25-08-2017, 09:32 PM
Information Processing Using Transient Dynamics of Semiconductor Lasers Subject to Delayed Feedback
Abstract
The increasing amount of data being generated in dif-
ferent areas of science and technology require novel and efficient
techniques of processing, going beyond traditional concepts. In this
paper, we numerically study the information processing capabil-
ities of semiconductor lasers subject to delayed optical feedback.
Based on the recent concept of reservoir computing, we show that
certain tasks, which are inherently hard for traditional computers,
can be efficiently tackled by such systems. Major advantages of this
approach comprise the possibility of simple and low-cost hardware
implementation of the reservoir and ultrafast processing speed. Ex-
perimental results corroborate the numerical predictions.
INTRODUCTION
HE increasing amount of information processing tasks
and the higher demands on the processing techniques
require novel computational concepts that go beyond those
implemented in traditional computers [1], [2]. Nowadays, not
only the application of optics in super-computation is receiving
reawakened interest [3], but also new concepts, partly neuro-
inspired, are being considered and developed [4], [5]. One of
the most promising neuro-inspired concepts is known as reser-
voir computing (RC) (comprising echo state networks [4] and
liquid state machines [6]). Traditional RC is based on the com-
putational power of complex recurrent networks, in particular
utilizing their transient dynamics. A schematic illustration is
given in Fig. 1. These complex networks, usually consist of a
large number (102 –103 ) of randomly connected nonlinear dy-
namical nodes, giving rise to a high-dimensional state space
of the reservoir. Traditionally, the dynamical nodes have mainly
been chosen as artificial neurons, modeled by a transfer function
with a hyperbolic tangent shape.
Spoken Digit Recognition Task
We first evaluate the performance of the system for the spo-
ken digit recognition task. The spoken digit dataset consists of
five female speakers uttering numbers from zero to nine with
a tenfold repetition for statistics (500 samples in total) [19].
Before injecting the information into the laser, we performed
standard preprocessing, creating cochleograms using the Lyon
ear model [20]. The information injected into the laser (S(t)) is
given by the product of the cochleograms (R(t)) and the input
matrix M [7], [11]. For the characterization of the classifica-
tion performance, we evaluate the word error rate (WER) as a
function of some key laser parameters and operating conditions.
It is important to note that for the WER evaluation, we choose
20 random partitions of 25 samples each out of the 500 spo-
ken digits, using 475 samples for training the readout weights,
keeping the remaining 25 for testing. Following this procedure,
each random partition and each sample are used exactly once
for testing (20-fold cross validation).
NUMERICAL RESULTS
In this section, we present numerical results obtained from
the simulations of a semiconductor laser subject to delayed
optical feedback. We study both polarization-maintained and
polarization-rotated feedback, respectively. For comparison, we
use electrical and optical injection for the input signal. In or-
der to compare our results with previously reported studies, we
elaborate on two well-accepted tasks in the machine learning
community: spoken digit recognition and time-series predic-
tion. While the former does not require much memory, and
consequently, the feedback is expected not to play an important
role, the latter is memory dependent and feedback is expected to
be essential. In our numerical analysis, the reservoir consisted
of N = 400 virtual nodes, resulting in a virtual node spacing of
Θ = 200 ps (τec /N ).
CONCLUSION
In conclusion, we have studied the computational capabili-
ties of a semiconductor laser subject to delayed optical feedback.
Our numerical simulations highlight the potential and robust-
ness of the proposed scheme. Moreover, the modeling provides
guidelines for the experimental implementation of the scheme.
Qualitative agreement with first experimental results has been
achieved.
We find that this configuration is offering excellent computa-
tional performance with at the same time low hardware require-
ments, high bandwidth, and low power consumption. The results
obtained for the spoken digit recognition task (WER = 0) are
better to those obtained with a system based on Hidden Marko-
vian Models (0.00168) [26] and with a traditional RC system
(0.005) [27].
For the case of time-series prediction, our numerical results
of NMSE = 0.02 for both PMOF and PROF configurations, a
bias current of Ib = 1.18Ithr and high-power signal injection,
are of the order of those obtained with more traditional tech-
niques (<0.01 [28]), although in the latter additional memory is
artificially added into the input data.