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Robust local stability of multilayer recurrent neural networks
J K Suykens1, B De Moor, J Vandewalle
1Katholieke Universiteit Leuven, Department of Electrical Engineering, ESAT-SISTA, Kardinaal Mercierlaan 94, B-3001 Leuven (Heverlee), Belgium.
IEEE Transactions on Neural Networks
|February 6, 2008
Summary
We established a condition for robust local stability in multilayer recurrent neural networks. This stability analysis enhances understanding of neural network dynamics and their basins of attraction.
Area of Science:
- Artificial Intelligence
- Computational Neuroscience
- Control Theory
Background:
- Multilayer recurrent neural networks (MRNNs) are complex dynamical systems.
- Ensuring the stability and predictability of MRNNs is crucial for their reliable application.
- Existing methods for analyzing MRNN stability often face limitations in robustness and basin characterization.
Purpose of the Study:
- To derive a novel condition for robust local stability in two-hidden-layer MRNNs.
- To characterize the basin of attraction for the origin in these networks.
- To explore modifications of dynamic backpropagation using the new stability criterion.
Main Methods:
- Linearization theory applied to neural network dynamics.
- Robustness analysis of linear systems under nonlinear perturbations.
- Utilizing matrix inequalities to establish stability conditions.
- Characterizing the basin of attraction via the level set of a quadratic Lyapunov function.
Main Results:
- A condition for robust local stability of two-hidden-layer MRNNs was successfully derived.
- The basin of attraction of the origin was characterized using a Lyapunov function.
- The derived criterion allows for enlarging the apparent basin of attraction, though the proven basin may be smaller due to criterion conservatism.
Conclusions:
- The new stability condition provides a valuable tool for analyzing and designing stable MRNNs.
- The findings contribute to a deeper theoretical understanding of MRNN dynamics and their stability properties.
- The proposed modification of dynamic backpropagation shows promise, as illustrated by simulation examples.
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