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A Quaternionic Rate-Based Synaptic Learning Rule Derived from Spike-Timing Dependent Plasticity

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 10261)

Abstract

Most of the differential Hebbian rules derived from Spike-Timing Dependent Plasticity (STDP) focus on the rates of change of post-synaptic activity that carries the information about the future and enables the neural network to predict. And the current model mainly consider three factors for the adjustment of synaptic weight, namely, the rate of pre- and post-synaptic activity and the rate of change of post-synaptic activity. We argue that the rate of change of pre-synaptic activity also plays an important role on the adjustment of synaptic weight. Hence, this paper proposes a quaternionic rate-based synaptic learning rule that depends on four elements, namely, the instantaneous firing rates of both pre- and post-synaptic neurons and their time derivatives.

Keywords

  • Spike-Timing Dependent Plasticity
  • Quaternionic rate-based synaptic learning rule
  • Instantaneous firing rate

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Fig. 1.

References

  1. Bengio, Y., Lee, D.H., Bornschein, J., Lin, Z.: Towards biologically plausible deep learning. arXiv preprint arXiv:1502.04156 (2015)

  2. Bengio, Y., Mesnard, T., Fischer, A., Zhang, S., Wu, Y.: STDP as presynaptic activity times rate of change of postsynaptic activity. arXiv preprint arXiv:1509.05936 (2015)

  3. Bi, G.Q., Poo, M.M.: Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type. J. Neurosci. 18(24), 10464–10472 (1998)

    Google Scholar 

  4. Chrol-Cannon, J., Grüning, A., Jin, Y.: The emergence of polychronous groups under varying input patterns, plasticity rules and network connectivities. In: The 2012 International Joint Conference on Neural Networks (IJCNN), pp. 1–6 (2012)

    Google Scholar 

  5. Froemke, R.C., Letzkus, J.J., Kampa, B.M., Hang, G.B., Stuart, G.J.: Dendritic synapse location and neocortical spike-timing-dependent plasticity. Front. Synaptic Neurosci. 2, 29 (2010)

    Google Scholar 

  6. Gabbiani, F., Cox, S.J.: Mathematics for neuroscientists. Academic Press, Cambridge (2010)

    MATH  Google Scholar 

  7. Gerstner, W., Kempter, R., van Hemmen, J.L., Wagner, H.: A neuronal learning rule for sub-millisecond temporal coding. Nature 383(6595), 76–78 (1996)

    CrossRef  Google Scholar 

  8. Gerstner, W., Kistler, W.M.: Mathematical formulations of hebbian learning. Biol. Cybern. 87(5–6), 404–415 (2002)

    CrossRef  MATH  Google Scholar 

  9. Guyonneau, R., VanRullen, R., Thorpe, S.J.: Neurons tune to the earliest spikes through STDP. Neural Comput. 17(4), 859–879 (2005)

    CrossRef  MATH  Google Scholar 

  10. Henneman, E., Mendell, L.M.: Functional organization of motoneuron pool and its inputs. In: Comprehensive Physiology, pp. 423–507 (2011). http://onlinelibrary.wiley.com/doi/10.1002/cphy.cp010211/abstract;jsessionid=DC8038A8B928C849064AFF986290D55A.f04t01

  11. Iakymchuk, T., Rosado-Muñoz, A., Guerrero-Martínez, J.F., Bataller-Mompeán, M., Francés-Víllora, J.V.: Simplified spiking neural network architecture and STDP learning algorithm applied to image classification. EURASIP J. Image Video Process. 2015(1), 1–11 (2015)

    CrossRef  Google Scholar 

  12. Izhikevich, E.M., Desai, N.S.: Relating STDP to BCM. Neural Comput. 15(7), 1511–1523 (2003)

    CrossRef  MATH  Google Scholar 

  13. Kempter, R., Gerstner, W., Van Hemmen, J.L.: Spike-based compared to rate-based hebbian learning. Adv. Neural Inf. Process. Syst. 11, 125–131 (1999)

    MATH  Google Scholar 

  14. Lass, Y., Abeles, M.: Transmission of information by the axon: I. Noise and memory in the myelinated nerve fiber of the frog. Biol. Cybern. 19(2), 61–67 (1975)

    CrossRef  Google Scholar 

  15. Markram, H., Sakmann, B.: Action potentials propagating back into dendrites trigger changes in efficacy of single-axon synapses between layer V pyramidal neurons. Soc. Neurosci. Abstr. 21, 2007 (1995)

    Google Scholar 

  16. Nessler, B., Pfeiffer, M., Maass, W.: STDP enables spiking neurons to detect hidden causes of their inputs. In: Advances in Neural Information Processing Systems, pp. 1357–1365 (2009)

    Google Scholar 

  17. Rao, R.P., Sejnowski, T.J.: Spike-timing-dependent hebbian plasticity as temporal difference learning. Neural Comput. 13(10), 2221–2237 (2001)

    CrossRef  MATH  Google Scholar 

  18. Roberts, P.D.: Computational consequences of temporally asymmetric learning rules: I. Differential hebbian learning. J. Comput. Neurosci. 7(3), 235–246 (1999)

    CrossRef  MATH  Google Scholar 

  19. Scellier, B., Bengio, Y.: Equilibrium propagation: bridging the gap between energy-based models and backpropagation. arXiv preprint arXiv:1602.05179 (2016)

  20. Senn, W., Pfister, J.P.: Spike-timing-dependent plasticity, learning rules. In: Jaeger, D., Jung, R. (eds.) Encyclopedia of Computational Neuroscience, pp. 1–10. Springer, Heidelberg (2014)

    Google Scholar 

  21. Sjöström, P.J., Rancz, E.A., Roth, A., Häusser, M.: Dendritic excitability and synaptic plasticity. Physiol. Rev. 88(2), 769–840 (2008)

    CrossRef  Google Scholar 

  22. Stevens, C.F., Wang, Y., et al.: Changes in reliability of synaptic function as a mechanism for plasticity. Nature 371(6499), 704–707 (1994)

    CrossRef  Google Scholar 

  23. Waddington, A., Appleby, P.A., De Kamps, M., Cohen, N.: Triphasic spike-timing-dependent plasticity organizes networks to produce robust sequences of neural activity. Front. Comput. Neurosci. 6, 88 (2012)

    CrossRef  Google Scholar 

  24. Xie, X., Seung, H.S.: Spike-based learning rules and stabilization of persistent neural activity. Adv. Neural Inf. Process. Syst. 12, 199–208 (2000)

    Google Scholar 

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Acknowledgement

This study was funded by the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB02060007), and Beijing Municipal Commission of Science and Technology (Z151100000915070, Z161100000216124). This research is conducted at Institute of Automation, Chinese Academy of Science.

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Correspondence to Yi Zeng .

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Qiao, G., Du, H., Zeng, Y. (2017). A Quaternionic Rate-Based Synaptic Learning Rule Derived from Spike-Timing Dependent Plasticity. In: Cong, F., Leung, A., Wei, Q. (eds) Advances in Neural Networks - ISNN 2017. ISNN 2017. Lecture Notes in Computer Science(), vol 10261. Springer, Cham. https://doi.org/10.1007/978-3-319-59072-1_54

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  • DOI: https://doi.org/10.1007/978-3-319-59072-1_54

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