Show Reference: "Optimal representation of sensory information by neural populations."

Optimal representation of sensory information by neural populations Nature Neuroscience, Vol. 9, No. 5. (16 May 2006), pp. 690-696, doi:10.1038/nn1691 by Mehrdad Jazayeri, Anthony A. Movshon
    abstract = {Sensory information is encoded by populations of neurons. The responses of individual neurons are inherently noisy, so the brain must interpret this information as reliably as possible. In most situations, the optimal strategy for decoding the population signal is to compute the likelihoods of the stimuli that are consistent with an observed neural response. But it has not been clear how the brain can directly compute likelihoods. Here we present a simple and biologically plausible model that can realize the likelihood function by computing a weighted sum of sensory neuron responses. The model provides the basis for an optimal decoding of sensory information. It explains a variety of psychophysical observations on detection, discrimination and identification, and it also directly predicts the relative contributions that different sensory neurons make to perceptual judgments.},
    address = {Center for Neural Science, 4 Washington Place, Room 809, New York University, New York, New York 10003, USA.},
    author = {Jazayeri, Mehrdad and Movshon, Anthony A.},
    day = {16},
    doi = {10.1038/nn1691},
    issn = {1097-6256},
    journal = {Nature Neuroscience},
    keywords = {population-coding},
    month = may,
    number = {5},
    pages = {690--696},
    pmid = {16617339},
    posted-at = {2013-01-09 14:26:48},
    priority = {2},
    publisher = {Nature Publishing Group},
    title = {Optimal representation of sensory information by neural populations},
    url = {},
    volume = {9},
    year = {2006}

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Jazayeri and Movshon call population vectors and winner-takes-all mechanisms "suboptimal under most conditions of interest."

Translating a population code into just one value (or vector) discards all information about uncertainty.

Jazayeri and Movshon present an ANN model for computing likelihood functions ($\approx$ probability density functions with uniform priors) from input population responses with arbitrary tuning functions.

Their assumptions are

  • restricted types of noise characteristics (eg. Poisson noise)
  • statistically independent noise

Since they work with log likelihoods, they can circumvent the problem of requiring neural multiplication.

In Jazayeri and Movshon's model decoding (or output) neurons calculate the logarithm of the input neurons' tuning functions.

This is not biologically plausible because that would give them transfer functions which are non-linear and non-sigmoid (and typically biologically plausible transfer functions said to be sigmoid).