## 5 Experiments and Results
### Positional Attentions Analysis from Respective Channels  
We discussed how the positional attention varies depending on observation methods. In this analysis, we further examined how the positional attention is correlated with respective observation channels. Figures 7 and 8 present the positional attention heatmaps of a trained eDA3-IQN agent using the local view (Figure 7a) and relative view methods (Figure 8a) as well as the heatmaps indicating how many times an agent, object, and wall were observed (i.e., count 1 or \(-1\)) at specific cells in respective observation channels over 5000 episodes of the training phase. Our experiments used \(N_{\text{C}}=8\) channels, and the second and third rows in Figures 7 and 8 show eight heatmaps. As with the example in Figure 1, the first six channels in the observation (Figures 7b-g and 8b-g are dedicated to agents, while the seventh and eighth channels (Figures 7h,i and 8h,i are for object observation and visible area. Note that the accumulated values in the visible sight heatmaps (Figures 7i and 8i) are multiplied by \(-1\) to visualize explicitly, as the visible sight within walls is encoded in \(\{0,-1\}\) as shown in Figure 1b,c. Figure 7: Positional attention and observation statistics with local view of _agent_ 1. Figure 7 displays the positional attention and the accumulated counts heatmap of _agent_ 1 that mainly explores the lower right region of the environment with the local view Figure 4(b). The positional attention heatmap of _agent_ 1 highlights only its center, which corresponds to its location (Figure 6(c)). According to the positional attention heatmap in Figure 6(a), _agent_ 1 mainly focuses on its four adjacent cells with attention weights of 0.075, 0.078, 0.041, and 0.125, corresponding to locations where objects have been frequently observed at the seventh channel (\(132,675\) times on the right, \(117,147\) times on the left, \(112,755\) times on the top, and \(105,387\) times at the bottom), as shown in Figure 6(h). In contrast, only an attention weight of 0.021 is assigned to the center despite objects appearing \(162,974\) times at this location (Figure 6(a),h). Therefore, we verify that eDA3-X agents tend to focus their attention on neighboring cells and less attention on distant location, anticipating immediate object collection and rewards from their subsequent actions and considering distant objects less influential in their decision-making process. Furthermore, the attention heatmap (Figure 6(a)) places significant attention weight where other agents are frequently detected (Figure 6(b)-e). For instance, _agent_ 0 and _agent_ 2, which mostly explored the left and lower region of the environment (Figure 4(a),c), were observed 2495 and 2824 times at two cells away in the upper direction from _agent_ 1. _Agent_ 4, which randomly moved in the environment, was also observed 3897 times at the same cell. As mentioned in Section 5.4, agents sometimes explored the same regions. Consequently, _agent_ 1 assigned an attention weight of 0.024 to the corresponding cell, which was relatively high when compared to that of other cells (Figure 6(a)). Similarly, _agent_ 3 was observed 9908 times at the two cells away in the right direction, resulting in a relatively high attention weight (0.032). _Agent_ 1 also focused on the lower segments, possibly because it frequently encountered walls on the lower side of the environment (Figure 6(i)). Thus, we confirmed that eDA3-X agents also pay close attention to the areas where other agents are detected, indicating that the agents aim to avoid collisions with them. Figure 8: Positional attention and observation statistics with relative view of _agent_ 0. The positional attention heatmap and observation of _agent_ 0 in Figure 8 reveal that the eDA3-X agent with relative view method mainly focuses on the area that _agent_ 0 explored, unlike the previous positional attention analysis with the local view method, as shown in Figure 8a,h,i.