Abstract

Reservoir computing is a recent bio-inspired approach for processing time-dependent signals. It has enabled a breakthrough in analog information processing, with several experiments, both electronic and optical, demonstrating state-of-the-art performance for hard tasks such as speech recognition, time series prediction, and nonlinear channel equalization. A proof-of-principle experiment using a linear optical circuit on a photonic chip to process digital signals was recently reported. Here we present a photonic implementation of a reservoir computer based on a coherently driven passive fiber cavity processing analog signals. Our experiment has error rate as low as or lower than previous experiments on a wide variety of tasks, and also has lower power consumption. Furthermore, the analytical model describing our experiment is also of interest, as it constitutes a very simple high-performance reservoir computer algorithm. The present experiment, given its good performance, low energy consumption, and conceptual simplicity, confirms the great potential of photonic reservoir computing for information processing applications ranging from artificial intelligence to telecommunications.

© 2015 Optical Society of America

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References

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2015 (1)

M. C. Soriano, S. Ortin, L. Keuninckx, L. Appeltant, J. Danckaert, L. Pesquera, G. Van Der Sande, “Delay-based reservoir computing: noise effects in a combined analog and digital implementation,” IEEE Trans. Neural Netw. Learn. Syst. 26, 388–393 (2015).
[Crossref]

2014 (6)

L. Appeltant, G. Van der Sande, J. Danckaert, I. Fischer, “Constructing optimized binary masks for reservoir computing with delay systems,” Sci. Rep. 4, 3629 (2014).
[Crossref]

M. A. A. Fiers, T. Van Varenbergh, F. Wyffels, D. Verstraeten, B. Schrauwen, J. Dambre, P. Bienstman, “Nanophotonic reservoir computing with photonic crystal cavities to generate periodic patterns,” IEEE Trans. Neural Netw. Learn. Syst. 25, 344–355 (2014).
[Crossref]

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun 5, 3541 (2014).
[Crossref]

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, G. Van der Sande, “Fast photonic information processing using semiconductor lasers with delayed optical feedback: role of phase dynamics,” Opt. Express 22, 8672–8686 (2014).
[Crossref]

A. Dejonckheere, F. Duport, A. Smerieri, L. Fang, J.-L. Oudar, M. Haelterman, S. Massar, “All-optical reservoir computer based on saturation of absorption,” Opt. Express 22, 10868–10881 (2014).
[Crossref]

H. Zhang, X. Feng, B. Li, Y. Wang, K. Cui, F. Liu, W. Dou, Y. Huang, “Integrated photonic reservoir computing based on hierarchical time-multiplexing structure,” Opt. Express 22, 31356–31370 (2014).
[Crossref]

2013 (5)

M. C. Soriano, S. Ortín, D. Brunner, L. Larger, C. R. Mirasso, I. Fischer, L. Pesquera, “Optoelectronic reservoir computing: tackling noise-induced performance degradation,” Opt. Express 21, 12–20 (2013).
[Crossref]

C. Mesaritakis, V. Papataxiarhis, D. Syvridis, “Micro ring resonators as building blocks for an all-optical high-speed reservoir-computing bit-pattern-recognition system,” J. Opt. Soc. Am. B 30, 3048–3055 (2013).
[Crossref]

D. Brunner, M. C. Soriano, C. R. Mirasso, I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nat. Commun. 4, 1364 (2013).
[Crossref]

D. Brunner, M. C. Soriano, I. Fischer, “High-speed optical vector and matrix operations using a semiconductor laser,” IEEE Photon. Technol. Lett. 25, 1680–1683 (2013).
[Crossref]

K. Hicke, M. A. Escalona-Moran, D. Brunner, M. C. Soriano, I. Fischer, C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19, 1501610 (2013).
[Crossref]

2012 (7)

J. Dambre, D. Verstraeten, B. Schrauwen, S. Massar, “Information processing capacity of dynamical systems,” Sci. Rep. 2, 514 (2012).
[Crossref]

R. Martinenghi, S. Rybalko, M. Jacquot, Y. K. Chembo, L. Larger, “Photonic nonlinear transient computing with multiple-delay wavelength dynamics,” Phys. Rev. Lett. 108, 244101 (2012).
[Crossref]

L. Boccato, A. Lopes, R. Attux, F. J. Von Zuben, “An extended echo state network using Volterra filtering and principal component analysis,” Neural Networks 32, 292–302 (2012).
[Crossref]

M. Lukoševičius, H. Jaeger, B. Schrauwen, “Reservoir computing trends,” Künstl. Intell. 26, 365–371 (2012).
[Crossref]

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 287 (2012).
[Crossref]

L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutierrez, L. Pesquera, C. R. Mirasso, I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20, 3241–3249 (2012).
[Crossref]

F. Duport, B. Schneider, A. Smerieri, M. Haelterman, S. Massar, “All-optical reservoir computing,” Opt. Express 20, 22783–22795 (2012).
[Crossref]

2011 (3)

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
[Crossref]

P. Buteneers, D. Verstraeten, P. Van Mierlo, T. Wyckhuys, D. Stroobandt, R. Raedt, H. Hallez, B. Schrauwen, “Automatic detection of epileptic seizures on the intra-cranial electroencephalogram of rats using reservoir computing,” Artificial Intelligence Medicine 53, 215–223 (2011).
[Crossref]

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22, 1469–1481 (2011).
[Crossref]

2009 (1)

M. Lukoševičius, H. Jaeger, “Reservoir computing approaches to recurrent neural network training,” Comput. Sci. Rev. 3, 127–149 (2009).
[Crossref]

2008 (2)

E. A. Antonelo, B. Schrauwen, D. Stroobandt, “Event detection and localization for small mobile robots using reservoir computing,” Neural Networks 21, 862–871 (2008).
[Crossref]

K. Vandoorne, W. Dierckx, B. Schrauwen, D. Verstraeten, R. Baets, P. Bienstman, J. Van Campenhout, “Toward optical signal processing using photonic reservoir computing,” Opt. Express 16, 11182–11192 (2008).
[Crossref]

2004 (1)

H. Jaeger, H. Haas, “Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication,” Science 304, 78–80 (2004).
[Crossref]

2002 (1)

W. Maass, T. Natschläger, H. Markram, “Real-time computing without stable states: a new framework for neural computation based on perturbations,” Neural Comput. 14, 2531–2560 (2002).
[Crossref]

Antonelo, E. A.

E. A. Antonelo, B. Schrauwen, D. Stroobandt, “Event detection and localization for small mobile robots using reservoir computing,” Neural Networks 21, 862–871 (2008).
[Crossref]

Appeltant, L.

M. C. Soriano, S. Ortin, L. Keuninckx, L. Appeltant, J. Danckaert, L. Pesquera, G. Van Der Sande, “Delay-based reservoir computing: noise effects in a combined analog and digital implementation,” IEEE Trans. Neural Netw. Learn. Syst. 26, 388–393 (2015).
[Crossref]

L. Appeltant, G. Van der Sande, J. Danckaert, I. Fischer, “Constructing optimized binary masks for reservoir computing with delay systems,” Sci. Rep. 4, 3629 (2014).
[Crossref]

L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutierrez, L. Pesquera, C. R. Mirasso, I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20, 3241–3249 (2012).
[Crossref]

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
[Crossref]

Attux, R.

L. Boccato, A. Lopes, R. Attux, F. J. Von Zuben, “An extended echo state network using Volterra filtering and principal component analysis,” Neural Networks 32, 292–302 (2012).
[Crossref]

L. Boccato, A. Lopes, R. Attux, F. J. Von Zuben, “An echo state network architecture based on Volterra filtering and PCA with application to the channel equalization problem,” in International Joint Conference on Neural Networks (IEEE, 2011), pp. 580–587.

Baets, R.

Bienstman, P.

M. A. A. Fiers, T. Van Varenbergh, F. Wyffels, D. Verstraeten, B. Schrauwen, J. Dambre, P. Bienstman, “Nanophotonic reservoir computing with photonic crystal cavities to generate periodic patterns,” IEEE Trans. Neural Netw. Learn. Syst. 25, 344–355 (2014).
[Crossref]

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun 5, 3541 (2014).
[Crossref]

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22, 1469–1481 (2011).
[Crossref]

K. Vandoorne, W. Dierckx, B. Schrauwen, D. Verstraeten, R. Baets, P. Bienstman, J. Van Campenhout, “Toward optical signal processing using photonic reservoir computing,” Opt. Express 16, 11182–11192 (2008).
[Crossref]

M. Hermans, M. Soriano, J. Dambre, P. Bienstman, I. Fischer, “Photonic delay systems as machine learning implementations,” arXiv:1501.02592v1 (2015).

Boccato, L.

L. Boccato, A. Lopes, R. Attux, F. J. Von Zuben, “An extended echo state network using Volterra filtering and principal component analysis,” Neural Networks 32, 292–302 (2012).
[Crossref]

L. Boccato, A. Lopes, R. Attux, F. J. Von Zuben, “An echo state network architecture based on Volterra filtering and PCA with application to the channel equalization problem,” in International Joint Conference on Neural Networks (IEEE, 2011), pp. 580–587.

Brunner, D.

D. Brunner, M. C. Soriano, C. R. Mirasso, I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nat. Commun. 4, 1364 (2013).
[Crossref]

D. Brunner, M. C. Soriano, I. Fischer, “High-speed optical vector and matrix operations using a semiconductor laser,” IEEE Photon. Technol. Lett. 25, 1680–1683 (2013).
[Crossref]

M. C. Soriano, S. Ortín, D. Brunner, L. Larger, C. R. Mirasso, I. Fischer, L. Pesquera, “Optoelectronic reservoir computing: tackling noise-induced performance degradation,” Opt. Express 21, 12–20 (2013).
[Crossref]

K. Hicke, M. A. Escalona-Moran, D. Brunner, M. C. Soriano, I. Fischer, C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19, 1501610 (2013).
[Crossref]

L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutierrez, L. Pesquera, C. R. Mirasso, I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20, 3241–3249 (2012).
[Crossref]

Buteneers, P.

P. Buteneers, D. Verstraeten, P. Van Mierlo, T. Wyckhuys, D. Stroobandt, R. Raedt, H. Hallez, B. Schrauwen, “Automatic detection of epileptic seizures on the intra-cranial electroencephalogram of rats using reservoir computing,” Artificial Intelligence Medicine 53, 215–223 (2011).
[Crossref]

Chembo, Y. K.

R. Martinenghi, S. Rybalko, M. Jacquot, Y. K. Chembo, L. Larger, “Photonic nonlinear transient computing with multiple-delay wavelength dynamics,” Phys. Rev. Lett. 108, 244101 (2012).
[Crossref]

Cui, K.

Dambre, J.

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun 5, 3541 (2014).
[Crossref]

M. A. A. Fiers, T. Van Varenbergh, F. Wyffels, D. Verstraeten, B. Schrauwen, J. Dambre, P. Bienstman, “Nanophotonic reservoir computing with photonic crystal cavities to generate periodic patterns,” IEEE Trans. Neural Netw. Learn. Syst. 25, 344–355 (2014).
[Crossref]

J. Dambre, D. Verstraeten, B. Schrauwen, S. Massar, “Information processing capacity of dynamical systems,” Sci. Rep. 2, 514 (2012).
[Crossref]

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 287 (2012).
[Crossref]

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
[Crossref]

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22, 1469–1481 (2011).
[Crossref]

M. Hermans, M. Soriano, J. Dambre, P. Bienstman, I. Fischer, “Photonic delay systems as machine learning implementations,” arXiv:1501.02592v1 (2015).

Danckaert, J.

M. C. Soriano, S. Ortin, L. Keuninckx, L. Appeltant, J. Danckaert, L. Pesquera, G. Van Der Sande, “Delay-based reservoir computing: noise effects in a combined analog and digital implementation,” IEEE Trans. Neural Netw. Learn. Syst. 26, 388–393 (2015).
[Crossref]

L. Appeltant, G. Van der Sande, J. Danckaert, I. Fischer, “Constructing optimized binary masks for reservoir computing with delay systems,” Sci. Rep. 4, 3629 (2014).
[Crossref]

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, G. Van der Sande, “Fast photonic information processing using semiconductor lasers with delayed optical feedback: role of phase dynamics,” Opt. Express 22, 8672–8686 (2014).
[Crossref]

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
[Crossref]

Dejonckheere, A.

Dierckx, W.

Dou, W.

Duport, F.

A. Dejonckheere, F. Duport, A. Smerieri, L. Fang, J.-L. Oudar, M. Haelterman, S. Massar, “All-optical reservoir computer based on saturation of absorption,” Opt. Express 22, 10868–10881 (2014).
[Crossref]

F. Duport, B. Schneider, A. Smerieri, M. Haelterman, S. Massar, “All-optical reservoir computing,” Opt. Express 20, 22783–22795 (2012).
[Crossref]

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 287 (2012).
[Crossref]

A. Smerieri, F. Duport, Y. Paquot, B. Schrauwen, M. Haelterman, S. Massar, “Analog readout for optical reservoir computers,” in Advances in Neural Information Processing Systems (2012), Vol. 25, pp. 953–961.

Escalona-Moran, M. A.

K. Hicke, M. A. Escalona-Moran, D. Brunner, M. C. Soriano, I. Fischer, C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19, 1501610 (2013).
[Crossref]

Fang, L.

Feng, X.

Fiers, M.

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun 5, 3541 (2014).
[Crossref]

Fiers, M. A. A.

M. A. A. Fiers, T. Van Varenbergh, F. Wyffels, D. Verstraeten, B. Schrauwen, J. Dambre, P. Bienstman, “Nanophotonic reservoir computing with photonic crystal cavities to generate periodic patterns,” IEEE Trans. Neural Netw. Learn. Syst. 25, 344–355 (2014).
[Crossref]

Fischer, I.

L. Appeltant, G. Van der Sande, J. Danckaert, I. Fischer, “Constructing optimized binary masks for reservoir computing with delay systems,” Sci. Rep. 4, 3629 (2014).
[Crossref]

K. Hicke, M. A. Escalona-Moran, D. Brunner, M. C. Soriano, I. Fischer, C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19, 1501610 (2013).
[Crossref]

D. Brunner, M. C. Soriano, C. R. Mirasso, I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nat. Commun. 4, 1364 (2013).
[Crossref]

D. Brunner, M. C. Soriano, I. Fischer, “High-speed optical vector and matrix operations using a semiconductor laser,” IEEE Photon. Technol. Lett. 25, 1680–1683 (2013).
[Crossref]

M. C. Soriano, S. Ortín, D. Brunner, L. Larger, C. R. Mirasso, I. Fischer, L. Pesquera, “Optoelectronic reservoir computing: tackling noise-induced performance degradation,” Opt. Express 21, 12–20 (2013).
[Crossref]

L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutierrez, L. Pesquera, C. R. Mirasso, I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20, 3241–3249 (2012).
[Crossref]

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
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M. Hermans, M. Soriano, J. Dambre, P. Bienstman, I. Fischer, “Photonic delay systems as machine learning implementations,” arXiv:1501.02592v1 (2015).

Gutierrez, J. M.

Haas, H.

H. Jaeger, H. Haas, “Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication,” Science 304, 78–80 (2004).
[Crossref]

Haelterman, M.

A. Dejonckheere, F. Duport, A. Smerieri, L. Fang, J.-L. Oudar, M. Haelterman, S. Massar, “All-optical reservoir computer based on saturation of absorption,” Opt. Express 22, 10868–10881 (2014).
[Crossref]

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 287 (2012).
[Crossref]

F. Duport, B. Schneider, A. Smerieri, M. Haelterman, S. Massar, “All-optical reservoir computing,” Opt. Express 20, 22783–22795 (2012).
[Crossref]

A. Smerieri, F. Duport, Y. Paquot, B. Schrauwen, M. Haelterman, S. Massar, “Analog readout for optical reservoir computers,” in Advances in Neural Information Processing Systems (2012), Vol. 25, pp. 953–961.

Hallez, H.

P. Buteneers, D. Verstraeten, P. Van Mierlo, T. Wyckhuys, D. Stroobandt, R. Raedt, H. Hallez, B. Schrauwen, “Automatic detection of epileptic seizures on the intra-cranial electroencephalogram of rats using reservoir computing,” Artificial Intelligence Medicine 53, 215–223 (2011).
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Hermans, M.

M. Hermans, M. Soriano, J. Dambre, P. Bienstman, I. Fischer, “Photonic delay systems as machine learning implementations,” arXiv:1501.02592v1 (2015).

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K. Hicke, M. A. Escalona-Moran, D. Brunner, M. C. Soriano, I. Fischer, C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19, 1501610 (2013).
[Crossref]

Huang, Y.

Jacquot, M.

R. Martinenghi, S. Rybalko, M. Jacquot, Y. K. Chembo, L. Larger, “Photonic nonlinear transient computing with multiple-delay wavelength dynamics,” Phys. Rev. Lett. 108, 244101 (2012).
[Crossref]

Jaeger, H.

M. Lukoševičius, H. Jaeger, B. Schrauwen, “Reservoir computing trends,” Künstl. Intell. 26, 365–371 (2012).
[Crossref]

M. Lukoševičius, H. Jaeger, “Reservoir computing approaches to recurrent neural network training,” Comput. Sci. Rev. 3, 127–149 (2009).
[Crossref]

H. Jaeger, H. Haas, “Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication,” Science 304, 78–80 (2004).
[Crossref]

H. Jaeger, “The “echo state” approach to analysing and training recurrent neural networks,” (German National Research Center for Information Technology, 2001).

H. Jaeger, “Short term memory in echo state networks,” (German National Research Center for Information Technology, 2002).

Jalal, A.

F. Triefenbach, A. Jalal, B. Schrauwen, J.-P. Martens, “Phoneme recognition with large hierarchical reservoirs,” in Advances in Neural Information Processing Systems (2010), Vol. 23, pp. 2307–2315.

Keuninckx, L.

M. C. Soriano, S. Ortin, L. Keuninckx, L. Appeltant, J. Danckaert, L. Pesquera, G. Van Der Sande, “Delay-based reservoir computing: noise effects in a combined analog and digital implementation,” IEEE Trans. Neural Netw. Learn. Syst. 26, 388–393 (2015).
[Crossref]

Larger, L.

Li, B.

Liu, F.

Lopes, A.

L. Boccato, A. Lopes, R. Attux, F. J. Von Zuben, “An extended echo state network using Volterra filtering and principal component analysis,” Neural Networks 32, 292–302 (2012).
[Crossref]

L. Boccato, A. Lopes, R. Attux, F. J. Von Zuben, “An echo state network architecture based on Volterra filtering and PCA with application to the channel equalization problem,” in International Joint Conference on Neural Networks (IEEE, 2011), pp. 580–587.

Lukoševicius, M.

M. Lukoševičius, H. Jaeger, B. Schrauwen, “Reservoir computing trends,” Künstl. Intell. 26, 365–371 (2012).
[Crossref]

M. Lukoševičius, H. Jaeger, “Reservoir computing approaches to recurrent neural network training,” Comput. Sci. Rev. 3, 127–149 (2009).
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R. Lyon, “A computational model of filtering, detection, and compression in the cochlea,” in IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP) (IEEE, 1982), Vol. 7, pp. 1282–1285.

Maass, W.

W. Maass, T. Natschläger, H. Markram, “Real-time computing without stable states: a new framework for neural computation based on perturbations,” Neural Comput. 14, 2531–2560 (2002).
[Crossref]

Markram, H.

W. Maass, T. Natschläger, H. Markram, “Real-time computing without stable states: a new framework for neural computation based on perturbations,” Neural Comput. 14, 2531–2560 (2002).
[Crossref]

Martens, J.-P.

F. Triefenbach, A. Jalal, B. Schrauwen, J.-P. Martens, “Phoneme recognition with large hierarchical reservoirs,” in Advances in Neural Information Processing Systems (2010), Vol. 23, pp. 2307–2315.

Martinenghi, R.

R. Martinenghi, S. Rybalko, M. Jacquot, Y. K. Chembo, L. Larger, “Photonic nonlinear transient computing with multiple-delay wavelength dynamics,” Phys. Rev. Lett. 108, 244101 (2012).
[Crossref]

Massar, S.

A. Dejonckheere, F. Duport, A. Smerieri, L. Fang, J.-L. Oudar, M. Haelterman, S. Massar, “All-optical reservoir computer based on saturation of absorption,” Opt. Express 22, 10868–10881 (2014).
[Crossref]

J. Dambre, D. Verstraeten, B. Schrauwen, S. Massar, “Information processing capacity of dynamical systems,” Sci. Rep. 2, 514 (2012).
[Crossref]

F. Duport, B. Schneider, A. Smerieri, M. Haelterman, S. Massar, “All-optical reservoir computing,” Opt. Express 20, 22783–22795 (2012).
[Crossref]

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 287 (2012).
[Crossref]

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
[Crossref]

A. Smerieri, F. Duport, Y. Paquot, B. Schrauwen, M. Haelterman, S. Massar, “Analog readout for optical reservoir computers,” in Advances in Neural Information Processing Systems (2012), Vol. 25, pp. 953–961.

Mechet, P.

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun 5, 3541 (2014).
[Crossref]

Mesaritakis, C.

Mirasso, C. R.

K. Hicke, M. A. Escalona-Moran, D. Brunner, M. C. Soriano, I. Fischer, C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19, 1501610 (2013).
[Crossref]

M. C. Soriano, S. Ortín, D. Brunner, L. Larger, C. R. Mirasso, I. Fischer, L. Pesquera, “Optoelectronic reservoir computing: tackling noise-induced performance degradation,” Opt. Express 21, 12–20 (2013).
[Crossref]

D. Brunner, M. C. Soriano, C. R. Mirasso, I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nat. Commun. 4, 1364 (2013).
[Crossref]

L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutierrez, L. Pesquera, C. R. Mirasso, I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20, 3241–3249 (2012).
[Crossref]

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
[Crossref]

Morthier, G.

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun 5, 3541 (2014).
[Crossref]

Natschläger, T.

W. Maass, T. Natschläger, H. Markram, “Real-time computing without stable states: a new framework for neural computation based on perturbations,” Neural Comput. 14, 2531–2560 (2002).
[Crossref]

Nguimdo, R. M.

Ortin, S.

M. C. Soriano, S. Ortin, L. Keuninckx, L. Appeltant, J. Danckaert, L. Pesquera, G. Van Der Sande, “Delay-based reservoir computing: noise effects in a combined analog and digital implementation,” IEEE Trans. Neural Netw. Learn. Syst. 26, 388–393 (2015).
[Crossref]

Ortín, S.

Oudar, J.-L.

Papataxiarhis, V.

Paquot, Y.

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 287 (2012).
[Crossref]

A. Smerieri, F. Duport, Y. Paquot, B. Schrauwen, M. Haelterman, S. Massar, “Analog readout for optical reservoir computers,” in Advances in Neural Information Processing Systems (2012), Vol. 25, pp. 953–961.

Pesquera, L.

Raedt, R.

P. Buteneers, D. Verstraeten, P. Van Mierlo, T. Wyckhuys, D. Stroobandt, R. Raedt, H. Hallez, B. Schrauwen, “Automatic detection of epileptic seizures on the intra-cranial electroencephalogram of rats using reservoir computing,” Artificial Intelligence Medicine 53, 215–223 (2011).
[Crossref]

Rodan, A.

A. Rodan, P. Tino, “Simple deterministically constructed recurrent neural networks,” in Intelligent Data Engineering and Automated Learning (IDEAL) (Springer, 2010), pp. 267–274.

Rybalko, S.

R. Martinenghi, S. Rybalko, M. Jacquot, Y. K. Chembo, L. Larger, “Photonic nonlinear transient computing with multiple-delay wavelength dynamics,” Phys. Rev. Lett. 108, 244101 (2012).
[Crossref]

Schneider, B.

Schrauwen, B.

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun 5, 3541 (2014).
[Crossref]

M. A. A. Fiers, T. Van Varenbergh, F. Wyffels, D. Verstraeten, B. Schrauwen, J. Dambre, P. Bienstman, “Nanophotonic reservoir computing with photonic crystal cavities to generate periodic patterns,” IEEE Trans. Neural Netw. Learn. Syst. 25, 344–355 (2014).
[Crossref]

J. Dambre, D. Verstraeten, B. Schrauwen, S. Massar, “Information processing capacity of dynamical systems,” Sci. Rep. 2, 514 (2012).
[Crossref]

M. Lukoševičius, H. Jaeger, B. Schrauwen, “Reservoir computing trends,” Künstl. Intell. 26, 365–371 (2012).
[Crossref]

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 287 (2012).
[Crossref]

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
[Crossref]

P. Buteneers, D. Verstraeten, P. Van Mierlo, T. Wyckhuys, D. Stroobandt, R. Raedt, H. Hallez, B. Schrauwen, “Automatic detection of epileptic seizures on the intra-cranial electroencephalogram of rats using reservoir computing,” Artificial Intelligence Medicine 53, 215–223 (2011).
[Crossref]

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22, 1469–1481 (2011).
[Crossref]

K. Vandoorne, W. Dierckx, B. Schrauwen, D. Verstraeten, R. Baets, P. Bienstman, J. Van Campenhout, “Toward optical signal processing using photonic reservoir computing,” Opt. Express 16, 11182–11192 (2008).
[Crossref]

E. A. Antonelo, B. Schrauwen, D. Stroobandt, “Event detection and localization for small mobile robots using reservoir computing,” Neural Networks 21, 862–871 (2008).
[Crossref]

F. Triefenbach, A. Jalal, B. Schrauwen, J.-P. Martens, “Phoneme recognition with large hierarchical reservoirs,” in Advances in Neural Information Processing Systems (2010), Vol. 23, pp. 2307–2315.

A. Smerieri, F. Duport, Y. Paquot, B. Schrauwen, M. Haelterman, S. Massar, “Analog readout for optical reservoir computers,” in Advances in Neural Information Processing Systems (2012), Vol. 25, pp. 953–961.

Smerieri, A.

A. Dejonckheere, F. Duport, A. Smerieri, L. Fang, J.-L. Oudar, M. Haelterman, S. Massar, “All-optical reservoir computer based on saturation of absorption,” Opt. Express 22, 10868–10881 (2014).
[Crossref]

F. Duport, B. Schneider, A. Smerieri, M. Haelterman, S. Massar, “All-optical reservoir computing,” Opt. Express 20, 22783–22795 (2012).
[Crossref]

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 287 (2012).
[Crossref]

A. Smerieri, F. Duport, Y. Paquot, B. Schrauwen, M. Haelterman, S. Massar, “Analog readout for optical reservoir computers,” in Advances in Neural Information Processing Systems (2012), Vol. 25, pp. 953–961.

Soriano, M.

M. Hermans, M. Soriano, J. Dambre, P. Bienstman, I. Fischer, “Photonic delay systems as machine learning implementations,” arXiv:1501.02592v1 (2015).

Soriano, M. C.

M. C. Soriano, S. Ortin, L. Keuninckx, L. Appeltant, J. Danckaert, L. Pesquera, G. Van Der Sande, “Delay-based reservoir computing: noise effects in a combined analog and digital implementation,” IEEE Trans. Neural Netw. Learn. Syst. 26, 388–393 (2015).
[Crossref]

D. Brunner, M. C. Soriano, I. Fischer, “High-speed optical vector and matrix operations using a semiconductor laser,” IEEE Photon. Technol. Lett. 25, 1680–1683 (2013).
[Crossref]

D. Brunner, M. C. Soriano, C. R. Mirasso, I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nat. Commun. 4, 1364 (2013).
[Crossref]

K. Hicke, M. A. Escalona-Moran, D. Brunner, M. C. Soriano, I. Fischer, C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19, 1501610 (2013).
[Crossref]

M. C. Soriano, S. Ortín, D. Brunner, L. Larger, C. R. Mirasso, I. Fischer, L. Pesquera, “Optoelectronic reservoir computing: tackling noise-induced performance degradation,” Opt. Express 21, 12–20 (2013).
[Crossref]

L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutierrez, L. Pesquera, C. R. Mirasso, I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20, 3241–3249 (2012).
[Crossref]

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
[Crossref]

Stroobandt, D.

P. Buteneers, D. Verstraeten, P. Van Mierlo, T. Wyckhuys, D. Stroobandt, R. Raedt, H. Hallez, B. Schrauwen, “Automatic detection of epileptic seizures on the intra-cranial electroencephalogram of rats using reservoir computing,” Artificial Intelligence Medicine 53, 215–223 (2011).
[Crossref]

E. A. Antonelo, B. Schrauwen, D. Stroobandt, “Event detection and localization for small mobile robots using reservoir computing,” Neural Networks 21, 862–871 (2008).
[Crossref]

Syvridis, D.

Tino, P.

A. Rodan, P. Tino, “Simple deterministically constructed recurrent neural networks,” in Intelligent Data Engineering and Automated Learning (IDEAL) (Springer, 2010), pp. 267–274.

Triefenbach, F.

F. Triefenbach, A. Jalal, B. Schrauwen, J.-P. Martens, “Phoneme recognition with large hierarchical reservoirs,” in Advances in Neural Information Processing Systems (2010), Vol. 23, pp. 2307–2315.

Van Campenhout, J.

Van Der Sande, G.

M. C. Soriano, S. Ortin, L. Keuninckx, L. Appeltant, J. Danckaert, L. Pesquera, G. Van Der Sande, “Delay-based reservoir computing: noise effects in a combined analog and digital implementation,” IEEE Trans. Neural Netw. Learn. Syst. 26, 388–393 (2015).
[Crossref]

L. Appeltant, G. Van der Sande, J. Danckaert, I. Fischer, “Constructing optimized binary masks for reservoir computing with delay systems,” Sci. Rep. 4, 3629 (2014).
[Crossref]

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, G. Van der Sande, “Fast photonic information processing using semiconductor lasers with delayed optical feedback: role of phase dynamics,” Opt. Express 22, 8672–8686 (2014).
[Crossref]

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
[Crossref]

Van Mierlo, P.

P. Buteneers, D. Verstraeten, P. Van Mierlo, T. Wyckhuys, D. Stroobandt, R. Raedt, H. Hallez, B. Schrauwen, “Automatic detection of epileptic seizures on the intra-cranial electroencephalogram of rats using reservoir computing,” Artificial Intelligence Medicine 53, 215–223 (2011).
[Crossref]

Van Vaerenbergh, T.

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun 5, 3541 (2014).
[Crossref]

Van Varenbergh, T.

M. A. A. Fiers, T. Van Varenbergh, F. Wyffels, D. Verstraeten, B. Schrauwen, J. Dambre, P. Bienstman, “Nanophotonic reservoir computing with photonic crystal cavities to generate periodic patterns,” IEEE Trans. Neural Netw. Learn. Syst. 25, 344–355 (2014).
[Crossref]

Vandoorne, K.

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun 5, 3541 (2014).
[Crossref]

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22, 1469–1481 (2011).
[Crossref]

K. Vandoorne, W. Dierckx, B. Schrauwen, D. Verstraeten, R. Baets, P. Bienstman, J. Van Campenhout, “Toward optical signal processing using photonic reservoir computing,” Opt. Express 16, 11182–11192 (2008).
[Crossref]

Verschaffelt, G.

Verstraeten, D.

M. A. A. Fiers, T. Van Varenbergh, F. Wyffels, D. Verstraeten, B. Schrauwen, J. Dambre, P. Bienstman, “Nanophotonic reservoir computing with photonic crystal cavities to generate periodic patterns,” IEEE Trans. Neural Netw. Learn. Syst. 25, 344–355 (2014).
[Crossref]

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun 5, 3541 (2014).
[Crossref]

J. Dambre, D. Verstraeten, B. Schrauwen, S. Massar, “Information processing capacity of dynamical systems,” Sci. Rep. 2, 514 (2012).
[Crossref]

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22, 1469–1481 (2011).
[Crossref]

P. Buteneers, D. Verstraeten, P. Van Mierlo, T. Wyckhuys, D. Stroobandt, R. Raedt, H. Hallez, B. Schrauwen, “Automatic detection of epileptic seizures on the intra-cranial electroencephalogram of rats using reservoir computing,” Artificial Intelligence Medicine 53, 215–223 (2011).
[Crossref]

K. Vandoorne, W. Dierckx, B. Schrauwen, D. Verstraeten, R. Baets, P. Bienstman, J. Van Campenhout, “Toward optical signal processing using photonic reservoir computing,” Opt. Express 16, 11182–11192 (2008).
[Crossref]

Von Zuben, F. J.

L. Boccato, A. Lopes, R. Attux, F. J. Von Zuben, “An extended echo state network using Volterra filtering and principal component analysis,” Neural Networks 32, 292–302 (2012).
[Crossref]

L. Boccato, A. Lopes, R. Attux, F. J. Von Zuben, “An echo state network architecture based on Volterra filtering and PCA with application to the channel equalization problem,” in International Joint Conference on Neural Networks (IEEE, 2011), pp. 580–587.

Wang, Y.

Wyckhuys, T.

P. Buteneers, D. Verstraeten, P. Van Mierlo, T. Wyckhuys, D. Stroobandt, R. Raedt, H. Hallez, B. Schrauwen, “Automatic detection of epileptic seizures on the intra-cranial electroencephalogram of rats using reservoir computing,” Artificial Intelligence Medicine 53, 215–223 (2011).
[Crossref]

Wyffels, F.

M. A. A. Fiers, T. Van Varenbergh, F. Wyffels, D. Verstraeten, B. Schrauwen, J. Dambre, P. Bienstman, “Nanophotonic reservoir computing with photonic crystal cavities to generate periodic patterns,” IEEE Trans. Neural Netw. Learn. Syst. 25, 344–355 (2014).
[Crossref]

Zhang, H.

Artificial Intelligence Medicine (1)

P. Buteneers, D. Verstraeten, P. Van Mierlo, T. Wyckhuys, D. Stroobandt, R. Raedt, H. Hallez, B. Schrauwen, “Automatic detection of epileptic seizures on the intra-cranial electroencephalogram of rats using reservoir computing,” Artificial Intelligence Medicine 53, 215–223 (2011).
[Crossref]

Comput. Sci. Rev. (1)

M. Lukoševičius, H. Jaeger, “Reservoir computing approaches to recurrent neural network training,” Comput. Sci. Rev. 3, 127–149 (2009).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

K. Hicke, M. A. Escalona-Moran, D. Brunner, M. C. Soriano, I. Fischer, C. R. Mirasso, “Information processing using transient dynamics of semiconductor lasers subject to delayed feedback,” IEEE J. Sel. Top. Quantum Electron. 19, 1501610 (2013).
[Crossref]

IEEE Photon. Technol. Lett. (1)

D. Brunner, M. C. Soriano, I. Fischer, “High-speed optical vector and matrix operations using a semiconductor laser,” IEEE Photon. Technol. Lett. 25, 1680–1683 (2013).
[Crossref]

IEEE Trans. Neural Netw. (1)

K. Vandoorne, J. Dambre, D. Verstraeten, B. Schrauwen, P. Bienstman, “Parallel reservoir computing using optical amplifiers,” IEEE Trans. Neural Netw. 22, 1469–1481 (2011).
[Crossref]

IEEE Trans. Neural Netw. Learn. Syst. (2)

M. A. A. Fiers, T. Van Varenbergh, F. Wyffels, D. Verstraeten, B. Schrauwen, J. Dambre, P. Bienstman, “Nanophotonic reservoir computing with photonic crystal cavities to generate periodic patterns,” IEEE Trans. Neural Netw. Learn. Syst. 25, 344–355 (2014).
[Crossref]

M. C. Soriano, S. Ortin, L. Keuninckx, L. Appeltant, J. Danckaert, L. Pesquera, G. Van Der Sande, “Delay-based reservoir computing: noise effects in a combined analog and digital implementation,” IEEE Trans. Neural Netw. Learn. Syst. 26, 388–393 (2015).
[Crossref]

J. Opt. Soc. Am. B (1)

Künstl. Intell. (1)

M. Lukoševičius, H. Jaeger, B. Schrauwen, “Reservoir computing trends,” Künstl. Intell. 26, 365–371 (2012).
[Crossref]

Nat. Commun (1)

K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun 5, 3541 (2014).
[Crossref]

Nat. Commun. (2)

L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
[Crossref]

D. Brunner, M. C. Soriano, C. R. Mirasso, I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nat. Commun. 4, 1364 (2013).
[Crossref]

Neural Comput. (1)

W. Maass, T. Natschläger, H. Markram, “Real-time computing without stable states: a new framework for neural computation based on perturbations,” Neural Comput. 14, 2531–2560 (2002).
[Crossref]

Neural Networks (2)

E. A. Antonelo, B. Schrauwen, D. Stroobandt, “Event detection and localization for small mobile robots using reservoir computing,” Neural Networks 21, 862–871 (2008).
[Crossref]

L. Boccato, A. Lopes, R. Attux, F. J. Von Zuben, “An extended echo state network using Volterra filtering and principal component analysis,” Neural Networks 32, 292–302 (2012).
[Crossref]

Opt. Express (7)

A. Dejonckheere, F. Duport, A. Smerieri, L. Fang, J.-L. Oudar, M. Haelterman, S. Massar, “All-optical reservoir computer based on saturation of absorption,” Opt. Express 22, 10868–10881 (2014).
[Crossref]

L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutierrez, L. Pesquera, C. R. Mirasso, I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20, 3241–3249 (2012).
[Crossref]

F. Duport, B. Schneider, A. Smerieri, M. Haelterman, S. Massar, “All-optical reservoir computing,” Opt. Express 20, 22783–22795 (2012).
[Crossref]

H. Zhang, X. Feng, B. Li, Y. Wang, K. Cui, F. Liu, W. Dou, Y. Huang, “Integrated photonic reservoir computing based on hierarchical time-multiplexing structure,” Opt. Express 22, 31356–31370 (2014).
[Crossref]

K. Vandoorne, W. Dierckx, B. Schrauwen, D. Verstraeten, R. Baets, P. Bienstman, J. Van Campenhout, “Toward optical signal processing using photonic reservoir computing,” Opt. Express 16, 11182–11192 (2008).
[Crossref]

M. C. Soriano, S. Ortín, D. Brunner, L. Larger, C. R. Mirasso, I. Fischer, L. Pesquera, “Optoelectronic reservoir computing: tackling noise-induced performance degradation,” Opt. Express 21, 12–20 (2013).
[Crossref]

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, G. Van der Sande, “Fast photonic information processing using semiconductor lasers with delayed optical feedback: role of phase dynamics,” Opt. Express 22, 8672–8686 (2014).
[Crossref]

Phys. Rev. Lett. (1)

R. Martinenghi, S. Rybalko, M. Jacquot, Y. K. Chembo, L. Larger, “Photonic nonlinear transient computing with multiple-delay wavelength dynamics,” Phys. Rev. Lett. 108, 244101 (2012).
[Crossref]

Sci. Rep. (3)

L. Appeltant, G. Van der Sande, J. Danckaert, I. Fischer, “Constructing optimized binary masks for reservoir computing with delay systems,” Sci. Rep. 4, 3629 (2014).
[Crossref]

J. Dambre, D. Verstraeten, B. Schrauwen, S. Massar, “Information processing capacity of dynamical systems,” Sci. Rep. 2, 514 (2012).
[Crossref]

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 287 (2012).
[Crossref]

Science (1)

H. Jaeger, H. Haas, “Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication,” Science 304, 78–80 (2004).
[Crossref]

Other (9)

F. Triefenbach, A. Jalal, B. Schrauwen, J.-P. Martens, “Phoneme recognition with large hierarchical reservoirs,” in Advances in Neural Information Processing Systems (2010), Vol. 23, pp. 2307–2315.

L. Boccato, A. Lopes, R. Attux, F. J. Von Zuben, “An echo state network architecture based on Volterra filtering and PCA with application to the channel equalization problem,” in International Joint Conference on Neural Networks (IEEE, 2011), pp. 580–587.

A. Rodan, P. Tino, “Simple deterministically constructed recurrent neural networks,” in Intelligent Data Engineering and Automated Learning (IDEAL) (Springer, 2010), pp. 267–274.

H. Jaeger, “The “echo state” approach to analysing and training recurrent neural networks,” (German National Research Center for Information Technology, 2001).

H. Jaeger, “Short term memory in echo state networks,” (German National Research Center for Information Technology, 2002).

Texas Instruments-Developed 46-Word Speaker-Dependent Isolated Word Corpus (TI46), NIST Speech Disc 7-1.1 (1 disc) (1991).

R. Lyon, “A computational model of filtering, detection, and compression in the cochlea,” in IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP) (IEEE, 1982), Vol. 7, pp. 1282–1285.

A. Smerieri, F. Duport, Y. Paquot, B. Schrauwen, M. Haelterman, S. Massar, “Analog readout for optical reservoir computers,” in Advances in Neural Information Processing Systems (2012), Vol. 25, pp. 953–961.

M. Hermans, M. Soriano, J. Dambre, P. Bienstman, I. Fischer, “Photonic delay systems as machine learning implementations,” arXiv:1501.02592v1 (2015).

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Figures (4)

Fig. 1.
Fig. 1. Experimental setup: Blue lines (dark gray) correspond to fiber optic and orange lines (light gray) to electrical connections. Laser, long coherence telecom wavelength laser; I, isolator; PC, polarization controller; M-Z, amplitude modulator (lithium niobate Mach–Zehnder interferometer in push–pull configuration); OA, optical attenuator; PFS, piezoelectric fiber stretcher; AWG, arbitrary waveform generator; DL, delay loop; HV ampli., high-voltage amplifier; PID, proportional–integral–derivative regulator; Ph., photodiode; Osc., oscilloscope. The PC inside the cavity is used to control the Jones matrix of the cavity, and the PCs before the cavity ensure that A ( t ) and the counterpropagating control signal are on the two different polarization eigenmodes of the cavity.
Fig. 2.
Fig. 2. Experimental and simulation results for the nonlinear channel equalization task. Horizontal axis, signal-to-noise ratio of the nonlinear channel; vertical axis, symbol error rate, i.e., number of misidentified symbols. These results were obtained with Δ φ = 0 rad , γ = 0.45 and without any precompensation of the masked input signal. To get the best performances for each SNR, α was scanned in the range [0.45,0.55], V 0 / V π , DC in the range [ 0.5 , 0.5 ] , and the ridge parameter from 10 6 to 10 4 . Note that at 28 and 32 dB SNR, the SER is zero for the passive coherent RC, both in simulation and in experiment.
Fig. 3.
Fig. 3. Resonances of the cavity. Two CW signals are coupled in counterpropagating directions in the cavity, on the two polarization eigenmodes of the cavity. A voltage ramp is applied to the piezoelectric fiber stretcher in order to scan the cavity phase, and the output power is recorded. The optical attenuator was set at its maximum transparency.
Fig. 4.
Fig. 4. Isolation system of the delay loop, open. It consists of two aluminum boxes: a small box made of 1 cm thick plates inside a bigger box made of 2 cm thick plates. The inner plates of both boxes are covered with stone wool. Each box is isolated from the base on which it rests by sorbothane sheets that absorb vibrations.

Tables (3)

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Table 1. Memory Capacity Evaluation a

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Table 2. Experimental and Simulation Results for the Isolated Spoken Digit Recognition Task a

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Table 3. Technical Description of the Most Important Hardware Components

Equations (8)

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A ( t ) = α exp ( j Δ φ ) A ( t T ) + β A in ( t ) ,
{ x i ( n ) = α x i k ( n 1 ) exp ( j Δ φ ) + β [ m i u ( n ) + A 0 ] k i N x i ( n ) = α x N + i k ( n 2 ) exp ( j Δ φ ) + β [ m i u ( n ) + A 0 ] 0 i k ,
y ( n ) = i = 0 N 1 W i | x i ( n ) | 2 .
A in ( t ) = sin [ π 2 ( γ m ( t ) u ( t ) V π , RF + V 0 V π , DC ) ] .
y * ( n + 1 ) = 0.3 y * ( n ) + 0.05 y * ( n ) [ i = 0 9 y * ( n i ) ] + 1.5 u ( n 9 ) u ( n ) + 0.1 .
NMSE = n [ y * ( n ) y ( n ) ] 2 n { y * ( n ) n [ y * ( n ) ] n } 2 .
q ( n ) = 0.08 d ( n + 2 ) 0.12 d ( n + 1 ) + d ( n ) + 0.18 d ( n 1 ) 0.1 d ( n 2 ) + 0.091 d ( n 3 ) 0.05 d ( n 4 ) + 0.04 d ( n 5 ) + 0.03 d ( n 6 ) + 0.01 d ( n 7 ) ,
u ( n ) = q ( n ) + 0.036 q 2 ( n ) 0.011 q 3 ( n ) + ν ( n ) .

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