Connectionists: paper on fractional neural coding

[Sander Bohte]

May I kindly draw your attention to our new paper on neural coding
with spiking neurons, which we believe may be of interest for people
both more experimentally inclined as well as those working on
(spiking) neural networks.

Fractionally Predictive Spiking Neurons
Sander M. Bohte, Jaldert O. Rombouts, to appear at NIPS 2010.

http://arxiv.org/abs/1010.6178

Recent experimental work suggests that the neural firing rate can be
interpreted as a (mild) fractional derivative, at least when signal
variation induces neural adaptation. Here, we show that the actual
neural spike-train itself can be considered as a fractional
derivative, provided that the neural signal is approximated by a sum
of power-law kernels. A simple standard thresholding spiking neuron
suffices to carry out such an approximation, given a suitable
refractory response. Empirically, we find that the online
approximation of signals with a sum of 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. As power-law kernels can be accurately approximated
using sums or cascades of weighted exponentials, we demonstrate that
the corresponding decoding of spike-trains by a receiving neuron
allows for natural and transparent spectral signal filtering by tuning
the weights of the decoding kernel.

Regards,
Sander Bohte
CWI Amsterdam