## 3 Methods
### SimFA Module  
In face parsing tasks, the semantic information of facial regions is highly diverse. For instance, areas such as the eyes, lips, and eyebrows typically exhibit sharp boundaries and rich textures, whereas regions like the cheeks and forehead tend to be smoother and lack distinct edges. Moreover, facial morphology varies significantly under different conditions such as pose, illumination, and occlusion, requiring the segmentation model to possess strong feature representation capabilities that can simultaneously capture the global structure and finely model local details. However, existing feature fusion methods still face numerous challenges in expressing local details, enabling effective feature interaction, and recovering information during upsampling. Conventional fusion strategies for high- and low-level features mostly rely on simple concatenation or weighted summation, which fail to adequately model pixel-wise fine-grained relationships, thus limiting the model's expressiveness for critical regions and resulting in blurred boundaries and loss of texture information. On the other hand, usingonly nonlocal attention mechanisms or local convolutional operations struggles to balance global and local representations, leading to information mismatch during multi-scale feature integration. Additionally, the semantic recovery capability during the upsampling process remains limited, often causing feature blurring and unclear boundaries, thereby degrading the final segmentation accuracy. Inspired by SMFANet [27], this study designs a Self-Modulation Attention Feature Integration (SimFA) module to address the aforementioned challenges, as illustrated in Figure 3. The SimFA module introduces a novel adaptive modulation strategy based on the basis of feature interaction and estimation, enabling the model to more precisely enhance the representation of critical facial regions during multi-scale feature integration. Simultaneously, it effectively suppresses background interference, thereby improving boundary sharpness and detail preservation in the segmentation results. Specifically, SimFA first extracts global structural information and local detailed features through two separate branches: nonlocal feature interaction and local detail estimation. Given an input feature map \(H\), it is first expanded in the channel dimension via a \(1\times 1\) convolution and then divided into a global branch \(E\) and a local branch \(L\), as follows:  
\[\{E,L\}=\text{Split}(\text{Conv}_{1\times 1}(H)), \tag{8}\]  
The \(E\) branch acquires global structural information through an efficient approximation of the self-attention mechanism and enhances nonlocal feature interaction via a variance-based modulation strategy. Specifically, it first employs adaptive max pooling to obtain low-frequency features and then applies a \(3\times 3\) depthwise separable convolution [28] to extract structural information, resulting in \(E_{s}\). Subsequently, the global variance of the input feature \(F\), denoted as \(\sigma^{2}(E)\), is computed as follows:  
\[\sigma^{2}(E)=\frac{1}{N}\sum_{i=1}^{N}(e_{i}-\mu)^{2}, \tag{9}\]  
The modulation is performed through a 1\(\times\)1 convolution as follows:  
\[E_{m}=\text{Conv}_{1\times 1}\Big{(}E_{s}+\sigma^{2}(E)\Big{)}. \tag{10}\]  
Subsequently, the GELU activation function [29] and nearest-neighbor upsampling are applied to obtain the final global feature representation \(E_{n}\), enabling adaptive nonlocal feature aggregation. The \(L\) branch captures edge and texture details using a \(3\times 3\) depthwise separable convolution, followed by nonlinear activation to enhance feature expression.