## 4 Methodology
### Uni-Modal Representation Extraction  
#### 4.1.1 Network Module  
We intended to capitalize on the process of information propagation among users during the growth of the post's cascade over time. The architecture of Network Module is illustrated in Figure 11. And the input features of this module is shown in Table 2.  
Figure 10: The architecture of our ExoFIA framework. We first enter information about a source tweet, including a dynamic graph constructed from the propagation of the tweets at the time of observation, the characteristics of the source tweets, information about the user who posted the source tweet, and Google Trends information. Then, the following embeddings are obtained by each representation extraction module: \(E_{net}\), the dynamic graph embedding with size \(d_{n}\); \(E_{tw}\), the source tweet feature with size \(d_{tw}\); \(E_{user}\), a feature of the user who posted the source tweet, with size \(d_{u}\); and \(E_{tr}\), the Google Trends embedding with size \(d_{tr}\). Finally, these four embeddings will be fed into the fusion module to predict the answers. Figure 9: Percentage distribution. **Dynamic graphs. ** Given the observation time \([0,T)\), we divided the observation time into \(n\) intervals, so the length of an interval was denoted as \(\lfloor\frac{T}{n}\rfloor\). Then, we transformed the original graph into a sequence of sub-graphs, i.e., \(\mathbb{G}_{T}^{s}=\{\mathbf{g}_{\lfloor\frac{T}{n}\rfloor+1}^{s}\mathbf{\delta}_{ \lfloor\frac{T}{n}\rfloor+2}^{s},\cdots,\mathbf{\delta}_{\lfloor\frac{T}{n} \rfloor+k}^{s}\}\), \(k\in[1,n]\), in which \(\mathbf{g}_{\lfloor\frac{T}{n}\rfloor+k}^{s}\) is the snapshot of the original graph at the time-instant \(\lfloor\frac{T}{n}\rfloor\ast k\). The dynamic graphs afford us a glimpse of the speed of spread and the scale of the early cascade. We leveraged GCN [25] to exploit the local structure of each sub-graph and then used GRU [26] to capture the evolving process of the graph structure. We adopted a heterogeneous graph convolutional network to jointly learn the structural characteristics of the diffusion graph and social graph mentioned in Section 3.2.1. Diffusion graphs are important for understanding representations of structural and temporal patterns, while social networks provide a structure for understanding the relationships between users. Social graphs are the basic means of tweets dissemination, which can reveal community information. GCN is a convolutional neural network that can work on a non-Euclidean structure and take advantage of a graph's structural information. Given an adjacency matrix \(\mathbf{A}\) and node feature matrix \(\mathbf{X}\), the convolution layers capture spatial features between nodes by their first-order neighborhoods. The GCN model can be built by stacking multiple convolution layers, which can be expressed as  
\[\mathbf{H}^{(\ell+1)}=\sigma(\hat{\mathbf{D}}^{-\frac{1}{2}}\hat{\mathbf{A}}\hat{\mathbf{D}}^{ -\frac{1}{2}}\mathbf{H}^{(\ell)}\mathbf{W}^{(\ell)}), \tag{1}\]  
in which \(\mathbf{H}^{(\ell)}\) is the output of the \(\ell\) layer, \(\hat{\mathbf{A}}=\mathbf{A}+\mathbf{I}\) denotes the matrix with added self-connections, \(\hat{\mathbf{D}}_{ii}=\sum_{j=0}\hat{\mathbf{A}}_{ij}\) is the diagonal degree matrix, \(\mathbf{W}^{(\ell)}\) are learnable parameters of the \(\ell\) layer, and \(\sigma(\cdot)\) represents the ReLU function. We stacked one convolution layer for each graph. \(\mathbf{H}^{(0)}\) was set as a node feature matrix \(\mathbf{X}\). \(H^{(0)}\) was fed into the GCN layer to compute the output matrix of the next layer. Seven user traits are specified in Section 4.1.3, as well as a time gap between the retweet node and the source tweet node. The new node feature matrix was denoted by \(\mathbf{H}^{(\ell+1)}\in\mathbb{R}^{n_{t}^{s}\times d}\), in which \(n_{t}^{s}\) is the node number of a graph and \(d\) is the dimensionality of the node embedding.