Abstract
In this paper, the singularity and its effect on learning dynamics in the complex-valued neural network are elucidated. It has learned that the linear combination structure in the updating rule of the complex-valued neural network increases the speed of moving away from the singular points, and the complex-valued neural network cannot be easily influenced by the singular points, whereas the learning of the usual real-valued neural network can be attracted in the neighborhood of singular points, which causes a standstill in learning. Simulation results on the learning dynamics of the three-layered real-valued and complex-valued neural networks in the neighborhood of singularities support the analytical results.
Highlights
Complex-valued neural networks have been applied in various fields dealing with complex numbers or twodimensional data such as signal processing and image processing [1,2]
We find that the linear combination structure in the updating rule of the complex-valued neural network increases the speed of moving away from the singular points; the complex-valued neural network cannot be influenced by the singular points, whereas the learning of the usual real-valued neural network can be attracted in the neighborhood of singular points, which causes a standstill in learning
Simulation results on the learning dynamics of the three-layered real-valued and complex-valued neural networks in the neighborhood of singularities support the analytical results
Summary
Complex-valued neural networks have been applied in various fields dealing with complex numbers or twodimensional data such as signal processing and image processing [1,2]. The complex-valued version of the Real-BP (called here, Complex-BP) can be considered, and was proposed by several researchers independently in the early 1990’s [3,4,5,9,10,11]. This algorithm enables the network to learn complex-valued patterns naturally. Simulation results on the learning dynamics of the three-layered real-valued and complex-valued neural networks in the neighborhood of singularities support the analytical results. Used in the analysis will have 3 layers: L-H-1 network
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