Multiple timescale Continuous-time Coding with Spiking Neurons
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1
CWI, Center for Mathematics and Computer Science, Dept Life Sciences, Netherlands
Recent experimental work has suggested that the neural firing rate can be interpreted as a fractional derivative, at least when signal variation induces neural adaptation [LHSF08]. We show that the actual neural spike-train itself can be considered as the fractional derivative, provided that the neural signal is approximated by a sum of power-law kernels. Empirically, we find that the online approximation of signals with a sum of fixed power-law kernels is beneficial for encoding signals with slowly varying components, like long-memory self-similar signals. For such signals, the online power-law kernel approximation typically required less than half the number of spikes for similar SNR as compared to sums of similar but exponentially decaying kernels. We also find that for encoding such signals, the optimal power-law exponent is similar to that reported for neural adaptation in experiments like [XPN96]. The magnitude of the kernel can be further optimized adaptively by considering the first moment of the fractional equivalent of the standard Taylor-expansion, the Taylor-Riemann series. This term is similar to the "speed" of the signal change, and has an inverse square dependence on interspike intervals. Qualitatively, this kernel modulation bears resembles `gain modulation' as observed experimentally, e.g. [HLF08]. Power-law kernels can be accurately approximated using sums or cascades of weighted exponentials on multiple timescales. With this in mind, we demonstrate by a receiving neuron can carry out natural and transparent temporal signal filtering by tuning the weighted exponentials that constitute its decoding kernel.
References
1)[HLF08] Hong, S., Lundstrom, B.N., and Fairhall, A.L. Intrinsic gain modulation and adaptive neural coding. PLoS Computational Biology, 4(7), 2008.
2)[LHSF08] Lundstrom, B.N., Higgs, M.H., Spain, W.J., Fairhall, A.L. Fractional differentiation by neocortical pyramidal neurons. Nature Neuroscience, 11(11):1335-1342, 2008.
3)[XPN96] Xu, Z., Payne, J.R., and Nelson, M.E. Logorithmic time course of sensory adaptation in electrosensory afferent nerve fibers in a weakly electric fish. Journal of Neurophysiology, 76(3):2020,1996.
Keywords:
computational neuroscience
Conference:
Bernstein Conference on Computational Neuroscience, Berlin, Germany, 27 Sep - 1 Oct, 2010.
Presentation Type:
Presentation
Topic:
Bernstein Conference on Computational Neuroscience
Citation:
Bohte
S and
Rombouts
J
(2010). Multiple timescale Continuous-time Coding with Spiking Neurons.
Front. Comput. Neurosci.
Conference Abstract:
Bernstein Conference on Computational Neuroscience.
doi: 10.3389/conf.fncom.2010.51.00113
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Received:
06 Sep 2010;
Published Online:
23 Sep 2010.
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Correspondence:
Dr. Sander Bohte, CWI, Center for Mathematics and Computer Science, Dept Life Sciences, Amsterdam, Netherlands, S.M.Bohte@cwi.nl