affected by the particular choice of the individual dynamics for the reservoir systems. For the case that the dynamics is polynomial, it appears to be important for the polynomial to have nonzero coefficients corresponding to at least one odd power (e.g., linear term) and one even power (e.g., quadratic term).

Reservoir computing system with double optoelectronic feedback loops

Reservoir computing (RC) by supervised training, a bio-inspired paradigm, is gaining popularity for processing time-dependent data. Compared to conventional recurrent neural networks, RC is facilely implemented by available hardware and overcomes some obstacles in training period, such as slow convergence and local optimum. In this paper, we propose and characterize a novel reservoir computing system based on a semiconductor laser with double optoelectronic feedback loops. This system shows obvious improvement on prediction, speech recognition and nonlinear channel equalization compared to the traditional reservoir computing systems with single feedback loop. Then some influencing factors to optimize the performance of the new RC are numerically studied, and its great potential of addressing more complex and troubling problems in information processing is expected to be exploited.

Application of the deep learning for the prediction of rainfall in Southern Taiwan

Precipitation is useful information for assessing vital water resources, agriculture, ecosystems and hydrology. Data-driven model predictions using deep learning algorithms are promising for these purposes. Echo state network (ESN) and Deep Echo state network (DeepESN), referred to as Reservoir Computing (RC), are effective and speedy algorithms to process a large amount of data. In this study, we used the ESN and the DeepESN algorithms to analyze the meteorological hourly data from 2002 to 2014 at the Tainan Observatory in the southern Taiwan. The results show that the correlation coefficient by using the DeepESN was better than that by using the ESN and commercial neuronal network algorithms (Back-propagation network (BPN) and support vector regression (SVR), MATLAB, The MathWorks co.), and the accuracy of predicted rainfall by using the DeepESN can be significantly improved compared with those by using ESN, the BPN and the SVR. In sum, the DeepESN is a trustworthy and good method to predict rainfall; it could be applied to global climate forecasts which need high-volume data processing.

Asynchronous Multiplex Communication Channels in 2-D Neural Network With Fluctuating Characteristics

Neurons behave like transistors, but have fluctuating characteristics. In this paper, we show that several asynchronous multiplex communication channels can be established in a 2-D mesh neural network with randomly generated weights between eight neighbors. Neurons were simulated by integrate-and-fire neuron models without leakage and with fluctuating refractory period and output delay. If one of the transmitting neuron groups is stimulated, the signal is propagated in the form of spike waves. The corresponding receiving neuron group is able to identify the signal after having learned to form an asynchronous multiplex communication channel. The channel is composed of many intermediate/interstitial neurons working as relays. Each neuron can work as an I/O and as a relay element, i.e., as a multiuse unit. Grouping and synchronic firing is often seen in natural neuronal networks and seems to be effective for stable/robust communication in conjunction with spatial multiplex communication. This communication pattern corresponds to our wet lab experiments on cultured neuronal networks and is similar to sound identification by the ear and mobile adaptive communication systems.

Sample-level sound synthesis with recurrent neural networks and conceptors

Conceptors are a recent development in the field of reservoir computing; they can be used to influence the dynamics of recurrent neural networks (RNNs), enabling generation of arbitrary patterns based on training data. Conceptors allow interpolation and extrapolation between patterns, and also provide a system of boolean logic for combining patterns together. Generation and manipulation of arbitrary patterns using conceptors has significant potential as a sound synthesis method for applications in computer music but has yet to be explored. Conceptors are untested with the generation of multi-timbre audio patterns, and little testing has been done on scalability to longer patterns required for audio. A novel method of sound synthesis based on conceptors is introduced. Conceptular Synthesis is based on granular synthesis; sets of conceptors are trained to recall varying patterns from a single RNN, then a runtime mechanism switches between them, generating short patterns which are recombined into a longer sound. The quality of sound resynthesis using this technique is experimentally evaluated. Conceptor models are shown to resynthesise audio with a comparable quality to a close equivalent technique using echo state networks with stored patterns and output feedback. Conceptor models are also shown to excel in their malleability and potential for creative sound manipulation, in comparison to echo state network models which tend to fail when the same manipulations are applied. Examples are given demonstrating creative sonic possibilities, by exploiting conceptor pattern morphing, boolean conceptor logic and manipulation of RNN dynamics. Limitations of conceptor models are revealed with regards to reproduction quality, and pragmatic limitations are also shown, where rises in computation and memory requirements preclude the use of these models for training with longer sound samples. The techniques presented here represent an initial exploration of the sound synthesis potential of conceptors, demonstrating possible creative applications in sound design; future possibilities and research questions are outlined.

Performance optimization research of reservoir computing system based on an optical feedback semiconductor laser under electrical information injection

Via Santa Fe time series prediction and nonlinear channel equalization tasks, the performances of a reservoir computing (RC) system based on an optical feedback semiconductor laser (SL) under electrical information injection are numerically investigated. The simulated results show that the feedback delay time and strength seriously affect the performances of this RC system. By adopting a current-related optimized feedback delay time and strength, the RC can achieve a good performance for an SL biased within a wide region of 1.1-3.5 times its threshold. The prediction errors are smaller than 0.01 when implementing the Santa Fe tests, and the symbol error rates (SERs) are very low on the order of 10^-5 for accomplishing nonlinear channel equalization tests under a signal-to-noise ratio (SNR) of 32 dB. Moreover, under a given RC performance level, the information processing rate of the RC can be improved by increasing the SL current.

Recent advances in physical reservoir computing: A review

Reservoir computing is a computational framework suited for temporal/sequential data processing. It is derived from several recurrent neural network models, including echo state networks and liquid state machines. A reservoir computing system consists of a reservoir for mapping inputs into a high-dimensional space and a readout for pattern analysis from the high-dimensional states in the reservoir. The reservoir is fixed and only the readout is trained with a simple method such as linear regression and classification. Thus, the major advantage of reservoir computing compared to other recurrent neural networks is fast learning, resulting in low training cost. Another advantage is that the reservoir without adaptive updating is amenable to hardware implementation using a variety of physical systems, substrates, and devices. In fact, such physical reservoir computing has attracted increasing attention in diverse fields of research. The purpose of this review is to provide an overview of recent advances in physical reservoir computing by classifying them according to the type of the reservoir. We discuss the current issues and perspectives related to physical reservoir computing, in order to further expand its practical applications and develop next-generation machine learning systems.

Fiber echo state network analogue for high-bandwidth dual-quadrature signal processing

All-optical platforms for recurrent neural networks can offer higher computational speed and energy efficiency. To produce a major advance in comparison with currently available digital signal processing methods, the new system would need to have high bandwidth and operate both signal quadratures (power and phase). Here we propose a fiber echo state network analogue (FESNA) - the first optical technology that provides both high (beyond previous limits) bandwidth and dual-quadrature signal processing. We demonstrate applicability of the designed system for prediction tasks and for the mitigation of distortions in optical communication systems with multilevel dual-quadrature encoded signals.

Temporal pattern recognition with delayed feedback spin-torque nano-oscillators

The recent demonstration of neuromorphic computing with spin-torque nano-oscillators has opened a path to energy efficient data processing. The success of this demonstration hinged on the intrinsic short-term memory of the oscillators. In this study, we extend the memory of the spin-torque nano-oscillators through time-delayed feedback. We leverage this extrinsic memory to increase the efficiency of solving pattern recognition tasks that require memory to discriminate different inputs. The large tunability of these non-linear oscillators allows us to control and optimize the delayed feedback memory using different operating conditions of applied current and magnetic field.

Photonic machine learning implementation for signal recovery in optical communications

Machine learning techniques have proven very efficient in assorted classification tasks. Nevertheless, processing time-dependent high-speed signals can turn into an extremely challenging task, especially when these signals have been nonlinearly distorted. Recently, analogue hardware concepts using nonlinear transient responses have been gaining significant interest for fast information processing. Here, we introduce a simplified photonic reservoir computing scheme for data classification of severely distorted optical communication signals after extended fibre transmission. To this end, we convert the direct bit detection process into a pattern recognition problem. Using an experimental implementation of our photonic reservoir computer, we demonstrate an improvement in bit-error-rate by two orders of magnitude, compared to directly classifying the transmitted signal. This improvement corresponds to an extension of the communication range by over 75%. While we do not yet reach full real-time post-processing at telecom rates, we discuss how future designs might close the gap.

Polarization chaos and random bit generation in nonlinear fiber optics induced by a time-delayed counter-propagating feedback loop

In this manuscript, we experimentally and numerically investigate the chaotic dynamics of the state-of-polarization in a nonlinear optical fiber due to the cross-interaction between an incident signal and its intense backward replica generated at the fiber-end through an amplified reflective delayed loop. Thanks to the cross-polarization interaction between the two-delayed counter-propagating waves, the output polarization exhibits fast temporal chaotic dynamics, which enable a powerful scrambling process with moving speeds up to 600-krad/s. The performance of this all-optical scrambler was then evaluated on a 10-Gbit/s On/Off Keying telecom signal achieving an error-free transmission. We also describe how these temporal and chaotic polarization fluctuations can be exploited as an all-optical random number generator. To this aim, a billion-bit sequence was experimentally generated and successfully confronted to the dieharder benchmarking statistic tools. Our experimental analysis are supported by numerical simulations based on the resolution of counter-propagating coupled nonlinear propagation equations that confirm the observed behaviors.

Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity

We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.

Reservoir Computing Beyond Memory-Nonlinearity Trade-off

Reservoir computing is a brain-inspired machine learning framework that employs a signal-driven dynamical system, in particular harnessing common-signal-induced synchronization which is a widely observed nonlinear phenomenon. Basic understanding of a working principle in reservoir computing can be expected to shed light on how information is stored and processed in nonlinear dynamical systems, potentially leading to progress in a broad range of nonlinear sciences. As a first step toward this goal, from the viewpoint of nonlinear physics and information theory, we study the memory-nonlinearity trade-off uncovered by Dambre et al. (2012). Focusing on a variational equation, we clarify a dynamical mechanism behind the trade-off, which illustrates why nonlinear dynamics degrades memory stored in dynamical system in general. Moreover, based on the trade-off, we propose a mixture reservoir endowed with both linear and nonlinear dynamics and show that it improves the performance of information processing. Interestingly, for some tasks, significant improvements are observed by adding a few linear dynamics to the nonlinear dynamical system. By employing the echo state network model, the effect of the mixture reservoir is numerically verified for a simple function approximation task and for more complex tasks.

Neuromorphic photonic networks using silicon photonic weight banks

Photonic systems for high-performance information processing have attracted renewed interest. Neuromorphic silicon photonics has the potential to integrate processing functions that vastly exceed the capabilities of electronics. We report first observations of a recurrent silicon photonic neural network, in which connections are configured by microring weight banks. A mathematical isomorphism between the silicon photonic circuit and a continuous neural network model is demonstrated through dynamical bifurcation analysis. Exploiting this isomorphism, a simulated 24-node silicon photonic neural network is programmed using “neural compiler” to solve a differential system emulation task. A 294-fold acceleration against a conventional benchmark is predicted. We also propose and derive power consumption analysis for modulator-class neurons that, as opposed to laser-class neurons, are compatible with silicon photonic platforms. At increased scale, Neuromorphic silicon photonics could access new regimes of ultrafast information processing for radio, control, and scientific computing.