Recurrent Neural Networks (RNNs) are classical models for processing sequential data, demonstrating excellent performance in tasks such as natural language processing and time series prediction. However, during the training of RNNs, the issues of vanishing and exploding gradients often arise, significantly impacting the model’s performance and efficiency. In this paper, we investigate why RNNs are more prone to gradient problems compared to other common sequential networks. To address this issue and enhance network performance, we propose a method for gradient normalization of network weights. This method suppresses the occurrence of gradient problems by altering the statistical properties of RNN weights, thereby improving training effectiveness. Additionally, we analyze the impact of weight gradient normalization on the probability-distribution characteristics of model weights and validate the sensitivity of this method to hyperparameters such as learning rate. The experimental results demonstrate that gradient normalization enhances the stability of model training and reduces the frequency of gradient issues. On the Penn Treebank dataset, this method achieves a perplexity level of 110.89, representing an 11.48% improvement over conventional gradient descent methods. For prediction lengths of 24 and 96 on the ETTm1 dataset, Mean Absolute Error (MAE) values of 0.778 and 0.592 are attained, respectively, resulting in 3.00% and 6.77% improvement over conventional gradient descent methods. Moreover, selected subsets of the UCR dataset show an increase in accuracy ranging from 0.4% to 6.0%. The gradient normalization method enhances the ability of RNNs to learn from sequential and causal data, thereby holding significant implications for optimizing the training effectiveness of RNN-based models.

Resource-constrained Internet of Things (IoT) devices demand efficient and robust intrusion detection systems (IDSs) to counter evolving cyber threats. The traditional IDS models, however, struggle with high computational complexity and inadequate feature extraction, limiting their accuracy and generalizability in IoT environments. To address this, we propose FFT-RDNet, a lightweight IDS framework leveraging depthwise separable convolution and frequency-domain feature fusion. An ADASYN-Tomek Links hybrid strategy first addresses class imbalances. The core innovation of FFT-RDNet lies in its novel two-dimensional spatial feature modeling approach, realized through a dedicated dual-path feature embedding module. One branch extracts discriminative statistical features in the time domain, while the other branch transforms the data into the frequency domain via Fast Fourier Transform (FFT) to capture the essential energy distribution characteristics. These time–frequency domain features are fused to construct a two-dimensional feature space, which is then processed by a streamlined residual network using depthwise separable convolution. This network effectively captures complex periodic attack patterns with minimal computational overhead. Comprehensive evaluation on the NSL-KDD and CIC-IDS2018 datasets shows that FFT-RDNet outperforms state-of-the-art neural network IDSs across accuracy, precision, recall, and F1 score (improvements: 0.22–1%). Crucially, it achieves superior accuracy with a significantly reduced computational complexity, demonstrating high efficiency for resource-constrained IoT security deployments.