## 2 Materials and Methods
### Residual Connection  
The residual connection method is founded on the understanding that in deep networks, the input might traverse numerous layers, leading to the vanishing or exploding gradients phenomenon. This occurrence can render the model difficult to train or even result in training failure [14]. However, integrating direct connections between distinct network layers enables the input to bypass intricate network layers, thereby alleviating gradient-related challenges. By merging the output of the direct connection with the output of the final layer, additional relevant information is assimilated into the initial output. This process ensures that the residual connection not only enhances the original output but also preserves its essence. Consequently, the introduction of residual connections typically yields improved experimental results, surpassing the baseline accuracy level.  
In the realm of license plate recognition, the employment of recurrent neural networks often gives rise to the challenge of gradient vanishing, primarily due to the vast diversity inherent in license plate data. This diversity manifests as variable-length character sequences within license plates. The introduction of Integrating Residual En-Decoding and Feature Attention Mechanisms (REDF-LSTM) by [PERSON] et al. [15] represents a significant advancement in deep learning architecture. This novel model seamlessly integrates residual learning encoder-decoder LSTM layers, enhanced LSTM layers, and feedforward attention mechanisms. Through rigorous experimentation and comparison with state-of-the-art models, REDF-LSTM has demonstrated superior predictive performance across key indicators. This underscores the efficacy of integrating residual connections in deep learning architectures to address gradient-related challenges and enhance predictive accuracy across diverse domains. In license plate recognition tasks, where deep networks often encounter gradient-related issues due to the traversal of numerous layers, integrating residual connections provides a robust solution. By leveraging residual network connections, the EAND-LPRM model can effectively capture intricate features and accurately discern influential factors. This capability results in substantial enhancements in predictive accuracy, highlighting the significance of residual connections in tackling challenges inherent in deep networks.  
Given the intricate nature of license plate recognition tasks, the integration of residual connections proves instrumental in mitigating the challenges encountered during training [16]. Suppose the input x denotes the output from the preceding layer following the rectified linear unit activation function. The mapping function \(F(x)\) comprises two 3 \(\times\) 3 convolutional layers. The resulting output \(H(x)\) after the implementation of the residual connection can be mathematically represented as follows:  
\[H(x)=F(x)+x,\]From the formula, it is evident that the output, following the introduction of residuals, is influenced not only by the convolutional transformations but also by the original input data, denoted as \(x\). This characteristic aids in mitigating the issues of gradient vanishing and exploding that may occur during the backpropagation process.