## 2 Related Work  
### Latent Space  
Latent space is a fundamental concept in data representation learning, where high-dimensional data are mapped to a lower-dimensional space. This transformation allows for the capture of key features within the data while reducing redundant information [16; 17]. Essentially, it serves as a process of feature abstraction, aiming to preserve the intrinsic structure of the data while enhancing computational efficiency and robustness for subsequent processing. In traditional machine learning methods, data are typically handled in its original high-dimensional form [18; 19; 20]. For instance, in image recognition tasks, each image is represented as a high-dimensional vector consisting of thousands of pixel values. The processing of such high-dimensional data is computationally expensive and prone to noise and redundant information, which may lead to inefficient learning algorithms and even overfitting [21]. To address these challenges, the introduction of latent space has proven to be an effective solution. The core idea of latent space is to map data from their original high-dimensional space to a lower-dimensional latent space. In this lower-dimensional space, the key features of the data are effectively preserved, while redundant or irrelevant information is discarded. This mapping is typically achieved through models such as deep neural networks or autoencoders [22; 23]. Within the autoencoder framework, input data are processed through the encoder and ultimately mapped to the latent space. Each point in the latent space \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Method** & **Privacy Protection** & **Model Utility** & **Computational Efficiency** & **Complexity** \\ \hline Differential Privacy & High & Moderate & Low & High \\ Homomorphic Encryption & Very High & Low & Very Low & Very High \\ Federated Learning & Moderate & High & Moderate & Moderate \\ Proposed Method & High & Very High & High & Low \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of privacy protection methods. represents a compressed version of the data, typically containing the essential information from the original input. The mapping process to latent space can be expressed as follows:  
\[z=f(x), \tag{1}\]  
where \(x\) denotes the input data and \(f\) is the mapping function that transforms the high-dimensional input \(x\) into the lower-dimensional representation \(z\) in the latent space. The mapping function \(f\) is typically learned via neural networks. In the autoencoder framework, the task of the encoder network is to learn the mapping function that converts the input data \(x\) into the low-dimensional representation \(z\) in the latent space. The decoder network then reconstructs the original data \(x\) based on \(z\). Through this process, the latent space representation retains the key information of the input data. To better understand the role of latent space, the relationship between the latent space and the input data can be further analyzed. Suppose the input data \(x\) belongs to a high-dimensional space with dimension \(d\), while the latent space has dimension \(k\), typically with \(k<d\). In this case, the objective of learning latent space is to compress the data from the \(d\)-dimensional space to the \(k\)-dimensional space while preserving the key features of the original data as much as possible. The model is trained by optimizing a loss function such that the resulting latent representation effectively retains the structural information of the original data [24]. The concept of latent space is not only applied in autoencoders and variational autoencoders but is also widely used in other deep learning models. For example, Generative Adversarial Networks (GANs) also utilize latent space in generating samples. In GANs, the generator maps a random noise vector to the latent space, and then generates realistic data samples based on the latent vectors [25].