## 3 Materials and Method
### Proposed Method
#### 3.3.3 Fusion Loss Function  
The proposed fusion loss function is designed to balance the trade-off between data obfuscation security and task performance, ensuring that the obfuscated data protect privacy while minimally impacting downstream task model training and inference. Unlike traditional loss functions that optimize a single objective (such as task performance or privacy protection), the fusion loss function combines security loss and performance loss into a multi-objective optimization framework. This approach ensures that the obfuscated data achieve an optimal balance between privacy and task relevance. The fusion loss function consists of two components: security loss and performance loss. It is defined as  
\[L_{\text{fusion}}=\lambda_{1}L_{\text{security}}+\lambda_{2}L_{\text{performance}}, \tag{23}\]  
where \(\lambda_{1}\) and \(\lambda_{2}\) are weighting parameters that balance the contributions of the two loss components to the overall optimization. Security loss quantifies the privacy protection effect of the obfuscation strategy by comparing the information entropy of the obfuscated data with that of the original data. It is defined as  
\[L_{\text{security}}=\frac{1}{n}\sum_{i=1}^{n}\lvert H(x_{i})-H(M(x_{i}))\rvert, \tag{24}\]  
where \(H(x_{i})\) and \(H(M(x_{i}))\) represent the information entropy of the original data \(x_{i}\) and the obfuscated data \(M(x_{i})\), respectively. Minimizing this loss ensures an appropriate entropy difference between the original and obfuscated data, enhancing privacy protection strength. Performance loss measures the impact of the obfuscated data on the task model and is defined as  
\[L_{\text{performance}}=\frac{1}{m}\sum_{j=1}^{m}\lvert f(x_{j})-f(M(x_{j})) \rvert^{2}, \tag{25}\]  
where \(f(x_{j})\) and \(f(M(x_{j}))\) denote the task model outputs for the original data \(x_{j}\) and the obfuscated data \(M(x_{j})\), respectively. Minimizing this loss ensures that the predictions on the obfuscated data remain as close as possible to those on the original data, reducing the performance impact. The fusion loss function is closely integrated with the information entropy fusion module, dynamically adjusting the obfuscation intensity to further optimize the data obfuscation strategy. The obfuscated data \(M(x)\) generated by the information entropy fusion module are defined as  
\[M(x)=\alpha\cdot G(x)+\beta\cdot T(x), \tag{26}\]  
where \(G(x)\) represents Gaussian noise-based obfuscation, \(T(x)\) represents gradient perturbation-based obfuscation, and the weights \(\alpha\) and \(\beta\) are dynamically generated based on information entropy, satisfying \(\alpha+\beta=1\). By substituting \(M(x)\) into the fusion loss function, the calculations for both security loss and performance loss are based on the dynamically adjusted obfuscated data, enabling more flexible privacy protection and task optimization. To demonstrate that the fusion loss function achieves a balance between privacy protection and task performance, we define the following optimization objective:  
\[\mathcal{L}=\lambda_{1}\Bigg{(}\frac{1}{n}\sum_{i=1}^{n}\lvert H(x_{i})-H(M(x _{i}))\rvert\Bigg{)}+\lambda_{2}\Bigg{(}\frac{1}{m}\sum_{j=1}^{m}\lvert f(x_{j} )-f(M(x_{j}))\rvert^{2}\Bigg{)}. \tag{27}\]The first term represents the privacy protection objective, while the second term represents the task performance objective. By jointly optimizing this objective function, the obfuscated data can meet privacy protection requirements while retaining features useful for the task model.