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Universal approximation by radial basis function networks of Delsarte translates
Cristian Arteaga1, Isabel Marrero
1Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, Tenerife, Spain. cclement@ull.es
Summary
Radial basis function neural networks using Delsarte translations, with consistent smoothing factors, achieve universal approximation. This finding expands the capabilities of these networks in function approximation tasks.
Area of Science:
- Artificial Intelligence
- Machine Learning
- Neural Networks
Background:
- Radial basis function (RBF) neural networks are powerful function approximators.
- Traditional RBF networks utilize standard translations, which can limit their approximation capabilities.
- Exploring alternative translation methods is crucial for enhancing network performance.
Purpose of the Study:
- To investigate the universal approximation property of RBF neural networks employing Delsarte translations.
- To determine the conditions under which these modified RBF networks exhibit universal approximation.
Main Methods:
- We analyzed RBF neural networks where the standard translation is replaced by the Delsarte translation.
- The study imposed mild conditions on the kernel (activation) functions.
- A consistent smoothing factor was applied across all kernel nodes.
Main Results:
- The modified family of RBF neural networks demonstrates the universal approximation property.
- This property holds under specific, mild conditions on the kernel function.
- The use of Delsarte translation is key to achieving this enhanced capability.
Conclusions:
- RBF neural networks with Delsarte translations offer a robust framework for universal approximation.
- The findings suggest potential improvements in modeling complex functions using these networks.
- This research contributes to the theoretical understanding of neural network approximation capabilities.
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