Reformulated radial basis neural networks trained by gradient descent

Area of Science:

• Artificial Intelligence
• Machine Learning
• Neural Networks

Background:

• Radial Basis Function (RBF) neural networks are widely used in machine learning.
• Existing methods for constructing RBF networks have limitations in model variety and training efficiency.

Purpose of the Study:

• To present an axiomatic approach for constructing a diverse range of RBF neural network models.
• To propose a novel supervised learning algorithm for training these reformulated RBF networks.
• To analyze the convergence properties of the proposed learning algorithm.

Main Methods:

• Developed an axiomatic framework for RBF network construction using generator functions.
• Proposed a gradient descent-based supervised learning algorithm for training.
• Conducted sensitivity analysis to link RBF properties with learning convergence.
• Experimented with RBF networks generated by linear and exponential functions.

Main Results:

• The axiomatic approach allows for a broad variety of admissible RBF models beyond Gaussian RBFs.
• The proposed gradient descent algorithm is simple and easily implementable.
• Reformulated RBF networks trained with the proposed algorithm outperform conventional RBF models.
• Sensitivity analysis provides insights into the relationship between RBF characteristics and learning convergence.

Conclusions:

• The proposed axiomatic construction and gradient descent training offer a flexible and effective method for developing RBF neural networks.
• This approach enhances the performance and applicability of RBF networks in various machine learning tasks.
• The findings suggest a promising direction for future research in neural network design and training.