Novel methods for information processing are highly desired in our information-driven society. Inspired by the brain's ability to process information, the recently introduced paradigm known as 'reservoir computing' shows that complex networks can efficiently perform computation. Here we introduce a novel architecture that reduces the usually required large number of elements to a single nonlinear node with delayed feedback. Through an electronic implementation, we experimentally and numerically demonstrate excellent performance in a speech recognition benchmark. Complementary numerical studies also show excellent performance for a time series prediction benchmark. These results prove that delay-dynamical systems, even in their simplest manifestation, can perform efficient information processing. This finding paves the way to feasible and resource-efficient technological implementations of reservoir computing.

Abstract:We review a novel paradigm that has emerged in analogue neuromorphic optical computing. The goal is to implement a reservoir computer in optics, where information is encoded in the intensity and phase of the optical field. Reservoir computing is a bio-inspired approach especially suited for processing time-dependent information. The reservoir's complex and high-dimensional transient response to the input signal is capable of universal computation. The reservoir does not need to be trained, which makes it very well suited for optics. As such, much of the promise of photonic reservoirs lies in their minimal hardware requirements, a tremendous advantage over other hardware-intensive neural network models. We review the two main approaches to optical reservoir computing: networks implemented with multiple discrete optical nodes and the continuous system of a single nonlinear device coupled to delayed feedback.

Coherent Ising machines (CIMs) constitute a promising approach to solve computationally hard optimization problems by mapping them to ground state searches of the Ising model and implementing them with optical artificial spin-networks. However, while CIMs promise speed-ups over conventional digital computers, they are still challenging to build and operate. Here, we propose and test a concept for a fully programmable CIM, which is based on opto-electronic oscillators subjected to self-feedback. Contrary to current CIM designs, the artificial spins are generated in a feedback induced bifurcation and encoded in the intensity of coherent states. This removes the necessity for nonlinear optical processes or large external cavities and offers significant advantages regarding stability, size and cost. We demonstrate a compact setup for solving MAXCUT optimization problems on regular and frustrated graphs with 100 spins and can report similar or better performance compared to CIMs based on degenerate optical parametric oscillators.

Reservoir computing is a paradigm in machine learning whose processing capabilities rely on the dynamical behavior of recurrent neural networks. We present a mixed analog and digital implementation of this concept with a nonlinear analog electronic circuit as a main computational unit. In our approach, the reservoir network can be replaced by a single nonlinear element with delay via time-multiplexing. We analyze the influence of noise on the performance of the system for two benchmark tasks: 1) a classification problem and 2) a chaotic time-series prediction task. Special attention is given to the role of quantization noise, which is studied by varying the resolution in the conversion interface between the analog and digital worlds.

Reservoir computing is a novel bio-inspired computing method, capable of solving complex tasks in a computationally efficient way. It has recently been successfully implemented using delayed feedback systems, allowing to reduce the hardware complexity of brain-inspired computers drastically. In this approach, the pre-processing procedure relies on the definition of a temporal mask which serves as a scaled time-mutiplexing of the input. Originally, random masks had been chosen, motivated by the random connectivity in reservoirs. This random generation can sometimes fail. Moreover, for hardware implementations random generation is not ideal due to its complexity and the requirement for trial and error. We outline a procedure to reliably construct an optimal mask pattern in terms of multipurpose performance, derived from the concept of maximum length sequences. Not only does this ensure the creation of the shortest possible mask that leads to maximum variability in the reservoir states for the given reservoir, it also allows for an interpretation of the statistical significance of the provided training samples for the task at hand.

We theoretically investigate the possibility of generating pulses in an excitable (asymmetric) semiconductor ring laser (SRL) using optical trigger pulses. We show that the phase difference between the injected field and the electric field inside the SRL determines the direction of the perturbation in phase space. Due to the folded shape of the excitability threshold, this has an important influence on the ability to cross it. A mechanism for exciting multiple consecutive pulses using a single trigger pulse (i.e., multipulse excitability) is revealed. We furthermore investigate the possibility of using asymmetric SRLs in a coupled configuration, which is a first step toward an all-optical neural network using SRLs as building blocks.

We report the first experimental observation of multistable states in a single-longitudinal mode semiconductor ring laser. We show how the operation of the device can be steered to either monostable, bistable, or multistable dynamical regimes in a controlled way. We observe that the dynamical regimes are organized in well-reproducible sequences that match the bifurcation diagrams of a two-dimensional model. By analyzing the phase space in this model, we predict how the stochastic transitions between multistable states take place and confirm it experimentally.

We study a ring cavity filled with a slab of a right-handed material and a slab of a left-handed material. Both layers are assumed to be nonlinear Kerr media. First, we derive a model for the propagation of light in a left-handed material. By constructing a mean-field model, we show that the sign of diffraction can be made either positive or negative in this resonator, depending on the thicknesses of the layers. Subsequently, we demonstrate that the dynamical behavior of the modulation instability is strongly affected by the sign of the diffraction coefficient. Finally, we study the dissipative structures in this resonator and reveal the predominance of a two-dimensional up-switching process over the formation of spatially periodic structures, leading to the truncation of the homogeneous hysteresis cycle.