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 method using numerical simulations of an experimentally feasible reservoir computer with an analogue readout layer. We also consider a nonlinear output layer, which would be very difficult to train with traditional methods. Results. We show numerically that online learning allows to circumvent the added complexity of the analogue layer and obtain the same level of performance as with a digital layer. Conclusion. This work paves the way to high-performance fully-analogue reservoir computers through the use of online training of the output layers.
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…
Photonic reservoir computing with dimensionally compressed readout
Université de Lorraine, CentraleSupélec（洛林大学、中央苏佩莱克）；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）
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…
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…
We propose a deep architecture for the classification of multivariate time series. By means of a recurrent and untrained reservoir we generate a vectorial representation that embeds temporal relationships in the data. To improve the memorization capability, we implement a bidirectional reservoir, whose last state captures also past dependencies in the input. We apply dimensionality reduction to the final reservoir states to obtain compressed fixed size representations of the time series. These are subsequently fed into a deep feedforward network trained to perform the final classification. We …
Recurrent neural network (RNN) based reinforcement learning (RL) is used for learning context-dependent tasks and has also attracted attention as a method with remarkable learning performance in recent research. However, RNN-based RL has some issues that the learning procedures tend to be more computationally expensive, and training with backpropagation through time (BPTT) is unstable because of vanishing/exploding gradients problem. An approach with replay memory introducing reservoir computing has been proposed, which trains an agent without BPTT and avoids these issues. The basic idea of th…
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…
As Moore's law comes to an end, neuromorphic approaches to computing are on the rise. One of these, passive photonic reservoir computing, is a strong candidate for computing at high bitrates (> 10 Gbps) and with low energy consumption. Currently though, both benefits are limited by the necessity to perform training and readout operations in the electrical domain. Thus, efforts are currently underway in the photonic community to design an integrated optical readout, which allows to perform all operations in the optical domain. In addition to the technological challenge of designing such a reado…
Echo state networks (ESN), a type of reservoir computing (RC) architecture, are efficient and accurate artificial neural systems for time series processing and learning. An ESN consists of a core of recurrent neural networks, called a reservoir, with a small number of tunable parameters to generate a high-dimensional representation of an input, and a readout layer which is easily trained using regression to produce a desired output from the reservoir states. Certain computational tasks involve real-time calculation of high-order time correlations, which requires nonlinear transformation either…
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…
Reservoir computing is a bio-inspired computing paradigm for processing time-dependent signals. Its hardware implementations have received much attention because of their simplicity and remarkable performance on a series of benchmark tasks. In previous experiments the output was uncoupled from the system and in most cases simply computed offline on a post-processing computer. However, numerical investigations have shown that feeding the output back into the reservoir would open the possibility of long-horizon time series forecasting. Here we present a photonic reservoir computer with output fe…
The universal approximation properties with respect to $L ^p $-type criteria of three important families of reservoir computers with stochastic discrete-time semi-infinite inputs is shown. First, it is proved that linear reservoir systems with either polynomial or neural network readout maps are universal. More importantly, it is proved that the same property holds for two families with linear readouts, namely, trigonometric state-affine systems and echo state networks, which are the most widely used reservoir systems in applications. The linearity in the readouts is a key feature in supervise…
We propose a novel molecular computing approach based on reservoir computing. In reservoir computing, a dynamical core, called a reservoir, is perturbed with an external input signal while a readout layer maps the reservoir dynamics to a target output. Computation takes place as a transformation from the input space to a high-dimensional spatiotemporal feature space created by the transient dynamics of the reservoir. The readout layer then combines these features to produce the target output. We show that coupled deoxyribozyme oscillators can act as the reservoir. We show that despite using on…
We propose a scalable photonic architecture for implementation of feedforward and recurrent neural networks to perform the classification of handwritten digits from the MNIST database. Our experiment exploits off-the-shelf optical and electronic components to currently achieve a network size of 16,384 nodes. Both network types are designed within the the reservoir computing paradigm with randomly weighted input and hidden layers. Using various feature extraction techniques (e.g. histograms of oriented gradients, zoning, Gabor filters) and a simple training procedure consisting of linear regres…
University of Vienna（维也纳大学）；Ludwig-Maximilians-Universität München（路德维希-马克西米利安慕尼黑大学）；Universität Konstanz（康斯坦茨大学）；Universität Sankt Gallen（圣加仑大学）；Centre National de la Recherche Scientifique (CNRS)（法国国家科学研究中心）；ETH Zürich（苏黎世联邦理工学院）
A new explanation of geometric nature of the reservoir computing phenomenon is presented. Reservoir computing is understood in the literature as the possibility of approximating input/output systems with randomly chosen recurrent neural systems and a trained linear readout layer. Light is shed on this phenomenon by constructing what is called strongly universal reservoir systems as random projections of a family of state-space systems that generate Volterra series expansions. This procedure yields a state-affine reservoir system with randomly generated coefficients in a dimension that is logar…
Dynamical Diversity for Reservoir Computing in Reconfigurable Nanomechanics
International Iberian Nanotechnology Laboratory (INL)（国际伊比利亚纳米技术实验室）；Bilkent University（比尔肯特大学）；UNAM - Institute of Materials Science and Nanotechnology, Bilkent University（比尔肯特大学 UNAM 材料科学与纳米技术研究所）；Sabanci University（萨班奇大学）；Koc University（科奇大学）
Photonic reservoir computing is a promising candidate for low-energy computing at high bandwidths. Despite recent successes, there are bounds to what one can achieve simply by making photonic reservoirs larger. Therefore, a switch from single-reservoir computing to multi-reservoir and even deep physical reservoir computing is desirable. Given that backpropagation can not be used directly to train multi-reservoir systems in our targeted setting, we propose an alternative approach that still uses its power to derive intermediate targets. In this work we report our findings on a conducted experim…
Current AI systems at the tactical edge lack the computational resources to support in-situ training and inference for situational awareness, and it is not always practical to leverage backhaul resources due to security, bandwidth, and mission latency requirements. We propose a solution through Deep delay Loop Reservoir Computing (DLR), a processing architecture supporting general machine learning algorithms on compact mobile devices by leveraging delay-loop (DL) reservoir computing in combination with innovative photonic hardware exploiting the inherent speed, and spatial, temporal and wavele…
The implementation of artificial neural networks in hardware substrates is a major interdisciplinary enterprise. Well suited candidates for physical implementations must combine nonlinear neurons with dedicated and efficient hardware solutions for both connectivity and training. Reservoir computing addresses the problems related with the network connectivity and training in an elegant and efficient way. However, important questions regarding impact of reservoir size and learning routines on the convergence-speed during learning remain unaddressed. Here, we study in detail the learning process …
