A Novel Ensemble Chaotic Maps for Stable Deep Neural Networks

The stability of neural networks plays a crucial role in ensuring consistent and reliable model performance, especially when handling dynamic time-series data. Traditional approaches for evaluating stability often fail to provide precise convergence guarantees, leading to unpredictable model behavior during training and forecasting. To address this limitation, the present reseach explores the use of the Chaotic Maps as a mathematical foundation to assess and ensure the stability of neural networks. For the investigating the stability of the model, Gated Recurrent Unit (GRU) model is employed for dynamic EEG data, which includes unpredictable patterns of information. As the next process, chaotic principle is applied to verify whether the GRU model converges toward a unique stable solution during the training phase. Experimental analysis demonstrates that the proposed approach effectively identifies stable operating regions of the network, reduces training fluctuations, and improves the reliability of EEG detection. The GRU model achieved an RMSE of 0.102, MAE of 0.076, and Covergence time of 0.389, indicating high prediction accuracy and strong network stability. Furthermore, the proposed approach achieved Lyapunov Stability Index (LSI) value of 0.0242, ensuring robust and reliable convergence of the GRU model. The results indicate that integrating chaotic theory with deep learning provides a robust framework for analyzing and enhancing neural network stability in real-world time-series applications.