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Synthesis of feedforward networks in supremum error bound
K Ciesielski1, J P Sacha, K J Cios
1Department of Mathematics, West Virginia University, Morgantown, WV 26506, USA. K_cies@math.wvu.edu
IEEE Transactions on Neural Networks
|February 6, 2008
Summary
This study provides a formula for bounding approximation errors in neural networks. This finding enables new methods for designing and initializing neural network weights for improved performance.
Area of Science:
- Computational mathematics
- Artificial intelligence
- Neural networks
Background:
- Multidimensional function approximation is a core problem in computational mathematics.
- Feedforward neural networks with sigmoidal units are widely used for function approximation.
- Quantifying approximation error bounds is crucial for network design and analysis.
Purpose of the Study:
- To derive a constructive proof for the upper bound of approximation error in the Linfinity norm for feedforward neural networks.
- To introduce a novel method for neural network synthesis based on the derived error bound.
- To explore applications of the error bound formula in estimating network complexity and initializing network weights.
Main Methods:
- Constructive proof methodology.
- Analysis of feedforward neural networks with one hidden layer and sigmoidal activation units.
- Application of supremum norm (Linfinity) for error quantification.
Main Results:
- A precise formula for the upper bound of approximation error in the Linfinity norm was established.
- A new method for synthesizing neural networks was formulated.
- The derived formula was shown to be applicable for estimating the complexity and initializing weights of maximum-error networks.
Conclusions:
- The derived error bound provides a theoretical foundation for understanding and controlling approximation accuracy in neural networks.
- The proposed synthesis method offers a systematic approach to designing neural networks with guaranteed error bounds.
- The results contribute to the theoretical understanding of neural network approximation capabilities and practical network design.
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