Reservoir Computing is a bio-inspired computing paradigm for processing time dependent signals (Jaeger andHaas 2004; Maass, Natschläger, and Markram 2002). It canbe easily implemented in hardware. The performance ofthese analogue devices matches digital algorithms on a series of benchmark tasks (see e.g. (Soriano et al. 2015) fora review). Their capacities could be extended by feedingthe output signal back into the reservoir, which would allow them to be applied to various signal generation tasks(Antonik et al. 2016b). In practice, this requires a high-speed readout layer for real-time output computation. Herewe achieve this by means of a field-programmable gate array (FPGA), and demonstrate the first photonic reservoircomputer with output feedback. We test our setup on theMackey-Glass chaotic time series generation task and obtain interesting prediction horizons, comparable to numerical simulations, with ample room for further improvement.Our work thus demonstrates the potential offered by the output feedback and opens a new area of novel applications forphotonic reservoir computing.

Reservoir Computing is a bio-inspired computing paradigm for processing time dependent signals. It can be easily implemented in hardware. The performance of these analogue devices matches digital algorithms on a series of benchmark tasks. Their capacities could be extended by feeding the output signal back into the reservoir, which would allow them to be applied to various signal generation tasks. In practice, this requires a high-speed readout layer for real-time output computation. Here we achieve this by means of an FPGA chip, and demonstrate the first photonic reservoir computer with output feedback. We test our setup on the Mackey-Glass chaotic time series generation task and obtain interesting prediction horizons, comparable to numerical simulations, with ample room for further improvement. Our work thus demonstrates the potential offered by the output feedback and opens a new area of novel applications for photonic reservoir computing.

Reservoir computing is a bioinspired computing paradigm for processing time-dependent signals. The performance of its analog implementation is 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 optoelectronic reservoir computer using a simple gradient descent algorithm, programmed on a field-programmable gate array chip. Our system was applied to wireless communications, a quickly growing domain with an increasing demand for fast analog devices to equalize the nonlinear distorted channels. We report error rates up to two orders of magnitude lower than previous implementations on this task. We show that our system is particularly well suited for realistic channel equalization by testing it on a drifting and a switching channel and obtaining good performances.

In the quest for alternatives to traditional complementary metal-oxide-semiconductor, it is being suggested that digital computing efficiency and power can be improved by matching the precision to the application. Many applications do not need the high precision that is being used today. In particular, large gains in area and power efficiency could be achieved by dedicated analog realizations of approximate computing engines. In this work we explore the use of memristor networks for analog approximate computation, based on a machine learning framework called reservoir computing. Most experimental investigations on the dynamics of memristors focus on their nonvolatile behavior. Hence, the volatility that is present in the developed technologies is usually unwanted and is not included in simulation models. In contrast, in reservoir computing, volatility is not only desirable but necessary. Therefore, in this work, we propose two different ways to incorporate it into memristor simulation models. The first is an extension of Strukov's model, and the second is an equivalent Wiener model approximation. We analyze and compare the dynamical properties of these models and discuss their implications for the memory and the nonlinear processing capacity of memristor networks. Our results indicate that device variability, increasingly causing problems in traditional computer design, is an asset in the context of reservoir computing. We conclude that although both models could lead to useful memristor-based reservoir computing systems, their computational performance will differ. Therefore, experimental modeling research is required for the development of accurate volatile memristor models.

Delay-coupled optoelectronic systems form promising candidates to act as powerful information processing devices. In this brief, we consider such a system that has been studied before in the context of reservoir computing (RC). Instead of viewing the system as a random dynamical system, we see it as a true machine-learning model, which can be fully optimized. We use a recently introduced extension of backpropagation through time, an optimization algorithm originally designed for recurrent neural networks, and use it to let the network perform a difficult phoneme recognition task. We show that full optimization of all system parameters of delay-coupled optoelectronics systems yields a significant improvement over the previously applied RC approach.

In the field of neural network simulation techniques, the common conception is that spiking neural network simulators can be divided in two categories: time-step-based and event-driven methods. In this letter, we look at state-of-the art simulation techniques in both categories and show that a clear distinction between both methods is increasingly difficult to define. In an attempt to improve the weak points of each simulation method, ideas of the alternative method are, sometimes unknowingly, incorporated in the simulation engine. Clearly the ideal simulation method is a mix of both methods. We formulate the key properties of such an efficient and generally applicable hybrid approach.

Time series often have a temporal hierarchy, with information that is spread out over multiple time scales. Common recurrent neural networks, however, do not explicitly accommodate such a hierarchy, and most research on them has been focusing on training algorithms rather than on their basic architecture. In this pa- per we study the effect of a hierarchy of recurrent neural networks on processing time series. Here, each layer is a recurrent network which receives the hidden state of the previous layer as input. This architecture allows us to perform hi- erarchical processing on difficult temporal tasks, and more naturally capture the structure of time series. We show that they reach state-of-the-art performance for recurrent networks in character-level language modelling when trained with sim- ple stochastic gradient descent. We also offer an analysis of the different emergent time scales.

Echo state networks (ESNs) are large, random recurrent neural networks with a single trained linear readout layer. Despite the untrained nature of the recurrent weights, they are capable of performing universal computations on temporal input data, which makes them interesting for both theoretical research and practical applications. The key to their success lies in the fact that the network computes a broad set of nonlinear, spatiotemporal mappings of the input data, on which linear regression or classification can easily be performed. One could consider the reservoir as a spatiotemporal kernel, in which the mapping to a high-dimensional space is computed explicitly. In this letter, we build on this idea and extend the concept of ESNs to infinite-sized recurrent neural networks, which can be considered recursive kernels that subsequently can be used to create recursive support vector machines. We present the theoretical framework, provide several practical examples of recursive kernels, and apply them to typical temporal tasks.

Reservoir Computing (RC) is a recently introduced scheme to employ recurrent neural networks while circumventing the difficulties that typically appear when training the recurrent weights. The `reservoir' is a fixed randomly initiated recurrent network which receives input via a random mapping. Only an instantaneous linear mapping from the network to the output is trained which can be done with linear regression. In this paper we study dynamical properties of reservoirs receiving a high number of inputs. More specifically, we investigate how the internal state of the network retains fading memory of its input signal. Memory properties for random recurrent networks have been thoroughly examined in past research, but only for one-dimensional input. Here we take into account statistics which will typically occur in high dimensional signals. We find useful empirical data which expresses how memory in recurrent networks is distributed over the individual principal components of the input.

Recurrent neural networks are very powerful engines for processing information that is coded in time, however, many problems with common training algorithms, such as Backpropagation Through Time, remain. Because of this, another important learning setup known as Reservoir Computing has appeared in recent years, where one uses an essentially untrained network to perform computations. Though very successful in many applications, using a random network can be quite inefficient when considering the required number of neurons and the associated computational costs. In this paper we introduce a highly simplified version of Backpropagation Through Time by basically truncating the error backpropagation to one step back in time, and we combine this with the classic Reservoir Computing setup using an instantaneous linear readout. We apply this setup to a spoken digit recognition task and show it to give very good results for small networks.