## 4 Methods
### Feature Learning Network Module (FLNM)
#### 4.2.1 Update of Node Features
The aggregation function \(h_{\Theta}\) is represented as  
\[h_{\Theta}(x_{i},x_{j})=h_{\Theta}(x_{i},x_{j}-x_{i}) \tag{4}\]  
where \(h_{\Theta}\) integrates the global shape structure encapsulated by the central coordinate \(x_{i}\) and the local proximity data represented by \(x_{j}-x_{i}\). Then it is fed into another perceptron to obtain the features. The specific formula for the \(m\)-th channel is given by  
\[E^{\prime}_{x_{ij_{m}}}=\text{ReLU}(\theta_{m}\cdot(x_{j}-x_{i})+\phi_{m}\cdot x _{i}) \tag{5}\]  
where \(\theta=(\theta_{1},\dots,\theta_{m},\phi_{1},\dots,\phi_{m})\) denotes the learnable parameters. The \(m\)-th channel represents the \(m\)-th dimension of the feature vector. In multi-channel feature representation, each channel can capture distinct feature information. ReLU stands for the Rectified Linear Unit function. The aggregation function is applied to update the values of the \(m\)-th channels of node \(i\):  
\[x^{\prime}_{im}=\max_{j:(i,j)\in E}E^{\prime}_{x_{ij_{m}}} \tag{6}\]  
where \(m\)-channels denote the m-th dimension in the feature vector. In multi-channel feature representation, each channel can capture different feature information. Despite its advantages, the EdgeConv layer has several limitations. It relies on a transformation network to offset nodes, which increases the network's size. Additionally, the deep features and their neighbors may be too similar to provide valuable edge vectors. Moreover, EdgeConv has many trainable parameters, making it difficult to find the optimal parameters during network training, especially for large-scale building data, resulting in slower processing speeds. While EdgeConv considers the coordinates of points and the distances to neighboring points, it neglects the vector directions between adjacent points, leading to a partial loss of local geometric information. Therefore, relying solely on the EdgeConv layer is insufficient. After the EdgeConv layer, the features are passed through an ELU (Exponential Linear Unit) activation function [49]. Compared to ReLU, ELU has negative values, which push the mean activations closer to zero. This speeds up learning because it brings the gradient closer to the natural gradient, reducing the bias shift effect. (b) GraphKAN  
Inspired by [PERSON] [50], Kolmogorov-Arnold Networks (KANs) are applied to graph neural networks (GNNs) to replace traditional multi-layer perceptrons (MLPs) and activation functions [51]. This approach enhances nonlinearity and representation capabilities by using spline-based univariate functions as learnable activation functions. It improves model efficiency and interpretability, addresses information loss issues, and enhances performance across different datasets. The content of this theorem is that any multivariate continuous function \(f(x_{1},\ldots,x_{n})\) on a bounded domain can be expressed as a finite combination of simpler one-dimensional continuous functions. The formula can be expressed as follows:  
\[f(x_{1},\ldots,x_{n})=\sum_{q=1}^{2n+1}\Phi_{q}\left(\sum_{p=1}^{n}\phi_{q,p}( x_{p})\right), \tag{7}\]  
where \(\phi_{q,p}\) maps the interval \([0,1]\) to \(\mathbb{R}\), and \(\Phi_{q}\) performs a mapping from \(\mathbb{R}\rightarrow\mathbb{R}\). However, these one-dimensional mappings can exhibit irregularities and even fractal properties, making them challenging to learn in real-world applications. Specifically, the Kolmogorov-Arnold Network (KAN) can be formulated as  
\[x_{l+1}=\Phi_{l}x_{l}, \tag{8}\]  
where \(\Phi_{l}\) denotes the following matrix:  
\[\Phi_{l}= \begin{pmatrix}\phi_{1,1}&\phi_{1,2}&\cdots&\phi_{1,n}\\ \phi_{2,1}&\phi_{2,2}&\cdots&\phi_{2,n}\\ \vdots&\vdots&\ddots&\vdots\\ \phi_{m,1}&\phi_{m,2}&\cdots&\phi_{m,n}\\ \end{pmatrix} .