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Related Experiment Videos

Rectification of correlation by a sigmoid nonlinearity

P Bedenbaugh1, G L Gerstein

  • 1Department of Neuroscience, University of Pennsylvania, School of Medicine, Philadelphia 19104-6085.

Biological Cybernetics
|January 1, 1994
PubMed
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The sigmoid function partially rectifies correlation coefficients in Gaussian noise, reducing output correlation more for negative inputs. This explains neural network sensitivity and low negative correlations in biological neurons.

Area of Science:

  • Computational Neuroscience
  • Signal Processing

Background:

  • The behavior of nonlinear systems with noisy inputs is crucial for understanding complex signal processing.
  • Autocovariance functions characterize the temporal dependencies within signals.

Purpose of the Study:

  • To investigate how an error function (erf) nonlinearity affects the autocovariance of Gaussian noise input.
  • To analyze the impact of sigmoid width, input mean, and noise variance on output correlation.

Main Methods:

  • Mathematical analysis of the normalized autocovariance function for an erf nonlinearity.
  • Consideration of jointly Gaussian inputs with identical mean and autocovariance.

Main Results:

  • Output correlation closely matches input correlation when the sigmoid is wide or the input mean is near the midpoint.

Related Experiment Videos

  • Sigmoid saturation significantly reduces output correlation, especially for negative correlations, demonstrating partial rectification.
  • The analysis is independent of input noise spectral properties.

    • Conclusions:

    • Sigmoid nonlinearities exhibit 'correlational rectification,' altering the input signal's temporal dependencies.
    • This property may explain parameter sensitivity in neural network models.
    • The findings offer a potential explanation for the scarcity of negative correlations observed in biological neural spike trains.