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Relaxed conditions for radial-basis function networks to be universal approximators
Yi Liao1, Shu-Cherng Fang, Henry L W Nuttle
1Operations Research and Industrial Engineering, North Carolina State University, Raleigh, NC 27695-7906, USA. yliao2@eos.ncsu.edu
Summary
Radial Basis Function (RBF) networks can approximate continuous functions without requiring integrable RBFs. This study details conditions for RBF networks to achieve universal approximation, enhancing machine learning theory.
Area of Science:
- Artificial Intelligence
- Machine Learning
- Computational Theory
Background:
- Radial Basis Function (RBF) networks are a class of artificial neural networks.
- Universal approximation property is a key theoretical aspect of neural networks.
- Integrability of RBFs was previously considered a requirement for universal approximation.
Purpose of the Study:
- To investigate the conditions under which Radial Basis Function networks exhibit universal approximation properties.
- To determine if integrability of RBFs is a necessary condition for universal approximation.
- To analyze the approximation capabilities of RBF networks in L(p) spaces.
Main Methods:
- Theoretical analysis of RBF network approximation capabilities.
- Examination of the properties of the radial basis activation function.
- Discussion of approximation in L(p) spaces.
Main Results:
- Radial Basis Function networks do not require integrable RBFs to be universal approximators.
- Continuous approximation is achievable if the RBF activation function is continuous almost everywhere, locally essentially bounded, and not a polynomial.
- The study also addresses approximation in L(p) spaces.
Conclusions:
- The findings relax the conditions for RBF network universal approximation.
- This research contributes to a deeper theoretical understanding of RBF networks.
- The results have implications for designing and analyzing neural network models.