Application of Banach's Fixed Point Theorem in Machine Learning for Recurrent Neural Network Architecture

AbstractTo improve the stability and convergence of recurrent neural networks (RNNs) for time series forecasting applications, this research explores the use of fixed-point theory. Our goal is to enhance the generalization performance of RNN models and reduce stability problems by including a contraction mapping check into the training process. We assess the performance of RNNs with and without contraction mapping versus conventional machine learning models using the airline passenger dataset as a case study. Our tests demonstrate how contraction mapping can improve model stability and lead to higher predicted accuracy. The findings support a comprehensive strategy that combines theoretical understanding with empirical study and highlights the significance of mathematical concepts in deep learning research.Keywords: Fixed point theorem, recurrent neural network, contraction mapping, machine learning.