Adaptive structures with algebraic loops.

Area of Science:

• Applied Mathematics
• Machine Learning
• Control Systems Theory

Background:

• The contraction theorem is a fundamental concept with broad applications in solving equations and optimization problems.
• Adaptive structures and multilayer neural networks are crucial for approximating complex functional relationships from data.
• Algebraic loops present computational challenges in training and implementing these structures.

Purpose of the Study:

• To demonstrate the application of contraction mapping for computing and training adaptive structures containing algebraic loops.
• To extend the contraction mapping technique to multilayer neural networks that incorporate algebraic loops.
• To illustrate the practical utility of this method through an application in breast cancer diagnosis.

Main Methods:

• Utilizing the contraction mapping theorem to develop computational and training algorithms for adaptive structures.
• Adapting the contraction mapping approach for neural networks with embedded algebraic loops.
• Implementing a two-layer neural network trained using this method for a medical diagnosis task.

Main Results:

• The contraction mapping approach provides an effective method for handling algebraic loops in adaptive structures.
• The technique is successfully extended to multilayer neural networks, enabling their training and computation.
• A two-layer neural network demonstrated promising results in breast cancer diagnosis using the proposed method.

Conclusions:

• Contraction mapping offers a robust mathematical framework for addressing challenges posed by algebraic loops in machine learning models.
• The developed technique enhances the training and application of neural networks, particularly in complex systems.
• This approach holds potential for improving diagnostic accuracy in medical applications like breast cancer detection.