## 6 Results
### Validation  
Figure 1 presents the RMSE achieved by five predictive models--ConvLSTM, LSTM, Extended LSTM, Transformer, and XGBoost--for both the base (left column) and exponential (right column) scenarios in three network types: Barabasi-Albert (top row), Erdos-Renyi (middle row), and Watts-Strogatz (bottom row). Each chart compares the models' RMSE for increasing node sizes (25, 50, 100, 200, 300). Overall, the exponential scenario reduces the RMSE relative to the base scenario, suggesting that multi-hop interactions improve predictive accuracy. These patterns highlight how network topology, including long-range interactions and model architecture, each influence consensus prediction accuracy.  
In Figure 2, we show the Mean Absolute Percentage Error (MAPE) across different network sizes (25, 50, 100, 200, 300 nodes) for three topologies: Barabasi-Albert, Erdos-Renyi, and Watts-Strogatz. The bars indicate that at smaller scales (25 and 50 nodes), Erdos-Renyi networks exhibit substantially higher MAPE values, suggesting more variability or unpredictability in their consensus dynamics. Watts-Strogatz networks present intermediate error levels, while Barabasi-Albert remains comparatively lower even for smaller node counts. As the number of nodes increases, the MAPE for all three topologies converges to very low values, implying that larger networks become easier to predict regardless of their underlying structure. This pattern highlights the strong influence of network topology--especially the randomness in Erdos-Renyi--on predictability at small scales, whereas scale-free (Barabasi-Albert) and small-world (Watts-Strogatz) networks remain more stable in smaller configurations. In addition, the higher MAPE variability at smaller scales, particularly for models like Extended LSTM, Transformer, and XGBoost, is likely due to the models' sensitivity to network sparsity at smaller node sizes. These models have a greater capacity to capture complex relationships, but at smaller scales, they may overfit to the specific realizations of the network, leading to higher variability in predictions.  
Figure 3 displays box-and-whisker plots of the Mean Absolute Percentage Error (MAPE) for five predictive models--ConvLSTM, LSTM, Extended LSTM, Transformer, and XGBoost--across varying network sizes (25, 50, 100, 200, 300). Each box illustrates the distribution of prediction errors, with taller boxes and whiskers indicating more consid  
Figure 1: Comparison of RMSE values for five models (ConvLSTM, LSTM, Extended LSTM, Transformer, XGBoost) in both base and exponential scenarios across three network topologies (Barabasi-Albert, Erdős-Renyi, Watts-Strogatz) and varying node sizes.  
erable variability. At small network sizes (25-50 nodes), specific methods (e.g., Extended LSTM, Transformer, and XGBoost) seem to produce slightly higher median MAPEs than ConvLSTM and LSTM. When you get to 200-300 nodes, the boxes for most methods become narrower and cluster closer together. In other words, as the network size increases, all models tend to converge toward lower MAPE values, reflecting improved stability and predictability. It is worth mentioning that the lack of hubs and strong clustering in Erdos-Renyi networks results in more uniform and homogeneous structures, where most nodes have similar degrees. This reduces the presence of highly connected nodes or local communities that can accelerate or concentrate the spreading in the network, resulting in a more variable and unpredictable diffusion.  
Overall, the results emphasize that both model architecture and mostly network size significantly affect prediction accuracy.  
Figure 3: Box-and-whisker plots of MAPE for ConvLSTM, LSTM, Extended LSTM, Transformer, and XGBoost at different network sizes.  
Figure 2: Mean Absolute Percentage Error (MAPE) for consensus predictions across network sizes for Barabási–Albert, Erdős–Renyi, and Watts–Strogatz models.