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 of a recently demonstrated photonic neural network based on a reservoir. We use a greedy algorithm to train our neural network for the task of chaotic signals prediction and analyze the learning-error landscape. Our results unveil fundamental properties of the system's optimization hyperspace. Particularly, we determine the convergence speed of learning as a function of reservoir size and find exceptional, close to linear scaling. This linear dependence, together with our parallel diffractive coupling, represent optimal scaling conditions for our photonic neural network scheme.
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 …
Reservoir computing is a recently introduced, highly efficient bio-inspired approach for processing time dependent data. The basic scheme of reservoir computing consists of a non linear recurrent dynamical system coupled to a single input layer and a single output layer. Within these constraints many implementations are possible. Here we report an opto-electronic implementation of reservoir computing based on a recently proposed architecture consisting of a single non linear node and a delay line. Our implementation is sufficiently fast for real time information processing. We illustrate its p…
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…
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…
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…
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…
Graduate school of Systems and Information Engineering（系统与信息工程研究生院）；University of Tsukuba（筑波大学）
Recently, reinforcement learning models have achieved great success, mastering complex tasks such as Go and other games with higher scores than human players. Many of these models store considerable data on the tasks and achieve high performance by extracting visual and time-series features using convolutional neural networks (CNNs) and recurrent neural networks, respectively. However, these networks have very high computational costs because they need to be trained by repeatedly using the stored data. In this study, we propose a novel practical approach called reinforcement learning with conv…
University Medical Center Hamburg-Eppendorf (UKE)（汉堡-埃彭多夫大学医学中心（UKE））；Jacobs University gGmbH（雅各布大学gGmbH）
The reservoir computing paradigm is employed to classify heartbeat anomalies online based on electrocardiogram signals. Inspired by the principles of information processing in the brain, reservoir computing provides a framework to design, train, and analyze recurrent neural networks (RNNs) for processing time-dependent information. Due to its computational efficiency and the fact that training amounts to a simple linear regression, this supervised learning algorithm has been variously considered as a strategy to implement useful computations not only on digital computers but also on emerging u…
School of Computer Science University of St. Gallen（圣加尔登大学计算机科学学院）；Donostia International Physics Center（多尼亚国际物理中心）；Department of Mathematics, Imperial College（帝国理工学院数学系）；School of Physical and Mathematical Sciences Nanyang Technological University（南洋理工大学物理与数学科学学院）
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…
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…
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…
Backpropagation algorithms on recurrent artificial neural networks require an unfolding of accumulated states over time. These states must be kept in memory for an undefined period of time which is task-dependent. This paper uses the reservoir computing paradigm where an untrained recurrent neural network layer is used as a preprocessor stage to learn temporal and limited data. These so-called reservoirs require either extensive fine-tuning or neuroplasticity with unsupervised learning rules. We propose a new local plasticity rule named P-CRITICAL designed for automatic reservoir tuning that t…
