## 4 Method
### Attention Module  
ADNet weighs important spatiotemporal features by incorporating an attention module. This module is integrated into the existing STDenseNet framework, which is positioned after the blocks that capture temporal and periodic characteristics. By doing so, it strengthens the model's ability to capture relationships related to temporal proximity and periodicity [15]. The attention module guides the network to focus on essential features by considering interactions between features across both temporal aspects. As a result, the model can better capture complex spatiotemporal dependencies in both temporal proximity and periodic patterns, leading to improved predictions. By enhancing the model's ability to extract valuable information from these interactions, the accuracy of mobile traffic prediction is significantly improved.  
We use several attention mechanisms in our method, including spatial attention, i.e., \(M_{S}(F)\) in Equation (3); channel attention, i.e., \(M_{C}(F)\) in Equation (4); triplet attention, i.e., \(M_{T}(F)\) in Equation (6); and self-attention, \(M_{Soft}(F)\), as shown in Equation (7). Additionally, Ref. [46] has shown that replacing the softmax function in non-local attention with a Gaussian kernel can improve performance. Based on this finding, we also use this modified attention mechanism (Equation (8)). Furthermore, we explore several attention module combinations, such as CBAM [32] and modified triplet attention, by replacing its spatial attention with self-attention to create additional variations. We express the operations of the aforementioned attention modules in the following way:  
\[Spatial\ Attention:M_{S}(F)=\sigma(f([AvgPool(F);MaxPool(F)])), \tag{3}\]  
where \(f()\) denotes a convolution layer, and each \(AvgPool()\) and \(MaxPool()\) denotes an average pooling layer and a max pooling layer.  
\[Channel\ Attention:M_{C}(F)=\sigma(MLP(AvgPool(F))+MLP(MaxPool(F))), \tag{4}\]  
\[MLP(x)=(W_{1}(ReLU(W_{0}x+b_{0}))+b_{1}), \tag{5}\]  
where \(\sigma()\) denotes a sigmoid activation function in Equation (4), and \(ReLU()\) denotes a Rectified Linear Unit activation function in Equation (5).  
\[Triplet\ Attention:M_{T}(F)=\frac{1}{3}\Big{(}\overline{F_{1}\cdot M_{S}(F_{1}) }+\overline{F_{2}\cdot M_{S}(F_{2})}+F\cdot M_{S}(F)\Big{)}, \tag{6}\]  
where \(F_{1}\) and \(F_{2}\) denote permuted feature maps from \((C\times H\times W)\) to \((W\times H\times C)\) and \((H\times C\times W)\) for each, and overlines in \(\overline{F_{1}\cdot M_{S}(F_{1})}\) and \(\overline{F_{2}\cdot M_{S}(F_{2})}\) denote the permuting tensor to retain the original shape, \((C\times H\times W)\), in Equation (6).  
\[Non\text{-}local\ Softmax\ Attention:M_{Soft}(F)=softmax\left(\frac{F^{T}W_{Q}^{T}W_{K}F}{ \sqrt{d_{k}}}\right)W_{V}F, \tag{7}\]  
\[Non\text{-}local\ Gaussian\ Attention:M_{Gauss}(F)=exp\left(\frac{\left\|W_{Q}F-W_{K}F \right\|^{2}}{2\sqrt{d_{k}}}\right)W_{V}F, \tag{8}\]  
where \(W_{Q}\), \(W_{K}\), and \(W_{V}\) denote the weights of query, key, and value, and \(d_{k}\) denotes the dimension of key tensor (\(W_{K}F\)) in Equations (7) and (8). \(exp()\) denotes an exponential function in Equation (8).