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Deterministic convergence of chaos injection-based gradient method for training feedforward neural networks.
Huisheng Zhang1, Ying Zhang2, Dongpo Xu3
1Department of Mathematics, Dalian Maritime University, Dalian, 116026 People's Republic of China ; Research Center of Information and Control, Dalian University of Technology, Dalian, 116024 People's Republic of China.
Cognitive Neurodynamics
|May 15, 2015
Summary
Chaos injection-based gradient method (CIBGM) improves neural network training over standard backpropagation. This study proves CIBGM
Area of Science:
- Artificial Intelligence
- Machine Learning
- Computational Neuroscience
Background:
- Standard backpropagation algorithm faces limitations in neural network training.
- Chaos injection offers a novel approach to enhance gradient-based learning methods.
Purpose of the Study:
- To provide a theoretical convergence analysis of the chaos injection-based gradient method (CIBGM).
- To evaluate CIBGM for both batch and online learning scenarios in feedforward neural networks.
Main Methods:
- Theoretical convergence analysis of CIBGM.
- Mathematical proofs for weak and strong convergence under specified conditions.
- Simulation example to validate theoretical findings.
Main Results:
- Weak convergence of CIBGM is proven, showing training error stabilization and gradient minimization.
- Strong convergence is achieved with an additional condition.
- CIBGM demonstrates superior performance compared to standard backpropagation.
Conclusions:
- CIBGM offers a theoretically sound and effective method for training feedforward neural networks.
- The convergence properties of CIBGM are well-defined for both batch and online learning.
- Chaos injection is a promising technique for improving neural network training efficiency and stability.
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