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Related Experiment Videos

Kolmogorov's Theorem Is Relevant.

Věra Kůrková1

  • 1Institute of Computer Science, Czechoslovak Academy of Sciences, P. O. Box 5, 182 07 Prague 8, Czechoslovakia.

Neural Computation
|June 7, 2019
PubMed
Summary
This summary is machine-generated.

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Kolmogorov

Area of Science:

  • Mathematics
  • Computer Science
  • Artificial Intelligence

Background:

  • Kolmogorov's theorem provides a theoretical basis for representing complex functions using simpler ones.
  • Neural networks are powerful function approximators used in artificial intelligence.
  • Understanding the theoretical underpinnings of neural networks is crucial for their development.

Purpose of the Study:

  • To demonstrate the relevance of Kolmogorov's theorem to neural network theory.
  • To adapt Kolmogorov's theorem for approximating functions using neural network components.
  • To establish theoretical bounds on the complexity of neural networks.

Main Methods:

  • Applying Kolmogorov's theorem to the architecture of neural networks.
  • Approximating single-variable functions using compositions of affine transformations and sigmoidal functions.

Related Experiment Videos

  • Deriving upper bounds for the number of hidden units required.

    • Main Results:

    • Kolmogorov's theorem is applicable to understanding neural network representations.
    • A version of the theorem allows approximating functions with specific neural network building blocks.
    • An upper estimate for the number of hidden units in neural networks was derived.

    Conclusions:

    • The study bridges theoretical mathematics and practical neural network design.
    • The findings offer insights into the representational capacity of neural networks.
    • The derived estimates can guide the efficient design of neural network architectures.