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Kolmogorov's Theorem Is Relevant
1Institute of Computer Science, Czechoslovak Academy of Sciences, P. O. Box 5, 182 07 Prague 8, Czechoslovakia.
Neural Computation
|June 7, 2019
Summary
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.
- 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.
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