Population models of temporal differentiation

Neural Computation
Bryan P Tripp, Chris Eliasmith

Abstract

Temporal derivatives are computed by a wide variety of neural circuits, but the problem of performing this computation accurately has received little theoretical study. Here we systematically compare the performance of diverse networks that calculate derivatives using cell-intrinsic adaptation and synaptic depression dynamics, feedforward network dynamics, and recurrent network dynamics. Examples of each type of network are compared by quantifying the errors they introduce into the calculation and their rejection of high-frequency input noise. This comparison is based on both analytical methods and numerical simulations with spiking leaky-integrate-and-fire (LIF) neurons. Both adapting and feedforward-network circuits provide good performance for signals with frequency bands that are well matched to the time constants of postsynaptic current decay and adaptation, respectively. The synaptic depression circuit performs similarly to the adaptation circuit, although strictly speaking, precisely linear differentiation based on synaptic depression is not possible, because depression scales synaptic weights multiplicatively. Feedback circuits introduce greater errors than functionally equivalent feedforward circuits, but they have the...Continue Reading

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Citations

Jul 31, 2013·Proceedings of the National Academy of Sciences of the United States of America·Stephen E ClarkeLeonard Maler
Oct 8, 2013·PLoS Computational Biology·Farzad FarkhooiMartin P Nawrot
Jun 13, 2014·PLoS Computational Biology·Bruce BobierChris Eliasmith
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Mar 11, 2016·Neural Networks : the Official Journal of the International Neural Network Society·Bryan Tripp, Chris Eliasmith
Mar 25, 2011·Cognitive Science·Paul Thagard, Terrence C Stewart
Mar 17, 2015·Neural Computation·Bryan P Tripp
Dec 9, 2017·Neural Computation·Aaron R Voelker, Chris Eliasmith
Oct 31, 2020·Proceedings of the National Academy of Sciences of the United States of America·Hannes Rapp, Martin Paul Nawrot

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