Multifunctionality is a well observed phenomenological feature of biological neural networks and considered to be of fundamental importance to the survival of certain species over time. These multifunctional neural networks are capable of performing more than one task without changing any network connections. In this paper we investigate how this neurological idiosyncrasy can be achieved in an artificial setting with a modern machine learning paradigm known as `Reservoir Computing'. A training technique is designed to enable a Reservoir Computer to perform tasks of a multifunctional nature. We explore the critical effects that changes in certain parameters can have on the Reservoir Computers' ability to express multifunctionality. We also expose the existence of several `untrained attractors'; attractors which dwell within the prediction state space of the Reservoir Computer that were not part of the training. We conduct a bifurcation analysis of these untrained attractors and discuss the implications of our results.
University College Cork（科克大学学院）；Ludwig-Maximilians University Munich（慕尼黑路德维希-马克西米利安大学）；Collins Aerospace（柯林斯航空航天公司）；Deutsches Zentrum für Luft-und Raumfahrt（德国航空航天中心）
Multifunctional neural networks are capable of performing more than one task without changing any network connections. In this paper we explore the performance of a continuous-time, leaky-integrator, and next-generation `reservoir computer' (RC), when trained on tasks which test the limits of multifunctionality. In the first task we train each RC to reconstruct a coexistence of chaotic attractors from different dynamical systems. By moving the data describing these attractors closer together, we find that the extent to which each RC can reconstruct both attractors diminishes as they begin to o…
Université Libre de Bruxelles（布鲁塞尔自由大学）；Ghent University（根特大学）
Reservoir computing is a new, powerful and flexible machine learning technique that is easily implemented in hardware. Recently, by using a time-multiplexed architecture, hardware reservoir computers have reached performance comparable to digital implementations. Operating speeds allowing for real time information operation have been reached using optoelectronic systems. At present the main performance bottleneck is the readout layer which uses slow, digital postprocessing. We have designed an analog readout suitable for time-multiplexed optoelectronic reservoir computers, capable of working i…
Reservoir computing is a neural network approach for processing time-dependent signals that has seen rapid development in recent years. Physical implementations of the technique using optical reservoirs have demonstrated remarkable accuracy and processing speed at benchmark tasks. However, these approaches require an electronic output layer to maintain high performance, which limits their use in tasks such as time-series prediction, where the output is fed back into the reservoir. We present here a reservoir computing scheme that has rapid processing speed both by the reservoir and the output …
Wyant College of Optical Sciences, University of Arizona（亚利桑那大学怀恩特光学科学学院）；School of Electrical Engineering and Telecommunications, University of New South Wales（新南威尔士大学电气工程与电信学院）
The University of Sydney（悉尼大学）；Humboldt-University of Berlin（柏林洪堡大学）；Bielefeld University（比勒费尔德大学）；National Research Council of Canada（加拿大国家研究委员会）
Differentiable neural computers extend artificial neural networks with an explicit memory without interference, thus enabling the model to perform classic computation tasks such as graph traversal. However, such models are difficult to train, requiring long training times and large datasets. In this work, we achieve some of the computational capabilities of differentiable neural computers with a model that can be trained very efficiently, namely an echo state network with an explicit memory without interference. This extension enables echo state networks to recognize all regular languages, inc…
Faculty of Physics, University of Duisburg-Essen（物理系，杜伊斯堡-埃森大学）；DyNaMat, Department of Solid State Sciences, Ghent University（DyNaMat，固态科学系，根特大学）；Senior Principle Engineer, Intel Corp. (Retired)（高级原则工程师，英特尔公司（退休））；Faculty of Physics（物理系）；Center for Nanointegration Duisburg-Essen (CENIDE), University of Duisburg-Essen（杜伊斯堡-埃森纳米集成中心（CENIDE），杜伊斯堡-埃森大学）
Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB)（跨学科物理与复杂系统研究所 (IFISC (CSIC-UIB))）；The University of Tokyo（东京大学）；The Ohio State University（俄亥俄州立大学）；ResCon Technologies, LLC（ResCon Technologies公司）
Reservoir computers are powerful tools for chaotic time series prediction. They can be trained to approximate phase space flows and can thus both predict future values to a high accuracy, as well as reconstruct the general properties of a chaotic attractor without requiring a model. In this work, we show that the ability to learn the dynamics of a complex system can be extended to systems with co-existing attractors, here a 4-dimensional extension of the well-known Lorenz chaotic system. We demonstrate that a reservoir computer can infer entirely unexplored parts of the phase space: a properly…
Optimizing the Network Topology of a Linear Reservoir Computer
K. N. Toosi University of Technology, Tehran, Iran（德黑兰技术大学）；Catholic University of America, Washington, D.C., United States（美国天主教大学）；University of New Mexico, Albuquerque, NM 87131, United States（新墨西哥大学）；Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany（复杂系统物理研究所）
Potomac Research, LLC（波托马克研究有限责任公司）；The Ohio State University（俄亥俄州立大学）
We propose and demonstrate a nonlinear control method that can be applied to unknown, complex systems where the controller is based on a type of artificial neural network known as a reservoir computer. In contrast to many modern neural-network-based control techniques, which are robust to system uncertainties but require a model nonetheless, our technique requires no prior knowledge of the system and is thus model-free. Further, our approach does not require an initial system identification step, resulting in a relatively simple and efficient learning process. Reservoir computers are well-suit…
What Makes a Bacterial Model a Good Reservoir Computer? Predicting Performance from Separability and Similarity
University Paris Saclay, INRAE, AgroParisTech, MICALIS Institute（巴黎萨克雷大学、法国国家农业研究院、阿格罗巴黎科技大学、MICALIS研究所）；LaBRI, Bordeaux INP, CNRS, UMR 5800, France（LaBRI、波尔多INP、CNRS、UMR 5800、法国）
Identifying Systems with Symmetries using Equivariant Autoregressive Reservoir Computers
Department of Statistics and Research, CNBS（统计与研究系，CNBS）；Department of Applied Mathematics, UNAH（应用数学系，UNAH）；Department of Chemical Engineering, Norwegian University of Science and Technology（化学工程系，挪威科学技术大学）
DTU Electro, Technical University of Denmark（丹麦技术大学DTU Electro）
We propose spectrum-sliced reservoir computer-based (RC) multi-symbol equalization for 32-GBd PAM4 transmission. RC with 17 symbols at the output achieves an order of magnitude reduction in multiplications/symbol versus single output case while maintaining simple training.
The Ohio State University（俄亥俄州立大学）；ResCon Technologies, LLC（ResCon技术有限责任公司）
Forecasting the behavior of high-dimensional dynamical systems using machine learning requires efficient methods to learn the underlying physical model. We demonstrate spatiotemporal chaos prediction using a machine learning architecture that, when combined with a next-generation reservoir computer, displays state-of-the-art performance with a computational time $10^3-10^4$ times faster for training process and training data set $\sim 10^2$ times smaller than other machine learning algorithms. We also take advantage of the translational symmetry of the model to further reduce the computational…
Modeling Nonlinear Oscillator Networks Using Physics-Informed Hybrid Reservoir Computing
University of Bristol, School of Computer Science（布里斯托大学计算机科学学院）；University of Bristol, School of Engineering Mathematics and Technology（布里斯托大学工程数学与技术学院）
The Ohio State University（俄亥俄州立大学）；ResCon Technologies LLC（ResCon技术有限责任公司）；Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB)（跨学科物理与复杂系统研究所（IFISC，西班牙国家研究委员会-巴利阿里群岛大学））；The University of Tokyo（东京大学）
Reservoir computing is a machine learning approach that can generate a surrogate model of a dynamical system. It can learn the underlying dynamical system using fewer trainable parameters and hence smaller training data sets than competing approaches. Recently, a simpler formulation, known as next-generation reservoir computing, removes many algorithm metaparameters and identifies a well-performing traditional reservoir computer, thus simplifying training even further. Here, we study a particularly challenging problem of learning a dynamical system that has both disparate time scales and multi…
Reservoir computers (RC) have proven useful as surrogate models in forecasting and replicating systems of chaotic dynamics. The quality of surrogate models based on RCs is crucially dependent on their optimal implementation that involves selecting optimal reservoir topology and hyperparameters. By systematically applying Bayesian hyperparameter optimization and using ensembles of reservoirs of various topology we show that connectednes of reservoirs is of significance only in forecasting and replication of chaotic system of sufficient complexity. By applying RCs of different topology in foreca…
Hybridizing Traditional and Next-Generation Reservoir Computing to Accurately and Efficiently Forecast Dynamical Systems
University of Maryland（马里兰大学）；University of Chicago（芝加哥大学）；Institute for Research in Electronics and Applied Physics (IREAP)（电子与应用物理研究所）；Institute for Physical Science and Technology (IPST)（物理科学与技术研究所）；Santa Fe Institute（圣达菲研究所）
Exploring the origins of switching dynamics in a multifunctional reservoir computer
School of Mathematical Sciences, University College Cork（科克大学学院数学科学学院）；INFANT Research Centre, University College Cork（科克大学学院INFANT研究中心）；Potsdam Institute for Climate Impact Research（波茨坦气候影响研究所）
We analyze the memory capacity of a delay based reservoir computer with a Hopf normal form as nonlinearity and numerically compute the linear as well as the higher order recall capabilities. A possible physical realisation could be a laser with external cavity, for which the information is fed via electrical injection. A task independent quantification of the computational capability of the reservoir system is done via a complete orthonormal set of basis functions. Our results suggest that even for constant readout dimension the total memory capacity is dependent on the ratio between the infor…
Harnessing Synthetic Active Particles for Physical Reservoir Computing
Peter Debye Institute for Soft Matter Physics, Leipzig University（莱比锡大学彼得·德拜软物质物理研究所）；Center for Scalable Data Analytics and Artificial Intelligence (ScaDS.AI) Dresden/Leipzig（德累斯顿/莱比锡可扩展数据分析与人工智能中心（ScaDS.AI））
Reservoir computers are a type of neuromorphic computer that may be built a an analog system, potentially creating powerful computers that are small, light and consume little power. Typically a reservoir computer is build by connecting together a set of nonlinear nodes into a network; connecting the nonlinear nodes may be difficult or expensive, however. This work shows how a reservoir computer may be expanded by adding functions to its output. The particular functions described here are linear filters, but other functions are possible. The design and construction of linear filters is well kno…
A reservoir computer is a way of using a high dimensional dynamical system for computation. One way to construct a reservoir computer is by connecting a set of nonlinear nodes into a network. Because the network creates feedback between nodes, the reservoir computer has memory. If the reservoir computer is to respond to an input signal in a consistent way (a necessary condition for computation), the memory must be fading; that is, the influence of the initial conditions fades over time. How long this memory lasts is important for determining how well the reservoir computer can solve a particul…
Using the machine learning approach known as reservoir computing, it is possible to train one dynamical system to emulate another. We show that such trained reservoir computers reproduce the properties of the attractor of the chaotic system sufficiently well to exhibit chaos synchronisation. That is, the trained reservoir computer, weakly driven by the chaotic system, will synchronise with the chaotic system. Conversely, the chaotic system, weakly driven by a trained reservoir computer, will synchronise with the reservoir computer. We illustrate this behaviour on the Mackey-Glass and Lorenz sy…
A reservoir computer is a complex dynamical system, often created by coupling nonlinear nodes in a network. The nodes are all driven by a common driving signal. In this work, three dimension estimation methods, false nearest neighbor, covariance and Kaplan-Yorke dimensions, are used to estimate the dimension of the reservoir dynamical system. It is shown that the signals in the reservoir system exist on a relatively low dimensional surface. Changing the spectral radius of the reservoir network can increase the fractal dimension of the reservoir signals, leading to an increase in testing error.
A reservoir computer is a dynamical system that may be used to perform computations. A reservoir computer usually consists of a set of nonlinear nodes coupled together in a network so that there are feedback paths. Training the reservoir computer consists of inputing a signal of interest and fitting the time series signals of the reservoir computer nodes to a training signal that is related to the input signal. It is believed that dynamical systems function most efficiently as computers at the "edge of chaos", the point at which the largest Lyapunov exponent of the dynamical system transitions…
It has been demonstrated that cellular automata had the highest computational capacity at the edge of chaos, the parameter at which their behavior transitioned from ordered to chaotic. This same concept has been applied to reservoir computers; a number of researchers have stated that the highest computational capacity for a reservoir computer is at the edge of chaos, although others have suggested that this rule is not universally true. Because many reservoir computers do not show chaotic behavior but merely become unstable, it is felt that a more accurate term for this instability transition …
This paper addresses the reservoir design problem in the context of delay-based reservoir computers for multidimensional input signals, parallel architectures, and real-time multitasking. First, an approximating reservoir model is presented in those frameworks that provides an explicit functional link between the reservoir parameters and architecture and its performance in the execution of a specific task. Second, the inference properties of the ridge regression estimator in the multivariate context is used to assess the impact of finite sample training on the decrease of the reservoir capacit…
A new class of non-homogeneous state-affine systems is introduced for use in reservoir computing. Sufficient conditions are identified that guarantee first, that the associated reservoir computers with linear readouts are causal, time-invariant, and satisfy the fading memory property and second, that a subset of this class is universal in the category of fading memory filters with stochastic almost surely uniformly bounded inputs. This means that any discrete-time filter that satisfies the fading memory property with random inputs of that type can be uniformly approximated by elements in the n…
Reservoir computing is a bio-inspired computing paradigm for processing time dependent signals. The performance of its analogue implementations matches other digital algorithms on a series of benchmark tasks. Their potential can be further increased by feeding the output signal back into the reservoir, which would allow to apply the algorithm to time series generation. This requires, in principle, implementing a sufficiently fast readout layer for real-time output computation. Here we achieve this with a digital output layer driven by a FPGA chip. We demonstrate the first opto-electronic reser…
Reservoir computing is a brain inspired approach for information processing, well suited to analogue implementations. We report a photonic implementation of a reservoir computer that exploits frequency domain multiplexing to encode neuron states. The system processes 25 comb lines simultaneously (i.e. 25 neurons), at a rate of 20 MHz. We illustrate performances on two standard benchmark tasks: channel equalization and time series forecasting. We also demonstrate that frequency multiplexing allows output weights to be implemented in the optical domain, through optical attenuation. We discuss th…
Biologically inspired recurrent neural networks, such as reservoir computers are of interest in designing spatio-temporal data processors from a hardware point of view due to the simple learning scheme and deep connections to Kalman filters. In this work we discuss using in-depth simulation studies a way to construct hardware reservoir computers using an analog stochastic neuron cell built from a low energy-barrier magnet based magnetic tunnel junction and a few transistors. This allows us to implement a physical embodiment of the mathematical model of reservoir computers. Compact implementati…
Introduction. Reservoir Computing is a bio-inspired computing paradigm for processing time-dependent signals. The performance of its hardware implementation is comparable to state-of-the-art digital algorithms on a series of benchmark tasks. The major bottleneck of these implementation is the readout layer, based on slow offline post-processing. Few analogue solutions have been proposed, but all suffered from notice able decrease in performance due to added complexity of the setup. Methods. Here we propose the use of online training to solve these issues. We study the applicability of this met…
The human brain's synapses have remarkable activity-dependent plasticity, where the connectivity patterns of neurons change dramatically, relying on neuronal activities. As a biologically inspired neural network, reservoir computing (RC) has unique advantages in processing spatiotemporal information. However, typical reservoir architectures only take static random networks into account or consider the dynamics of neurons and connectivity separately. In this paper, we propose a structural autonomous development reservoir computing model (sad-RC), which structure can adapt to the specific proble…
Introduction. Reservoir computing is a growing paradigm for simplified training of recurrent neural networks, with a high potential for hardware implementations. Numerous experiments in optics and electronics yield comparable performance to digital state-of-the-art algorithms. Many of the most recent works in the field focus on large-scale photonic systems, with tens of thousands of physical nodes and arbitrary interconnections. While this trend significantly expands the potential applications of photonic reservoir computing, it also complicates the optimisation of the high number of hyper-par…
Reservoir Computing is a bio-inspired computing paradigm for processing time dependent signals. The performance of its analogue implementation are comparable to other state of the art algorithms for tasks such as speech recognition or chaotic time series prediction, but these are often constrained by the offline training methods commonly employed. Here we investigated the online learning approach by training an opto-electronic reservoir computer using a simple gradient descent algorithm, programmed on an FPGA chip. Our system was applied to wireless communications, a quickly growing domain wit…
This paper extends the notion of information processing capacity for non-independent input signals in the context of reservoir computing (RC). The presence of input autocorrelation makes worthwhile the treatment of forecasting and filtering problems for which we explicitly compute this generalized capacity as a function of the reservoir parameter values using a streamlined model. The reservoir model leading to these developments is used to show that, whenever that approximation is valid, this computational paradigm satisfies the so called separation and fading memory properties that are usuall…
