Linear photonic reservoir computer based on
coherently driven passive cavity Quentin Vinckier1, François Duport1, Anteo Smerieri1, Kristof Vandoorne2, Peter Bienstman2, Marc Haelterman1 et Serge Massar3
1 Service OPERA-Photonique, CP 194/5, Université Libre de Bruxelles (U.L.B.), avenue F.D. Roosevelt 50,1050 Bruxelles, Belgique
2 Photonics Research Group, Dept. of Information Technology, Ghent University – IMEC, Sint-Pietersnieuwstraat 41, 9000 Gent, Belgium
3 Laboratoire d’Information Quantique, CP 225, Université Libre de Bruxelles (U.L.B.), Boulevard du Triomphe, 1050 Bruxelles, Belgique
We present the first experimental implementation of a passive linear reservoir computer working in coherent light for analogue
signal processing. By using an optical cavity, the neuron states are coded by temporal multiplexing in the amplitude and the
phase of a coherent electromagnetic field. We report the performances obtained with our experimental setup compared to
simulations on some benchmark tasks. In the future, our goal will be to realise a high-speed implementation of our system in
integrated photonics.
Abstract
Experimental setup
Acknowledgements: Fonds pour la formation à la Recherche dans l’Industrie et dans l’Agriculture (FRIA, Belgique), the Photonics@be project of
the Interuniversity Attraction Poles Photonics@be Program (Belgian Science Policy) and the Fond de la Recherche Scientifique FRS-FNRS.
- September 2014 -
Sequential processing of the neurons coded in A(t)
The nonlinearity, provided by a photodiode, is in the output layer
Computer post-processing (for the readout weights)
N+1 neurons
in 1 round-
trip time
2 steps:
1 Training: the readout weights Wi are
optimised by Ridge regression to
minimize (𝑦 𝑡 − 𝑦(𝑡))²𝑡2𝑡1 , where
y(t) is the desired output.
2 Testing: the readout weights Wi are
kept fixed. Evaluation of 𝑦 (𝑡) and
the error (NMSE).
- Traditional Recurrent Neural
Network: Mask Mi, aij and Wi are
optimised.
- Reservoir Computer: only the
readout weights Wi are optimised:
Mask Mi and aij are randomly
chosen.
Next step: analog readout
Goals:
No digital post-
processing
Rapidity
Goal: Differentiate digits spoken 10 times by 5 female speakers.
Inputs of the reservoir: pre-processed signals according to the Lyon
Ear Model.
We’ve presented the first experimental passive all-optical linear
reservoir computer working with coherent light for analogue
signal processing. The performances are state of the art for all
the benchmark tasks that we tested. The next step will be to
implement an analog readout layer. In the future, the challenge
will be to realise a high-speed implementation of our system on
a chip.
Conclusion
Memory Capacities Speech Recognition Task
Channel Equalization Task Radar Task
𝒒 𝒕 = 0.08𝑑 𝑡 + 2 − 0.12𝑑 𝑡 + 1 +d(t) +0.18d(t-1)-0.1d(t-2)+0.091d(t-3)-0.05d(t-4) +0.04d(t-5)+0.03d(t-6)+0.01d(t-7) e (t ) =q(t)+0.036q²(t)-0.011q³(t)+noise
Goal: Recover an input symbol
sequence d(t), at the output e(t) of a
standardised nonlinear multipath
RF channel defined as follows:
LMF(k):
P(e(t-k))=e(t-k)
CL= LMF(k)𝑘𝑚𝑎𝑥𝑘=0
CL=
Memory Function MF = 1-NMSE ∈ [0,1] : ability to recall P(e(t-k))
QMF(k):
P(e(t-k))=3e2(t-k)-1
CQ= QMF(k)𝑘𝑚𝑎𝑥𝑘=0
CQ=
XMF(k,k’):
P(e(t-k),e(t-k’))=e(t-k)e(t-k’)
CX= XMF(k,k′)𝑘′𝑚𝑎𝑥𝑘′=0𝑘′≠𝑘
𝑘𝑚𝑎𝑥𝑘=0
CX=
Input data from soma.ece.mcmaster.ca/ipix/
Goal: Predict the X-band (λ=3 cm)
radar signal reflected from the sea
surface.
2 inputs: in-phase and quadrature
components of the reflected signal
(VV polarization).
With 50 neurons and 10 data
samples of 6000 symbols
With 50 neurons
and 10 data samples
of 2200 inputs
Word Error Rate using 5 data samples of 100 digits
200 neurons, no noise
500 neurons, SNR = 3dB
Experimental performances compared to simulations:
Results are state of the art
Will be partially integrated on a chip
With 50 neurons and 10 data
samples of 1000 inputs
Recurrent Neural Network:
« The Reservoir »
Input Signal 𝑒(𝑡)
Input Mask
Mi 𝐸𝑖 𝑡 = 𝑀𝑖 . 𝑒 𝑡
Neuron
States
𝑥𝑖(𝑡)
Readout
Weights
𝑊𝑖 Output Signal
𝑦 𝑡 = 𝑊𝑖 . 𝑥𝑖(𝑡)
𝑖
𝑥𝑖(t)=FNL 𝛽𝐸𝑖 𝑡 + 𝑏𝑖𝑎𝑠 + 𝛼𝑎𝑖𝑗𝑥𝑗(𝑡 − 1)
𝑗
𝑎𝑖𝑗
𝑎𝑖𝑗
=0
=1
Experimental performances compared to simulations:
Results are state of the art
Reservoir computer principle:
a non traditional neural network
Simulation WER= 0% WER= 0.6(+0.9)%
Experiment WER=0% WER=0.8(+0.8)%
• Simulation
• Experiment
Linear memory Quadratic memory Cross memory Total Memory
22.61+ 0.07 13.25+ 0.23 33.90+ 0.82
21.14+ 0.34 12.07+ 0.10 30.20+ 0.46
C=CL+CQ+CX
C=
* With 10 data samples of 60000
inputs
49.99+ 0.13 *
48.37+ 0.47