## 2 Materials and Methods
### Proposed Method
#### 2.3.2 Information Infusion Network  
As shown in Figure 4, the information infusion network consists of two modules: a graph construction module (GCM) and an information infusion module (IFM). The GCM builds a graph to model the agent relationships based on the agents' states, while the IFM processes the graph data with a GAT, integrates feature information from heterogeneous agents, and generates a unified team-level information vector accessible to each agent.  
The experiments in this paper were conducted in the Starcraft Multi-Agent Challenge (SMAC) environment [27], where agents have fixed visual and attack radii. Agents connect to their \(k\) closest neighbors within their visual/attack range and form a \(k\)-nearest neighbor graph based on spatial proximity, as in Figure 5. Specifically, for each agent, we calculate pairwise Euclidean distances to visible agents, select the \(k\) nearest agents as neighbors, and establish bidirectional edges between neighbors.  
After generating the graph, the GAT can be used to integrate the information of the agents. The multi-agent information fusion process is shown in Figure 6. Each agent first fuses the information from its \(k\)-neighbors, then the information from the agents is enriched with neighbor data and further fused to form the team information.  
First, the similarity coefficient \(e\) between each agent and its \(k\) nearest neighbors is computed as follows:  
\[e_{ij}^{h}=a_{h}^{T}\cdot\left[o_{i}^{r}\,||\,o_{j}^{r}\right], \tag{8}\]  
where \(e_{ij}^{h}\) is the attention coefficient between nodes \(i\) and \(j\) for head \(h\), \(a_{h}^{T}\) represents the learnable weight vector of attention head \(h\), \(||\) is the concatenation operator, and \(\left[o_{i}^{r}\,||\,o_{j}^{r}\right]\) denotes the concatenation of the transformed feature matrices of nodes \(i\) and \(j\).  
Figure 4: Structure of the information infusion network.  
Figure 5: Establishing edges between agents and their neighboring agents to form a \(k\)-nearest neighbors graph.  
Figure 6: Information infusion of multiple agents.  
The node features of the graph are the projected features \(o^{\prime}\). The edge relationships are stored in the adjacency matrix \(A\), \(A\in\mathbb{R}^{n\times n}\), and \(\mathcal{N}_{i}\) denotes the set of \(k\)-nearest neighbors for agent \(i\). Then, the similarity coefficients are normalized via the softmax operation to obtain the attention coefficients \(\alpha_{ij}\) between neighboring agents, ensuring that the sum of attention coefficients for each node equals 1. The computation is formulated as follows:  
\[\alpha_{ij}^{h}=\text{softmax}_{j}\Big{(}e_{ij}^{h}\Big{)}=\frac{\exp\left(e_{ ij}^{h}\right)}{\sum_{z\in\mathcal{N}_{i}}\exp\left(e_{iz}^{h}\right)}. \tag{9}\]  
After obtaining the attention coefficients between agents, the features of each agent's \(k\)-nearest neighbors are aggregated through a weighted summation using these coefficients, resulting in the feature \(v\) that integrates neighborhood information. The computation is as follows:  
\[v_{i}=\sum_{j\in\mathcal{N}_{i}}\alpha_{ij}^{h}\cdot\text{W}o_{j}^{\prime}. \tag{10}\]  
The fused features of the agent across multiple attention heads are obtained by concatenating the outputs of all heads, as shown in Equation (11):  
\[z_{i}=\underset{h=1}{|\overset{H}{|}}v_{i}^{h}, \tag{11}\]  
where \(H\) is the total number of attention heads. Then, a pooling operation is applied to the aggregated neighborhood features to derive the team-level feature vector \(o_{all}\), which integrates the information from all agents. The computation is formalized as follows:  
\[o_{all}=\frac{1}{N}\sum_{i=1}^{N}z_{i}. \tag{12}\]  
In summary, the team-level feature \(o_{all}\) which integrates information from all agents can be described as follows:  
\[o_{all}=\frac{1}{N}\sum_{i=1}^{N}\left(\underset{h=1}{|\overset{H}{|}}\left( \underset{v\in\mathcal{N}_{i}}{\sum_{z\in\mathcal{N}_{i}}\exp\left(e_{iz}^{h} \right)}o_{j}^{\prime}\right)\right). \tag{13}\]