Inverse mapping of continuous functions using local and global information

Area of Science:

• Artificial Intelligence
• Machine Learning
• Neural Networks

Background:

• Multilayer feedforward mapping networks are used for complex function approximation.
• Solving the inverse mapping problem is crucial for many applications but often suffers from local minima.
• Existing methods using Jacobian pseudo-inverse or transpose can be computationally intensive and prone to convergence issues.

Purpose of the Study:

• To develop an efficient and robust method for solving the inverse mapping of continuous functions learned by multilayer feedforward networks.
• To address the challenge of local minima in the inverse mapping process.
• To improve computational complexity and convergence properties compared to existing methods.

Main Methods:

• An iterative input vector update strategy is employed, guided by the pseudo-inverse of the Lyapunov function gradient.
• Local minima are detected via 'update explosion' and escaped using 'global information' or probability density function (PDF) relocation.
• A PDF is constructed using Parzen estimates, incorporating historical data of detected local minima.

Main Results:

• The proposed method successfully escapes local minima during the inverse mapping search.
• The technique demonstrates superior computational complexity and convergence properties compared to Jacobian-based methods.
• The PDF-based relocation provides a probabilistic approach to navigate the input vector space effectively.

Conclusions:

• The presented method offers a significant advancement in solving inverse mapping problems for neural networks.
• The approach provides a more efficient and reliable alternative to conventional techniques, particularly in complex function approximation scenarios.
• The integration of global information and probabilistic methods enhances the robustness and performance of the inverse mapping solution.