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Hierarchical Temporal Representation in Linear Reservoir Computing

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Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 102))

Abstract

Recently, studies on deep Reservoir Computing (RC) highlighted the role of layering in deep recurrent neural networks (RNNs). In this paper, the use of linear recurrent units allows us to bring more evidence on the intrinsic hierarchical temporal representation in deep RNNs through frequency analysis applied to the state signals. The potentiality of our approach is assessed on the class of Multiple Superimposed Oscillator tasks. Furthermore, our investigation provides useful insights to open a discussion on the main aspects that characterize the deep learning framework in the temporal domain.

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References

  1. Angelov, P., Sperduti, A.: Challenges in deep learning. In: Proceedings of the 24th European Symposium on Artificial Neural Networks (ESANN), pp. 489–495. i6doc.com (2016)

    Google Scholar 

  2. Čerňanskỳ, M., Tiňo, P.: Predictive modeling with echo state networks. Artif. Neural Netw ICANN 2008, 778–787 (2008)

    Google Scholar 

  3. Frigo, M., Johnson, S.G.: FFTW: An adaptive software architecture for the FFT. In: Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, vol. 3, pp. 1381–1384. IEEE (1998)

    Google Scholar 

  4. Gallicchio, C., Martin-Guerrero, J., Micheli, A., Soria-Olivas, E.: Randomized machine learning approaches: Recent developments and challenges. In: Proceedings of the 25th European Symposium on Artificial Neural Networks (ESANN), pp. 77–86. i6doc.com (2017)

    Google Scholar 

  5. Gallicchio, C., Micheli, A.: Deep reservoir computing: a critical analysis. In: Proceedings of the 24th European Symposium on Artificial Neural Networks (ESANN), pp. 497–502. i6doc.com (2016)

    Google Scholar 

  6. Gallicchio, C., Micheli, A.: Echo state property of deep reservoir computing networks. Cogn. Comput. 337–350 (2017). https://doi.org/10.1007/s12559-017-9461-9

    Article  Google Scholar 

  7. Gallicchio, C., Micheli, A., Pedrelli, L.: Deep reservoir computing: a critical experimental analysis. Neurocomputing 87–99 (2017). https://doi.org/10.1016/j.neucom.2016.12.089

    Article  Google Scholar 

  8. Gallicchio, C., Micheli, A., Silvestri, L.: Local Lyapunov Exponents of Deep RNN. In: Proceedings of the 25th European Symposium on Artificial Neural Networks (ESANN), pp. 559–564. i6doc.com (2017)

    Google Scholar 

  9. Hermans, M., Schrauwen, B.: Training and analysing deep recurrent neural networks. In: NIPS, pp. 190–198 (2013)

    Google Scholar 

  10. Hihi, S.E., Bengio, Y.: Hierarchical recurrent neural networks for long-term dependencies. In: NIPS, pp. 493–499 (1995)

    Google Scholar 

  11. Holzmann, G., Hauser, H.: Echo state networks with filter neurons and a delay & sum readout. Neural Netw. 23(2), 244–256 (2010)

    Article  Google Scholar 

  12. Jaeger, H., Haas, H.: Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication. Science 304(5667), 78–80 (2004)

    Article  Google Scholar 

  13. Jaeger, H., Lukoševičius, M., Popovici, D., Siewert, U.: Optimization and applications of echo state networks with leaky-integrator neurons. Neural Netw. 20(3), 335–352 (2007)

    Article  Google Scholar 

  14. Koryakin, D., Lohmann, J., Butz, M.: Balanced echo state networks. Neural Netw. 36, 35–45 (2012)

    Article  Google Scholar 

  15. Lukoševičius, M., Jaeger, H.: Reservoir computing approaches to recurrent neural network training. Comput. Sci. Rev. 3(3), 127–149 (2009)

    Article  Google Scholar 

  16. Otte, S., Butz, M.V., Koryakin, D., Becker, F., Liwicki, M., Zell, A.: Optimizing recurrent reservoirs with neuro-evolution. Neurocomputing 192, 128–138 (2016)

    Article  Google Scholar 

  17. Pasa, L., Sperduti, A.: Pre-training of recurrent neural networks via linear autoencoders. In: Advances in Neural Information Processing Systems, pp. 3572–3580 (2014)

    Google Scholar 

  18. Pascanu, R., Gülçehre, Ç., Cho, K., Bengio, Y.: How to construct deep recurrent neural networks, pp. 1–13. arXiv preprint arXiv:1312.6026v5 (2014)

  19. Schmidhuber, J.: Deep learning in neural networks: an overview. Neural Netw. 61, 85–117 (2015)

    Article  Google Scholar 

  20. Schmidhuber, J., Wierstra, D., Gagliolo, M., Gomez, F.: Training recurrent networks by evolino. Neural Comput. 19(3), 757–779 (2007)

    Article  Google Scholar 

  21. Verstraeten, D., Schrauwen, B., d’Haene, M., Stroobandt, D.: An experimental unification of reservoir computing methods. Neural Netw. 20(3), 391–403 (2007)

    Article  Google Scholar 

  22. Wierstra, D., Gomez, F.J., Schmidhuber, J.: Modeling systems with internal state using evolino. In: Proceedings of the 7th Annual Conference on Genetic and Evolutionary Computation, pp. 1795–1802. ACM (2005)

    Google Scholar 

  23. Xue, Y., Yang, L., Haykin, S.: Decoupled echo state networks with lateral inhibition. Neural Netw. 20(3), 365–376 (2007)

    Article  Google Scholar 

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Correspondence to Claudio Gallicchio .

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Gallicchio, C., Micheli, A., Pedrelli, L. (2019). Hierarchical Temporal Representation in Linear Reservoir Computing. In: Esposito, A., Faundez-Zanuy, M., Morabito, F., Pasero, E. (eds) Neural Advances in Processing Nonlinear Dynamic Signals. WIRN 2017 2017. Smart Innovation, Systems and Technologies, vol 102. Springer, Cham. https://doi.org/10.1007/978-3-319-95098-3_11

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