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Robust stochastic resonance for simple threshold neurons.

Bart Kosko1, Sanya Mitaim

  • 1Department of Electrical Engineering, Signal and Image Processing Institute, University of Southern California, Los Angeles, California 90089-2564, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 5, 2004
PubMed
Summary

Adding small amounts of noise enhances threshold neuron performance, a phenomenon known as stochastic resonance (SR). This effect is robust across various noise types, including those with infinite variance, demonstrating its broad applicability in neural systems.

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Area of Science:

  • Computational neuroscience
  • Nonlinear dynamics
  • Information theory

Background:

  • Memoryless threshold neurons are fundamental components in neural processing.
  • Stochastic resonance (SR) describes how noise can enhance signal detection in nonlinear systems.
  • Understanding noise effects is crucial for modeling neural function and developing artificial intelligence.

Purpose of the Study:

  • To investigate the impact of various additive noise types on the performance of memoryless threshold neurons.
  • To establish the conditions under which stochastic resonance (SR) occurs in these systems.
  • To explore the robustness of SR with different noise probability distributions, including alpha-stable noise.

Main Methods:

  • Utilized simulation and theoretical analysis to model neuron behavior.

Related Experiment Videos

  • Employed input-output mutual information to quantify system performance.
  • Investigated a wide range of noise probability density functions (PDFs), including finite variance and alpha-stable distributions.
  • Performed regression analysis to identify relationships between noise characteristics and SR performance.

    • Main Results:

    • Demonstrated that small amounts of additive noise enhance the performance of memoryless threshold neurons, inducing the stochastic resonance (SR) effect.
    • Established that SR occurs for a broad class of noise PDFs, provided the noise mean is outside a specific controllable interval.
    • Showed that SR is robust even with alpha-stable noise, which features infinite variance and models impulsive environments.
    • Identified quantitative relationships between noise properties (dispersion, tail thickness) and SR-maximal mutual information.

    Conclusions:

    • Stochastic resonance is a widespread phenomenon in threshold systems, benefiting from various noise types.
    • The SR effect in threshold neurons is remarkably robust, persisting even under extreme noise conditions like those modeled by alpha-stable distributions.
    • The findings provide a theoretical foundation for understanding noise-enhanced computation in neural systems and have implications for designing noise-tolerant artificial systems.