Abstract
Reservoir computing is a bio-inspired computing paradigm for processing time-dependent signals. The performance of its hardware implementation is comparable to state-of-the-art digital algorithms on a series of benchmark tasks. The major bottleneck of its implementations is the readout layer, based on slow offline post-processing. Few analogue solutions have been proposed, but all suffered from noticeable decrease in performance due to added complexity of the setup. Here, we propose the use of online training to solve these issues. We study the applicability of this method using numerical simulations of an experimentally feasible reservoir computer with an analogue readout layer. We also consider a nonlinear output layer, which would be very difficult to train with traditional methods. We show numerically that online learning allows to circumvent the added complexity of the analogue layer and obtain the same level of performance as with a digital layer. This work paves the way to high-performance fully analogue reservoir computers through the use of online training of the output layers.
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References
Jaeger H, Haas H. Science 2004;304:78.
Maass W., Natschläger T., Markram H. Neural comput 2002;14:2531.
Lukoševičius M., Jaeger H. Comp Sci Rev 2009;3:127.
Triefenbach F., Jalalvand A., Schrauwen B., Martens J. P. Adv Neural Inf Process Syst 2010;23: 2307.
Meftah B., Lézoray O., Benyettou A. Cogn Comput 2016;8(2):237.
Malik Z. K., Hussain A., Wu J. Cogn Comput 2014;6(3):595.
Scardapane S., Uncini A. Cogn Comput 2016:1–11.
2006. The 2006/07 forecasting competition for neural networks computational intelligence. http://www.neural-forecasting-competition.com/NN3/.
Arsenault H. Optical processing and computing: Elsevier; 2012.
Appeltant L., Soriano M. C., Van der Sande G., Danckaert J., Massar S., Dambre J., Schrauwen B., Mirasso C. R., Fischer I. Nat Commun 2011;2:468.
Paquot Y., Duport F., Smerieri A., Dambre J., Schrauwen B., Haelterman M., Massar S. Sci Rep 2012;2:287.
Larger L., Soriano M., Brunner D., Appeltant L., Gutiérrez J. M., Pesquera L., Mirasso C. R., Fischer I. Opt Express 2012;20:3241.
Martinenghi R., Rybalko S., Jacquot M., Chembo Y. K., Larger L. Phys Rev Let 2012;108: 244101.
Duport F., Schneider B., Smerieri A., Haelterman M., Massar S. Opt Express 2012;20:22783.
Brunner D., Soriano M. C., Mirasso C. R., Fischer I. Nat Commun 2012;4:1364.
Vinckier Q., Duport F., Smerieri A., Vandoorne K., Bienstman P., Haelterman M., Massar S. Optica 2015;2(5):438.
Vandoorne K., Mechet P., Van Vaerenbergh T., Fiers M., Morthier G., Verstraeten D., Schrauwen B., Dambre J., Bienstman P. Nat Commun 2014;5:3541.
Woods D., Naughton T. J. Nat Phys 2012;8(4):257.
Smerieri A., Duport F., Paquot Y., Schrauwen B., Haelterman M., Massar S. 2012:944–952.
Duport F., Smerieri A., Akrout A., Haelterman M., Massar S. Sci Rep 2016;6:22381.
Vinckier Q., Bouwens A., Haelterman M., Massar S. Opt Soc Amer 2016:SF1F.1.
Bottou L. In: Online learning and neural networks: Cambridge University Press; 1998. http://leon.bottou.org/papers/bottou-98x.
Shalev-Shwartz S. Found Trends Mach Learn 2012;4(2):107.
Antonik P., Duport F., Hermans M., Smerieri A., Haelterman M., Massar S. IEEE Trans Neural Netw Learn Syst 2016;PP(99):1.
Rodan A., Tino P. IEEE Trans Neural Netw 2011;22:131.
Arfken G. B. Mathematical methods for physicists. Orlando, FL: Academic Press; 1985.
Bishop CM. Pattern recognition and machine learning: Springer; 2006.
Press W. H., Flannery B. P., Teukolsky S. A., Vetterling W.T. 1986. Numerical recipes: the art of scientific computing.
Bottou L. In: Advanced lectures on machine learning: Springer Verlag; 2004, pp. 146–168.
Mathews V. J., Lee J. In: SPIE’s 1994 International Symposium on Optics, Imaging, and Instrumentation: International Society for Optics and Photonics; 1994, pp. 317–327.
Horowitz P., Hill W. The art of electronics: Cambridge University Press; 1980.
Tikhonov A. N., Goncharsky A., Stepanov V., Yagola A. G., Vol. 328. Numerical methods for the solution of ill-posed problems. Netherlands: Springer; 1995.
Soriano M. C., Ortín S., Brunner D., Larger L., Mirasso C. R., Fischer I., Pesquera L. Opt Express 2013;21(1):12.
Soriano M. C., Ortín S., Keuninckx L., Appeltant L., Danckaert J., Pesquera L., Van der Sande G. IEEE Trans Neural Netw Learn Syst 2015;26(2):388.
Antonik P., Hermans M., Duport F., Haelterman M., Massar S. In: SPIE’s 2016 Laser Technology and Industrial Laser Conference 2016;9732:97320B.
Bauduin M., Vinckier Q., Massar S., Horlin F. In: 2016 IEEE 17th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC): IEEE; 2016, pp. 1–5.
Antonik P., Hermans M., Haelterman M., Massar S., Vol. 9948. APNNS’s 23th International Conference on Neural Information Processing: LNCS; 2016, pp. 318–325.
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This study was funded by the Interuniversity Attraction Poles program of the Belgian Science Policy Office (grant IAP P7-35 “photonics@be”), by the Fonds de la Recherche Scientifique FRS-FNRS and by the Action de Recherche Concertée of the Académie Universitaire Wallonie-Bruxelles (grant AUWB-2012-12/17-ULB9).
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Antonik, P., Haelterman, M. & Massar, S. Online Training for High-Performance Analogue Readout Layers in Photonic Reservoir Computers. Cogn Comput 9, 297–306 (2017). https://doi.org/10.1007/s12559-017-9459-3
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DOI: https://doi.org/10.1007/s12559-017-9459-3