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Absolute exponential stability of recurrent neural networks with generalized activation function.
Jun Xu1, Yong-Yan Cao, Youxian Sun
1System Research Institute & Department of Advanced Technologies, Alcorn State University, Alcorn State, MS 39096 USA. xujung@gmail.com
IEEE Transactions on Neural Networks
|June 11, 2008
Summary
This study introduces a novel generalized activation function class for recurrent neural networks (RNNs), proving their absolute exponential stability (AEST) using M-matrix theory for enhanced model reliability.
Area of Science:
- Artificial Intelligence
- Computational Neuroscience
- Dynamical Systems
Background:
- Recurrent Neural Networks (RNNs) are crucial for sequential data processing.
- Stability analysis of RNNs is essential for reliable performance.
- Existing activation functions have limitations in flexibility and generalization.
Purpose of the Study:
- To propose a novel generalized activation function class for RNNs.
- To analyze the absolute exponential stability (AEST) of RNNs with this new function class.
- To demonstrate the effectiveness of the proposed method with a two-neuron RNN model.
Main Methods:
- Defining a generalized activation function class bounded by piecewise linear functions.
- Proving the equivalence between the stability of the original RNN and RNNs under vertex functions.
- Transforming RNNs to systems with saturated linear activation functions.
- Utilizing M-matrix theory for stability analysis and existence of equilibrium points.
Main Results:
- A novel, flexible, and generalizable activation function class for RNNs is introduced.
- The absolute exponential stability (AEST) of RNNs with the generalized activation function class is demonstrated.
- The proposed method is validated through a two-neuron RNN example, confirming its effectiveness.
Conclusions:
- The proposed generalized activation function class offers enhanced flexibility and descriptive power.
- The established AEST provides a robust theoretical foundation for RNNs with these functions.
- This work contributes to the theoretical understanding and practical application of stable RNNs.
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