Show Reference: "Simple models for reading neuronal population codes"

Simple models for reading neuronal population codes Proceedings of the National Academy of Sciences, Vol. 90, No. 22. (15 November 1993), pp. 10749-10753, doi:10.1073/pnas.90.22.10749 by H. Sebastian Seung, Haim Sompolinsky
    abstract = {In many neural systems, sensory information is distributed throughout a population of neurons. We study simple neural network models for extracting this information. The inputs to the networks are the stochastic responses of a population of sensory neurons tuned to directional stimuli. The performance of each network model in psychophysical tasks is compared with that of the optimal maximum likelihood procedure. As a model of direction estimation in two dimensions, we consider a linear network that computes a population vector. Its performance depends on the width of the population tuning curves and is maximal for width, which increases with the level of background activity. Although for narrowly tuned neurons the performance of the population vector is significantly inferior to that of maximum likelihood estimation, the difference between the two is small when the tuning is broad. For direction discrimination, we consider two models: a perceptron with fully adaptive weights and a network made by adding an adaptive second layer to the population vector network. We calculate the error rates of these networks after exhaustive training to a particular direction. By testing on the full range of possible directions, the extent of transfer of training to novel stimuli can be calculated. It is found that for threshold linear networks the transfer of perceptual learning is nonmonotonic. Although performance deteriorates away from the training stimulus, it peaks again at an intermediate angle. This nonmonotonicity provides an important psychophysical test of these models.},
    address = {AT\&T Bell Laboratories, Murray Hill, NJ 07974.},
    author = {Seung, H. Sebastian and Sompolinsky, Haim},
    day = {15},
    doi = {10.1073/pnas.90.22.10749},
    issn = {0027-8424},
    journal = {Proceedings of the National Academy of Sciences},
    keywords = {ann, math, population-coding},
    month = nov,
    number = {22},
    pages = {10749--10753},
    pmid = {8248166},
    posted-at = {2012-09-24 10:57:52},
    priority = {2},
    title = {Simple models for reading neuronal population codes},
    url = {},
    volume = {90},
    year = {1993}

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MLE provides an optimal method of reading population codes.

It's hard to implement MLE on population codes using neural networks.

Depending on the application, tuning curves, and noise properties, threshold linear networks calculating population vectors can have similar performance as MLE.

There seems to be a linear relationship between the mean and variance of neural responses in cortex. This is similar to a Poisson distribution where the variance equals the mean, however, the linearity constant does not seem to be one in biology.

Seung and Sempolinsky introduce maximum likelihood estimation (MLE) as one possible mechanism for neural read-out. However, they state that it is not clear whether MLE can be implemented in a biologically plausible way.

Seung and Sempolinsky show that, in a population code with wide tuning curves and poisson noise and under the conditions described in their paper, the response of neurons near threshold carries exceptionally high information.