Abstract

Reservoir computing (RC) by supervised training, a bio-inspired paradigm, is gaining popularity for processing time-dependent data. Compared to conventional recurrent neural networks, RC is facilely implemented by available hardware and overcomes some obstacles in training period, such as slow convergence and local optimum. In this paper, we propose and characterize a novel reservoir computing system based on a semiconductor laser with double optoelectronic feedback loops. This system shows obvious improvement on prediction, speech recognition and nonlinear channel equalization compared to the traditional reservoir computing systems with single feedback loop. Then some influencing factors to optimize the performance of the new RC are numerically studied, and its great potential of addressing more complex and troubling problems in information processing is expected to be exploited.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  4. W. Mo, C. L. Gutterman, Y. Li, G. Zussman, and D. C. Kilper, “Deep neural network based dynamic resource reallocation of bbu pools in 5g c-ran roadm networks,” in Optical Fiber Communication Conference, (Optical Society of America, 2018).
    [Crossref]
  5. Y. Luo and Y. Huang, “Text steganography with high embedding rate: Using recurrent neural networks to generate chinese classic poetry,” in Proceedings of the 5th ACM Workshop on Information Hiding and Multimedia Security, (ACM, 2017), pp. 99–104.
    [Crossref]
  6. H. Jaeger, “The “echo state” approach to analysing and training recurrent neural networks-with an erratum note,” Ger. Natl. Res. Cent. Inf. Technol. GMD Tech. Rep. 148, 13 (2001).
  7. W. Maass, T. Natschlädger, and H. Markram, “Real-time computing without stable states: A new framework for neural computation based on perturbations,” Neural Comput. 14, 2531–2560 (2002).
    [Crossref] [PubMed]
  8. D. Verstraeten, B. Schrauwen, M. D’Haene, and D. Stroobandt, “An experimental unification of reservoir computing methods,” Neural Networks 20, 391–403 (2007).
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  9. F. Triefenbach, A. Jalalvand, B. Schrauwen, and J. P. Martens, “Phoneme recognition with large hierarchical reservoirs,” in Proceedings of the 23rd International Conference on Neural Information Processing Systems, vol. 2 (Curran Associates Inc., 2010), pp. 2307–2315.
  10. L. Boccato, A. Lopes, R. Attux, and F. J. Von Zuben, “An echo state network architecture based on volterra filtering and pca with application to the channel equalization problem,” in The 2011 International Joint Conference on Neural Networks, (2011), pp. 580–587.
    [Crossref]
  11. H. Jaeger and H. Haas, “Harnessing nonlinearity: Predicting chaotic systems and saving energy in wireless communication,” Science 304, 78–80 (2004).
    [Crossref] [PubMed]
  12. F. Duport, A. Akrout, A. Smerieri, M. Haelterman, and S. Massar, “Analog input layer for optical reservoir computers,” Eprint Arxiv 146, 460–464 (2014).
  13. J. Qin, Q. Zhao, H. Yin, Y. Jin, and C. Liu, “Numerical simulation and experiment on optical packet header recognition utilizing reservoir computing based on optoelectronic feedback,” IEEE Photonics J. 9, 1–11 (2017).
  14. Yu Jin, Q. Zhao, H. Yin, and Hehe Yue, “Handwritten numeral recognition utilizing reservoir computing subject to optoelectronic feedback,” in 2015 11th International Conference on Natural Computation (ICNC), (2015), pp. 1165–1169.
    [Crossref]
  15. L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, “Information processing using a single dynamical node as complex system,” Nat. Commun. 2, 468 (2011).
    [Crossref] [PubMed]
  16. K. Vandoorne, W. Dierckx, B. Schrauwen, D. Verstraeten, R. Baets, P. Bienstman, and J. V. Campenhout, “Toward optical signal processing using photonic reservoir computing,” Opt. Express 16, 11182–11192 (2008).
    [Crossref] [PubMed]
  17. Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, and S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 287 (2012).
    [Crossref] [PubMed]
  18. F. Duport, B. Schneider, A. Smerieri, M. Haelterman, and S. Massar, “All-optical reservoir computing,” Opt. Express 20, 22783–22795 (2012).
    [Crossref] [PubMed]
  19. L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutierrez, L. Pesquera, C. R. Mirasso, and I. Fischer, “Photonic information processing beyond turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20, 3241–3249 (2012).
    [Crossref] [PubMed]
  20. R. Martinenghi, A. Baylón-Fuentes, F. Xiaole, M. Jacquot, Y. Chembo, and L. Larger, “Optoelectronic nonlinear transient computing with multiple delays,” in 2013 Conference on Lasers Electro-Optics Europe International Quantum Electronics Conference CLEO EUROPE/IQEC, (2013).
    [Crossref]
  21. F. Duport, A. Smerieri, A. Akrout, M. Haelterman, and S. Massar, “Fully analogue photonic reservoir computer,” Sci. Rep. 6, 22381 (2016).
    [Crossref] [PubMed]
  22. A. Dejonckheere, F. Duport, A. Smerieri, L. Fang, J.-L. Oudar, M. Haelterman, and S. Massar, “All-optical reservoir computer based on saturation of absorption,” Opt. Express 22, 10868–10881 (2014).
    [Crossref] [PubMed]
  23. C. Mesaritakis, A. Kapsalis, and D. Syvridis, “All-optical reservoir computing system based on ingaasp ring resonators for high-speed identification and optical routing in optical networks,” Proc. SPIE 9370, 1269–1277 (2015).
  24. R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Simultaneous computation of two independent tasks using reservoir computing based on a single photonic nonlinear node with optical feedback,” IEEE Trans. Neural Networks Learn. Syst. 26, 3301–3307 (2015).
    [Crossref]
  25. Y. Hou, G. Xia, W. Yang, D. Wang, E. Jayaprasath, Z. Jiang, C. Hu, and Z. Wu, “Prediction performance of reservoir computing system based on a semiconductor laser subject to double optical feedback and optical injection,” Opt. Express 26, 10211–10219 (2018).
    [Crossref] [PubMed]
  26. G. Cybenko, “Approximation by superpositions of a sigmoidal function,” Math. Control. Signals Syst. 2, 303–314 (1989).
    [Crossref]
  27. K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Networks 2, 359–366 (1989).
    [Crossref]
  28. A. Rodan and P. Tiňo, “Simple deterministically constructed recurrent neural networks,” in Intelligent Data Engineering and Automated Learning, (SpringerBerlin Heidelberg, 2010), pp. 267–274.
  29. D. Verstraeten, B. Schrauwen, D. Stroobandt, and J. V. Campenhout, “Isolated word recognition with the liquid state machine: a case study,” Inf. Process. Lett. 95, 521–528 (2005).
    [Crossref]
  30. T. Instruments-Developed, “46-word speaker-dependent isolated word corpus (ti46),” NIST Speech Disc pp. 7–1.1 (1991).
  31. R. Lyon, “A computational model of filtering, detection, and compression in the cochlea,” in IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 7 (1982), pp. 1282–1285.
    [Crossref]
  32. A. Graves, D. Eck, N. Beringer, and J. Schmidhuber, “Biologically plausible speech recognition with lstm neural nets,” in Biologically Inspired Approaches to Advanced Information Technology, (SpringerBerlin Heidelberg, 2004), pp. 127–136.
    [Crossref]
  33. D. Verstraeten, B. Schrauwen, and D. Stroobandt, “Reservoir-based techniques for speech recognition,” in The 2006 IEEE International Joint Conference on Neural Network Proceedings, (2006), pp. 1050–1053.

2018 (1)

2017 (1)

J. Qin, Q. Zhao, H. Yin, Y. Jin, and C. Liu, “Numerical simulation and experiment on optical packet header recognition utilizing reservoir computing based on optoelectronic feedback,” IEEE Photonics J. 9, 1–11 (2017).

2016 (1)

F. Duport, A. Smerieri, A. Akrout, M. Haelterman, and S. Massar, “Fully analogue photonic reservoir computer,” Sci. Rep. 6, 22381 (2016).
[Crossref] [PubMed]

2015 (2)

C. Mesaritakis, A. Kapsalis, and D. Syvridis, “All-optical reservoir computing system based on ingaasp ring resonators for high-speed identification and optical routing in optical networks,” Proc. SPIE 9370, 1269–1277 (2015).

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Simultaneous computation of two independent tasks using reservoir computing based on a single photonic nonlinear node with optical feedback,” IEEE Trans. Neural Networks Learn. Syst. 26, 3301–3307 (2015).
[Crossref]

2014 (3)

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

F. Duport, A. Akrout, A. Smerieri, M. Haelterman, and S. Massar, “Analog input layer for optical reservoir computers,” Eprint Arxiv 146, 460–464 (2014).

C. L. P. Chen and C. Y. Zhang, “Data-intensive applications, challenges, techniques and technologies: A survey on big data,” Inf. Sci. 275, 314–347 (2014).
[Crossref]

2012 (3)

2011 (1)

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

2008 (1)

2007 (1)

D. Verstraeten, B. Schrauwen, M. D’Haene, and D. Stroobandt, “An experimental unification of reservoir computing methods,” Neural Networks 20, 391–403 (2007).
[Crossref] [PubMed]

2005 (1)

D. Verstraeten, B. Schrauwen, D. Stroobandt, and J. V. Campenhout, “Isolated word recognition with the liquid state machine: a case study,” Inf. Process. Lett. 95, 521–528 (2005).
[Crossref]

2004 (1)

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

2002 (1)

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

2001 (1)

H. Jaeger, “The “echo state” approach to analysing and training recurrent neural networks-with an erratum note,” Ger. Natl. Res. Cent. Inf. Technol. GMD Tech. Rep. 148, 13 (2001).

1989 (2)

G. Cybenko, “Approximation by superpositions of a sigmoidal function,” Math. Control. Signals Syst. 2, 303–314 (1989).
[Crossref]

K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Networks 2, 359–366 (1989).
[Crossref]

Akrout, A.

F. Duport, A. Smerieri, A. Akrout, M. Haelterman, and S. Massar, “Fully analogue photonic reservoir computer,” Sci. Rep. 6, 22381 (2016).
[Crossref] [PubMed]

F. Duport, A. Akrout, A. Smerieri, M. Haelterman, and S. Massar, “Analog input layer for optical reservoir computers,” Eprint Arxiv 146, 460–464 (2014).

Appeltant, L.

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

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

Attux, R.

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

Baets, R.

Baylón-Fuentes, A.

R. Martinenghi, A. Baylón-Fuentes, F. Xiaole, M. Jacquot, Y. Chembo, and L. Larger, “Optoelectronic nonlinear transient computing with multiple delays,” in 2013 Conference on Lasers Electro-Optics Europe International Quantum Electronics Conference CLEO EUROPE/IQEC, (2013).
[Crossref]

Beringer, N.

A. Graves, D. Eck, N. Beringer, and J. Schmidhuber, “Biologically plausible speech recognition with lstm neural nets,” in Biologically Inspired Approaches to Advanced Information Technology, (SpringerBerlin Heidelberg, 2004), pp. 127–136.
[Crossref]

Bienstman, P.

Boccato, L.

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

Brunner, D.

Campenhout, J. V.

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

D. Verstraeten, B. Schrauwen, D. Stroobandt, and J. V. Campenhout, “Isolated word recognition with the liquid state machine: a case study,” Inf. Process. Lett. 95, 521–528 (2005).
[Crossref]

Chembo, Y.

R. Martinenghi, A. Baylón-Fuentes, F. Xiaole, M. Jacquot, Y. Chembo, and L. Larger, “Optoelectronic nonlinear transient computing with multiple delays,” in 2013 Conference on Lasers Electro-Optics Europe International Quantum Electronics Conference CLEO EUROPE/IQEC, (2013).
[Crossref]

Chen, C. L. P.

C. L. P. Chen and C. Y. Zhang, “Data-intensive applications, challenges, techniques and technologies: A survey on big data,” Inf. Sci. 275, 314–347 (2014).
[Crossref]

Cybenko, G.

G. Cybenko, “Approximation by superpositions of a sigmoidal function,” Math. Control. Signals Syst. 2, 303–314 (1989).
[Crossref]

D’Haene, M.

D. Verstraeten, B. Schrauwen, M. D’Haene, and D. Stroobandt, “An experimental unification of reservoir computing methods,” Neural Networks 20, 391–403 (2007).
[Crossref] [PubMed]

Dambre, J.

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

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

Danckaert, J.

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Simultaneous computation of two independent tasks using reservoir computing based on a single photonic nonlinear node with optical feedback,” IEEE Trans. Neural Networks Learn. Syst. 26, 3301–3307 (2015).
[Crossref]

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

Dejonckheere, A.

Dierckx, W.

Duport, F.

F. Duport, A. Smerieri, A. Akrout, M. Haelterman, and S. Massar, “Fully analogue photonic reservoir computer,” Sci. Rep. 6, 22381 (2016).
[Crossref] [PubMed]

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

F. Duport, A. Akrout, A. Smerieri, M. Haelterman, and S. Massar, “Analog input layer for optical reservoir computers,” Eprint Arxiv 146, 460–464 (2014).

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

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

Eagen, C. F.

L. A. Feldkamp, D. V. Prokhorov, C. F. Eagen, and F. Yuan, Enhanced Multi-Stream Kalman Filter Training for Recurrent Networks (SpringerUS, 1998), pp. 29–54.

Eck, D.

A. Graves, D. Eck, N. Beringer, and J. Schmidhuber, “Biologically plausible speech recognition with lstm neural nets,” in Biologically Inspired Approaches to Advanced Information Technology, (SpringerBerlin Heidelberg, 2004), pp. 127–136.
[Crossref]

Fang, L.

Feldkamp, L. A.

L. A. Feldkamp, D. V. Prokhorov, C. F. Eagen, and F. Yuan, Enhanced Multi-Stream Kalman Filter Training for Recurrent Networks (SpringerUS, 1998), pp. 29–54.

Fischer, I.

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

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

Graves, A.

A. Graves, A. Mohamed, and G. Hinton, “Speech recognition with deep recurrent neural networks,” in 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, (2013), pp. 6645–6649.
[Crossref]

A. Graves, D. Eck, N. Beringer, and J. Schmidhuber, “Biologically plausible speech recognition with lstm neural nets,” in Biologically Inspired Approaches to Advanced Information Technology, (SpringerBerlin Heidelberg, 2004), pp. 127–136.
[Crossref]

Gutierrez, J. M.

Gutterman, C. L.

W. Mo, C. L. Gutterman, Y. Li, G. Zussman, and D. C. Kilper, “Deep neural network based dynamic resource reallocation of bbu pools in 5g c-ran roadm networks,” in Optical Fiber Communication Conference, (Optical Society of America, 2018).
[Crossref]

Haas, H.

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

Haelterman, M.

F. Duport, A. Smerieri, A. Akrout, M. Haelterman, and S. Massar, “Fully analogue photonic reservoir computer,” Sci. Rep. 6, 22381 (2016).
[Crossref] [PubMed]

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

F. Duport, A. Akrout, A. Smerieri, M. Haelterman, and S. Massar, “Analog input layer for optical reservoir computers,” Eprint Arxiv 146, 460–464 (2014).

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

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

Hinton, G.

A. Graves, A. Mohamed, and G. Hinton, “Speech recognition with deep recurrent neural networks,” in 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, (2013), pp. 6645–6649.
[Crossref]

Hornik, K.

K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Networks 2, 359–366 (1989).
[Crossref]

Hou, Y.

Hu, C.

Huang, Y.

Y. Luo and Y. Huang, “Text steganography with high embedding rate: Using recurrent neural networks to generate chinese classic poetry,” in Proceedings of the 5th ACM Workshop on Information Hiding and Multimedia Security, (ACM, 2017), pp. 99–104.
[Crossref]

Instruments-Developed, T.

T. Instruments-Developed, “46-word speaker-dependent isolated word corpus (ti46),” NIST Speech Disc pp. 7–1.1 (1991).

Jacquot, M.

R. Martinenghi, A. Baylón-Fuentes, F. Xiaole, M. Jacquot, Y. Chembo, and L. Larger, “Optoelectronic nonlinear transient computing with multiple delays,” in 2013 Conference on Lasers Electro-Optics Europe International Quantum Electronics Conference CLEO EUROPE/IQEC, (2013).
[Crossref]

Jaeger, H.

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

H. Jaeger, “The “echo state” approach to analysing and training recurrent neural networks-with an erratum note,” Ger. Natl. Res. Cent. Inf. Technol. GMD Tech. Rep. 148, 13 (2001).

Jalalvand, A.

F. Triefenbach, A. Jalalvand, B. Schrauwen, and J. P. Martens, “Phoneme recognition with large hierarchical reservoirs,” in Proceedings of the 23rd International Conference on Neural Information Processing Systems, vol. 2 (Curran Associates Inc., 2010), pp. 2307–2315.

Jayaprasath, E.

Jiang, Z.

Jin, Y.

J. Qin, Q. Zhao, H. Yin, Y. Jin, and C. Liu, “Numerical simulation and experiment on optical packet header recognition utilizing reservoir computing based on optoelectronic feedback,” IEEE Photonics J. 9, 1–11 (2017).

Jin, Yu

Yu Jin, Q. Zhao, H. Yin, and Hehe Yue, “Handwritten numeral recognition utilizing reservoir computing subject to optoelectronic feedback,” in 2015 11th International Conference on Natural Computation (ICNC), (2015), pp. 1165–1169.
[Crossref]

Kapsalis, A.

C. Mesaritakis, A. Kapsalis, and D. Syvridis, “All-optical reservoir computing system based on ingaasp ring resonators for high-speed identification and optical routing in optical networks,” Proc. SPIE 9370, 1269–1277 (2015).

Kilper, D. C.

W. Mo, C. L. Gutterman, Y. Li, G. Zussman, and D. C. Kilper, “Deep neural network based dynamic resource reallocation of bbu pools in 5g c-ran roadm networks,” in Optical Fiber Communication Conference, (Optical Society of America, 2018).
[Crossref]

Larger, L.

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

R. Martinenghi, A. Baylón-Fuentes, F. Xiaole, M. Jacquot, Y. Chembo, and L. Larger, “Optoelectronic nonlinear transient computing with multiple delays,” in 2013 Conference on Lasers Electro-Optics Europe International Quantum Electronics Conference CLEO EUROPE/IQEC, (2013).
[Crossref]

Li, Y.

W. Mo, C. L. Gutterman, Y. Li, G. Zussman, and D. C. Kilper, “Deep neural network based dynamic resource reallocation of bbu pools in 5g c-ran roadm networks,” in Optical Fiber Communication Conference, (Optical Society of America, 2018).
[Crossref]

Liu, C.

J. Qin, Q. Zhao, H. Yin, Y. Jin, and C. Liu, “Numerical simulation and experiment on optical packet header recognition utilizing reservoir computing based on optoelectronic feedback,” IEEE Photonics J. 9, 1–11 (2017).

Lopes, A.

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

Luo, Y.

Y. Luo and Y. Huang, “Text steganography with high embedding rate: Using recurrent neural networks to generate chinese classic poetry,” in Proceedings of the 5th ACM Workshop on Information Hiding and Multimedia Security, (ACM, 2017), pp. 99–104.
[Crossref]

Lyon, R.

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

Maass, W.

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

Markram, H.

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

Martens, J. P.

F. Triefenbach, A. Jalalvand, B. Schrauwen, and J. P. Martens, “Phoneme recognition with large hierarchical reservoirs,” in Proceedings of the 23rd International Conference on Neural Information Processing Systems, vol. 2 (Curran Associates Inc., 2010), pp. 2307–2315.

Martinenghi, R.

R. Martinenghi, A. Baylón-Fuentes, F. Xiaole, M. Jacquot, Y. Chembo, and L. Larger, “Optoelectronic nonlinear transient computing with multiple delays,” in 2013 Conference on Lasers Electro-Optics Europe International Quantum Electronics Conference CLEO EUROPE/IQEC, (2013).
[Crossref]

Massar, S.

F. Duport, A. Smerieri, A. Akrout, M. Haelterman, and S. Massar, “Fully analogue photonic reservoir computer,” Sci. Rep. 6, 22381 (2016).
[Crossref] [PubMed]

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

F. Duport, A. Akrout, A. Smerieri, M. Haelterman, and S. Massar, “Analog input layer for optical reservoir computers,” Eprint Arxiv 146, 460–464 (2014).

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

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

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

Mesaritakis, C.

C. Mesaritakis, A. Kapsalis, and D. Syvridis, “All-optical reservoir computing system based on ingaasp ring resonators for high-speed identification and optical routing in optical networks,” Proc. SPIE 9370, 1269–1277 (2015).

Mirasso, C. R.

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

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

Mo, W.

W. Mo, C. L. Gutterman, Y. Li, G. Zussman, and D. C. Kilper, “Deep neural network based dynamic resource reallocation of bbu pools in 5g c-ran roadm networks,” in Optical Fiber Communication Conference, (Optical Society of America, 2018).
[Crossref]

Mohamed, A.

A. Graves, A. Mohamed, and G. Hinton, “Speech recognition with deep recurrent neural networks,” in 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, (2013), pp. 6645–6649.
[Crossref]

Natschlädger, T.

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

Nguimdo, R. M.

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Simultaneous computation of two independent tasks using reservoir computing based on a single photonic nonlinear node with optical feedback,” IEEE Trans. Neural Networks Learn. Syst. 26, 3301–3307 (2015).
[Crossref]

Oudar, J.-L.

Paquot, Y.

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

Pesquera, L.

Prokhorov, D. V.

L. A. Feldkamp, D. V. Prokhorov, C. F. Eagen, and F. Yuan, Enhanced Multi-Stream Kalman Filter Training for Recurrent Networks (SpringerUS, 1998), pp. 29–54.

Qin, J.

J. Qin, Q. Zhao, H. Yin, Y. Jin, and C. Liu, “Numerical simulation and experiment on optical packet header recognition utilizing reservoir computing based on optoelectronic feedback,” IEEE Photonics J. 9, 1–11 (2017).

Rodan, A.

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

Schmidhuber, J.

A. Graves, D. Eck, N. Beringer, and J. Schmidhuber, “Biologically plausible speech recognition with lstm neural nets,” in Biologically Inspired Approaches to Advanced Information Technology, (SpringerBerlin Heidelberg, 2004), pp. 127–136.
[Crossref]

Schneider, B.

Schrauwen, B.

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

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

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

D. Verstraeten, B. Schrauwen, M. D’Haene, and D. Stroobandt, “An experimental unification of reservoir computing methods,” Neural Networks 20, 391–403 (2007).
[Crossref] [PubMed]

D. Verstraeten, B. Schrauwen, D. Stroobandt, and J. V. Campenhout, “Isolated word recognition with the liquid state machine: a case study,” Inf. Process. Lett. 95, 521–528 (2005).
[Crossref]

D. Verstraeten, B. Schrauwen, and D. Stroobandt, “Reservoir-based techniques for speech recognition,” in The 2006 IEEE International Joint Conference on Neural Network Proceedings, (2006), pp. 1050–1053.

F. Triefenbach, A. Jalalvand, B. Schrauwen, and J. P. Martens, “Phoneme recognition with large hierarchical reservoirs,” in Proceedings of the 23rd International Conference on Neural Information Processing Systems, vol. 2 (Curran Associates Inc., 2010), pp. 2307–2315.

Smerieri, A.

F. Duport, A. Smerieri, A. Akrout, M. Haelterman, and S. Massar, “Fully analogue photonic reservoir computer,” Sci. Rep. 6, 22381 (2016).
[Crossref] [PubMed]

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

F. Duport, A. Akrout, A. Smerieri, M. Haelterman, and S. Massar, “Analog input layer for optical reservoir computers,” Eprint Arxiv 146, 460–464 (2014).

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

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

Soriano, M. C.

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

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

Stinchcombe, M.

K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Networks 2, 359–366 (1989).
[Crossref]

Stroobandt, D.

D. Verstraeten, B. Schrauwen, M. D’Haene, and D. Stroobandt, “An experimental unification of reservoir computing methods,” Neural Networks 20, 391–403 (2007).
[Crossref] [PubMed]

D. Verstraeten, B. Schrauwen, D. Stroobandt, and J. V. Campenhout, “Isolated word recognition with the liquid state machine: a case study,” Inf. Process. Lett. 95, 521–528 (2005).
[Crossref]

D. Verstraeten, B. Schrauwen, and D. Stroobandt, “Reservoir-based techniques for speech recognition,” in The 2006 IEEE International Joint Conference on Neural Network Proceedings, (2006), pp. 1050–1053.

Syvridis, D.

C. Mesaritakis, A. Kapsalis, and D. Syvridis, “All-optical reservoir computing system based on ingaasp ring resonators for high-speed identification and optical routing in optical networks,” Proc. SPIE 9370, 1269–1277 (2015).

Tino, P.

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

Triefenbach, F.

F. Triefenbach, A. Jalalvand, B. Schrauwen, and J. P. Martens, “Phoneme recognition with large hierarchical reservoirs,” in Proceedings of the 23rd International Conference on Neural Information Processing Systems, vol. 2 (Curran Associates Inc., 2010), pp. 2307–2315.

Van der Sande, G.

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Simultaneous computation of two independent tasks using reservoir computing based on a single photonic nonlinear node with optical feedback,” IEEE Trans. Neural Networks Learn. Syst. 26, 3301–3307 (2015).
[Crossref]

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

Vandoorne, K.

Verschaffelt, G.

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Simultaneous computation of two independent tasks using reservoir computing based on a single photonic nonlinear node with optical feedback,” IEEE Trans. Neural Networks Learn. Syst. 26, 3301–3307 (2015).
[Crossref]

Verstraeten, D.

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

D. Verstraeten, B. Schrauwen, M. D’Haene, and D. Stroobandt, “An experimental unification of reservoir computing methods,” Neural Networks 20, 391–403 (2007).
[Crossref] [PubMed]

D. Verstraeten, B. Schrauwen, D. Stroobandt, and J. V. Campenhout, “Isolated word recognition with the liquid state machine: a case study,” Inf. Process. Lett. 95, 521–528 (2005).
[Crossref]

D. Verstraeten, B. Schrauwen, and D. Stroobandt, “Reservoir-based techniques for speech recognition,” in The 2006 IEEE International Joint Conference on Neural Network Proceedings, (2006), pp. 1050–1053.

Von Zuben, F. J.

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

Wang, D.

White, H.

K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Networks 2, 359–366 (1989).
[Crossref]

Wu, Z.

Xia, G.

Xiaole, F.

R. Martinenghi, A. Baylón-Fuentes, F. Xiaole, M. Jacquot, Y. Chembo, and L. Larger, “Optoelectronic nonlinear transient computing with multiple delays,” in 2013 Conference on Lasers Electro-Optics Europe International Quantum Electronics Conference CLEO EUROPE/IQEC, (2013).
[Crossref]

Yang, W.

Yin, H.

J. Qin, Q. Zhao, H. Yin, Y. Jin, and C. Liu, “Numerical simulation and experiment on optical packet header recognition utilizing reservoir computing based on optoelectronic feedback,” IEEE Photonics J. 9, 1–11 (2017).

Yu Jin, Q. Zhao, H. Yin, and Hehe Yue, “Handwritten numeral recognition utilizing reservoir computing subject to optoelectronic feedback,” in 2015 11th International Conference on Natural Computation (ICNC), (2015), pp. 1165–1169.
[Crossref]

Yuan, F.

L. A. Feldkamp, D. V. Prokhorov, C. F. Eagen, and F. Yuan, Enhanced Multi-Stream Kalman Filter Training for Recurrent Networks (SpringerUS, 1998), pp. 29–54.

Yue, Hehe

Yu Jin, Q. Zhao, H. Yin, and Hehe Yue, “Handwritten numeral recognition utilizing reservoir computing subject to optoelectronic feedback,” in 2015 11th International Conference on Natural Computation (ICNC), (2015), pp. 1165–1169.
[Crossref]

Zhang, C. Y.

C. L. P. Chen and C. Y. Zhang, “Data-intensive applications, challenges, techniques and technologies: A survey on big data,” Inf. Sci. 275, 314–347 (2014).
[Crossref]

Zhao, Q.

J. Qin, Q. Zhao, H. Yin, Y. Jin, and C. Liu, “Numerical simulation and experiment on optical packet header recognition utilizing reservoir computing based on optoelectronic feedback,” IEEE Photonics J. 9, 1–11 (2017).

Yu Jin, Q. Zhao, H. Yin, and Hehe Yue, “Handwritten numeral recognition utilizing reservoir computing subject to optoelectronic feedback,” in 2015 11th International Conference on Natural Computation (ICNC), (2015), pp. 1165–1169.
[Crossref]

Zussman, G.

W. Mo, C. L. Gutterman, Y. Li, G. Zussman, and D. C. Kilper, “Deep neural network based dynamic resource reallocation of bbu pools in 5g c-ran roadm networks,” in Optical Fiber Communication Conference, (Optical Society of America, 2018).
[Crossref]

Eprint Arxiv (1)

F. Duport, A. Akrout, A. Smerieri, M. Haelterman, and S. Massar, “Analog input layer for optical reservoir computers,” Eprint Arxiv 146, 460–464 (2014).

Ger. Natl. Res. Cent. Inf. Technol. GMD Tech. Rep. (1)

H. Jaeger, “The “echo state” approach to analysing and training recurrent neural networks-with an erratum note,” Ger. Natl. Res. Cent. Inf. Technol. GMD Tech. Rep. 148, 13 (2001).

IEEE Photonics J. (1)

J. Qin, Q. Zhao, H. Yin, Y. Jin, and C. Liu, “Numerical simulation and experiment on optical packet header recognition utilizing reservoir computing based on optoelectronic feedback,” IEEE Photonics J. 9, 1–11 (2017).

IEEE Trans. Neural Networks Learn. Syst. (1)

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Simultaneous computation of two independent tasks using reservoir computing based on a single photonic nonlinear node with optical feedback,” IEEE Trans. Neural Networks Learn. Syst. 26, 3301–3307 (2015).
[Crossref]

Inf. Process. Lett. (1)

D. Verstraeten, B. Schrauwen, D. Stroobandt, and J. V. Campenhout, “Isolated word recognition with the liquid state machine: a case study,” Inf. Process. Lett. 95, 521–528 (2005).
[Crossref]

Inf. Sci. (1)

C. L. P. Chen and C. Y. Zhang, “Data-intensive applications, challenges, techniques and technologies: A survey on big data,” Inf. Sci. 275, 314–347 (2014).
[Crossref]

Math. Control. Signals Syst. (1)

G. Cybenko, “Approximation by superpositions of a sigmoidal function,” Math. Control. Signals Syst. 2, 303–314 (1989).
[Crossref]

Nat. Commun. (1)

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

Neural Comput. (1)

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

Neural Networks (2)

D. Verstraeten, B. Schrauwen, M. D’Haene, and D. Stroobandt, “An experimental unification of reservoir computing methods,” Neural Networks 20, 391–403 (2007).
[Crossref] [PubMed]

K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Networks 2, 359–366 (1989).
[Crossref]

Opt. Express (5)

Proc. SPIE (1)

C. Mesaritakis, A. Kapsalis, and D. Syvridis, “All-optical reservoir computing system based on ingaasp ring resonators for high-speed identification and optical routing in optical networks,” Proc. SPIE 9370, 1269–1277 (2015).

Sci. Rep. (2)

F. Duport, A. Smerieri, A. Akrout, M. Haelterman, and S. Massar, “Fully analogue photonic reservoir computer,” Sci. Rep. 6, 22381 (2016).
[Crossref] [PubMed]

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

Science (1)

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

Other (13)

R. Martinenghi, A. Baylón-Fuentes, F. Xiaole, M. Jacquot, Y. Chembo, and L. Larger, “Optoelectronic nonlinear transient computing with multiple delays,” in 2013 Conference on Lasers Electro-Optics Europe International Quantum Electronics Conference CLEO EUROPE/IQEC, (2013).
[Crossref]

Yu Jin, Q. Zhao, H. Yin, and Hehe Yue, “Handwritten numeral recognition utilizing reservoir computing subject to optoelectronic feedback,” in 2015 11th International Conference on Natural Computation (ICNC), (2015), pp. 1165–1169.
[Crossref]

F. Triefenbach, A. Jalalvand, B. Schrauwen, and J. P. Martens, “Phoneme recognition with large hierarchical reservoirs,” in Proceedings of the 23rd International Conference on Neural Information Processing Systems, vol. 2 (Curran Associates Inc., 2010), pp. 2307–2315.

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

L. A. Feldkamp, D. V. Prokhorov, C. F. Eagen, and F. Yuan, Enhanced Multi-Stream Kalman Filter Training for Recurrent Networks (SpringerUS, 1998), pp. 29–54.

A. Graves, A. Mohamed, and G. Hinton, “Speech recognition with deep recurrent neural networks,” in 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, (2013), pp. 6645–6649.
[Crossref]

W. Mo, C. L. Gutterman, Y. Li, G. Zussman, and D. C. Kilper, “Deep neural network based dynamic resource reallocation of bbu pools in 5g c-ran roadm networks,” in Optical Fiber Communication Conference, (Optical Society of America, 2018).
[Crossref]

Y. Luo and Y. Huang, “Text steganography with high embedding rate: Using recurrent neural networks to generate chinese classic poetry,” in Proceedings of the 5th ACM Workshop on Information Hiding and Multimedia Security, (ACM, 2017), pp. 99–104.
[Crossref]

T. Instruments-Developed, “46-word speaker-dependent isolated word corpus (ti46),” NIST Speech Disc pp. 7–1.1 (1991).

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

A. Graves, D. Eck, N. Beringer, and J. Schmidhuber, “Biologically plausible speech recognition with lstm neural nets,” in Biologically Inspired Approaches to Advanced Information Technology, (SpringerBerlin Heidelberg, 2004), pp. 127–136.
[Crossref]

D. Verstraeten, B. Schrauwen, and D. Stroobandt, “Reservoir-based techniques for speech recognition,” in The 2006 IEEE International Joint Conference on Neural Network Proceedings, (2006), pp. 1050–1053.

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

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Figures (6)

Fig. 1
Fig. 1 (a) Schematic diagrams of traditional RC scheme. (b) Schematic diagrams of photonic RC scheme.

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Fig. 2
Fig. 2 The novel RC with double optoelectronic feedback loops. (a) Structure of the novel RC based on a SL with double feedback loops. SL, semiconductor laser; MZM, Mach-Zehnder modulator; OC, optical coupler; PD, photoelectric detector; OSC, oscilloscope; ODL, optical delay time; VOA, optical attenuator; PA, power amplifier; LPF, low pass filter; AWG, arbitrary waveform generator; PS, power splitter; EDL, electrical delay line. (b) Schematic of the novel RC based on a SL with two feedback loops. NL denotes the nonlinear transformation for the system. h(t) stands for the system’s impulse response. (c) The process of input signal multiplied by mask signal in the input layer.

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Fig. 3
Fig. 3 Simulation results for the nonlinear channel equalization task.

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Fig. 4
Fig. 4 NMSE dependence on Δτ from 0.1 ns to 3.4 ns for the first task.

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Fig. 5
Fig. 5 NMSE as a function of the feedback strength β in the novel RC for the first task.

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Fig. 6
Fig. 6 Color distribution map of NMSE obtained by ϕ1 and ϕ2 ranging from −π to π.

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Tables (2)

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Table 1 Comparison to simulation results for NARMA10 task

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Table 2 Comparison to simulation results for isolated spoken digits recognition

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Equations (6)

Equations on this page are rendered with MathJax. Learn more.

τ d x ( t ) d t + x ( t ) + 1 σ ∫ t 0 t x ( ε ) d ε = β cos 2 [ α p x ( t − τ 2 ) + ϕ 2 ] * cos 2 [ ( 1 − p ) x ( t − τ 1 ) + ϕ 1 + s ( t ) ]
{ d x ( t ) d t = − x / τ = y / ( τ σ ) + β cos 2 [ α p x ( t − τ 2 + ϕ 2 ]                                           * cos 2 [ ( 1 − p ) x ( t − τ 1 ) + ϕ 1 + s ( t ) ] / τ d y d t = x
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 ( n ) 2 − 0.011 q ( n ) 3 + v ( n )

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