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In today's age, companies employ machine learning to extract information from large quantities of data. One of those techniques, reservoir computing (RC), is a decade old and has achieved state-of-the-art performance for processing sequential data. Dedicated hardware realizations of RC could enable speed gains and power savings. Here we propose the first integrated passive silicon photonics reservoir. We demonstrate experimentally and through simulations that, thanks to the RC paradigm, this generic chip can be used to perform arbitrary Boolean logic operations with memory as well as 5-bit header recognition up to 12.5 Gbit s À 1 , without power consumption in the reservoir. It can also perform isolated spoken digit recognition. Our realization exploits optical phase for computing. It is scalable to larger networks and much higher bitrates, up to speeds 4100 Gbit s À 1 . These results pave the way for the application of integrated photonic RC for a wide range of applications.

Many dynamical systems, both natural and artificial, are stimulated by time dependent external signals, somehow processing the information contained therein. We demonstrate how to quantify the different modes in which information can be processed by such systems and combine them to define the computational capacity of a dynamical system. This is bounded by the number of linearly independent state variables of the dynamical system, equaling it if the system obeys the fading memory condition. It can be interpreted as the total number of linearly independent functions of its stimuli the system can compute. Our theory combines concepts from machine learning (reservoir computing), system modeling, stochastic processes, and functional analysis. We illustrate our theory by numerical simulations for the logistic map, a recurrent neural network, and a two-dimensional reaction diffusion system, uncovering universal trade-offs between the non-linearity of the computation and the system's short-term memory.

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Reservoir computing (RC), a computational paradigm inspired on neural systems, has become increasingly popular in recent years for solving a variety of complex recognition and classification problems. Thus far, most implementations have been software-based, limiting their speed and power efficiency. Integrated photonics offers the potential for a fast, power efficient and massively parallel hardware implementation. We have previously proposed a network of coupled semiconductor optical amplifiers as an interesting test case for such a hardware implementation. In this paper, we investigate the important design parameters and the consequences of process variations through simulations. We use an isolated word recognition task with babble noise to evaluate the performance of the photonic reservoirs with respect to traditional software reservoir implementations, which are based on leaky hyperbolic tangent functions. Our results show that the use of coherent light in a well-tuned reservoir architecture offers significant performance benefits. The most important design parameters are the delay and the phase shift in the system's physical connections. With optimized values for these parameters, coherent semiconductor optical amplifier (SOA) reservoirs can achieve better results than traditional simulated reservoirs. We also show that process variations hardly degrade the performance, but amplifier noise can be detrimental. This effect must therefore be taken into account when designing SOA-based RC implementations.

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We propose photonic reservoir computing as a new approach to optical signal processing in the context of large scale pattern recognition problems. Photonic reservoir computing is a photonic implementation of the recently proposed reservoir computing concept, where the dynamics of a network of nonlinear elements are exploited to perform general signal processing tasks. In our proposed photonic implementation, we employ a network of coupled Semiconductor Optical Amplifiers (SOA) as the basic building blocks for the reservoir. Although they differ in many key respects from traditional software-based hyperbolic tangent reservoirs, we show using simulations that such a photonic reservoir can outperform traditional reservoirs on a benchmark classification task. Moreover, a photonic implementation offers the promise of massively parallel information processing with low power and high speed.

Embodiment has led to a revolution in robotics by not thinking of the robot body and its controller as two separate units, but taking into account the interaction of the body with its environment. By investigating the effect of the body on the overall control computation, it has been suggested that the body is effectively performing computations, leading to the term morphological computation. Recent work has linked this to the field of reservoir computing, allowing one to endow morphologies with a theory of universal computation. In this work, we study a family of highly dynamic body structures, called tensegrity structures, controlled by one of the simplest kinds of "brains." These structures can be used to model biomechanical systems at different scales. By analyzing this extreme instantiation of compliant structures, we demonstrate the existence of a spectrum of choices of how to implement control in the body-brain composite. We show that tensegrity structures can maintain complex gaits with linear feedback control and that external feedback can intrinsically be integrated in the control loop. The various linear learning rules we consider differ in biological plausibility, and no specific assumptions are made on how to implement the feedback in a physical system.