Prediction performance of reservoir computing systems based on a diode-pumped erbium-doped microchip laser subject to optical feedback

Abstract

Reservoir computing (RC) systems are computational tools for information processing that can be fully implemented in optics. Here, we experimentally and numerically show that an optically pumped laser subject to optical delayed feedback can yield similar results to those obtained for electrically pumped lasers. Unlike with previous implementations, the input data are injected at a time interval that is much larger than the time-delay feedback. These data are directly coupled to the feedback light beam. Our results illustrate possible new avenues for RC implementations for prediction tasks. Reservoir computing (RC) is a brain-inspired concept for information processing that has been recently demonstrated to be efficient for solving practical time-dependent tasks [1,2]. RC systems operate by ensuring nonlinear mapping between the input and the output, thereby allowing a variety of information processing through training. To perform well, an RC system typically requires high dimensionality and nonlinearity. Traditionally, high dimensionality is obtained by randomly interconnecting a large number of neurons, while the needed nonlinearity can be implemented through sigmoidal activation functions. For example, with an ensemble of 16 interconnected semiconductor optical amplifiers, state-of-the-art performance has been achieved [3].Alternatively, state-of-the-art performance also has been obtained by relying on a single dynamical nonlinear node subject to delayed feedback [4]. This configuration (typically referred to as the delay-based RC) has the advantage of being easy to train and to implement experimentally. It has led to several implementations, even at high processing speeds, using stand-alone commercial telecommunication components [5][6][7][8]. The main differences between these experiments are the type of nonlinearity used and how the input matches with the period of the delay line. In those implementations, the nonlinear response of the reservoir is provided by passive nonlinearity such as saturable absorption of a semiconductor mirror [9][10][11] or by active devices such as optoelectronic modulators [5,8], optical amplifiers [3], or semiconductor lasers [7]. These experiments have been supported by numerical simulations [8,[12][13][14][15]. Numerical simulations also have shown that the different modes of multimode lasers subject to optical delayed feedback can be used independently to process independent tasks in parallel [16]. In all cases, the readout layer is trained (using some form of regression) from the state vectors of the reservoir in response to the training data.Until now, only one experiment has been dedicated to RC systems, in which the processing was done from the response provided by a laser subject to optical delayed feedback [7]. The laser used in this experiment was an electrically pumped singlelongitudinal-mode laser, and the input data were either electrically injected by modulating the pump current or optically injected into the reservoir through optical injection using another laser....

Limitations of the Recall Capabilities in Delay-Based Reservoir Computing Systems

“…Many different realizations have been presented in the last years, ranging from a bucket of water [4] over field programmable gate arrays (FPGAs) [5] to dissociated neural cell cultures [6], being used for satellite communications [7], real-time audio processing [8,9], bit-error correction for optical data transmission [10], amplitude of chaotic laser pulse prediction [11] and cross-predicting the dynamics of an injected laser [12]. Especially opto-electronic [13,14] and optical setups [15][16][17][18][19] were frequently studied because their high speed and low energy consumption make them preferable for hardware realizations.…”

Multiplexed networks: reservoir computing with virtual and real nodes

“…Instead of an extended physical system or large network of single units, this virtual network approach uses a long delay-line to produce a high dimensional phase-space in time. Several groups have successfully implemented such a delay-line based reservoir computer using both optic [16][17][18] and opto-electronic [19,20] experiments. Possible extensions to the virtual network scheme have also been considered, among others are hierarchical time-multiplexing [21] or the use of counter-propagating fields in a ring laser for simultaneous tasks [22].…”

Enhanced performances of a photonic reservoir computer based on a single delayed quantum cascade laser

“…Delay systems provide an exciting prospect for the implementation of brain-inspired computing tools such as reservoir computing (RC) systems to emulate the dynamic complexity traditionally achieved by a network of neurons [1][2][3][4][5][6][7]. These tools can be used to perform a wide variety of time-dependent tasks such as speech recognition [3,4,8] and prediction [1,[3][4][5][6][7]. In Internet technology and multimedia digital communication, for example, high-speed data transmission over wireless channels typically get distorted in amplitude and phase.…”

“…The readout signals are finally weighted such that their linear combination approaches the associated target as closely as possible. The optimal weights are obtained through either an off-line [1][2][3][4][5][6][7] or online [24] training process. An inherent characteristic of QCLs is that the active region consists of a period of Z 0 (where Z 0 is typically 25-35) cascaded gain stages and electron injectors.…”

“…The considered chaotic time series, referred to as Santa Fe time series, are experimentally recorded data from a far-infrared laser operating in a chaotic state. This data is available online [26] and has been widely used in machine learning [3][4][5][6][7]. The goal for this task is to predict the next sample in a chaotic time trace before it has been injected into the RC system.…”