## 4 Experiments
### Results  
Table 3 presents the experimental results obtained under our evaluation settings. The table reports the accuracy of each method across different datasets, with the results organized by row. The topmost row provides the accuracy of the pretrained model, which serves as a baseline and is labeled as zero-shot. Our findings indicate that, despite its simplicity and ease of implementation, the averaging method achieves accuracy comparable to or exceeding that of other model merging techniques. These results are consistent with the effectiveness of FedAvg in conventional FL. A key advantage of the averaging method is its ability to achieve relatively consistent accuracy across different datasets, exhibiting less variance in performance compared to other model merging strategies. Although it did not exhibit a particular advantage on any single dataset, its overall average accuracy exceeded \begin{table}
\begin{tabular}{c l c c c c} \hline \hline  & **Dataset** & **Training Data** & **Validation Data** & **Testing Data** & **Classes** \\ \hline \multirow{8}{*}{Clients Dataset} & Cars [48] & 7330 & 814 & 8041 & 196 \\  & DTD [49] & 3384 & 376 & 1880 & 47 \\  & EuroSAT [50] & 21,600 & 2700 & 2700 & 10 \\  & GTSRB [51] & 23,976 & 2664 & 12,630 & 43 \\  & KITTI [52] & 6347 & 423 & 711 & 4 \\  & MNIST [53] & 55,000 & 5000 & 10,000 & 10 \\  & RESISC45 [54] & 17,010 & 1890 & 6300 & 45 \\  & SUN397 [55] & 17,865 & 1985 & 19,850 & 397 \\  & SVHN [56] & 68,257 & 5000 & 26,032 & 10 \\ \hline Reference Dataset & ImageNet [47] & 1,255,167 & 26,000 & 50,000 & 1000 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistics for client and reference datasets. that of PAINT and MagMax. This suggests that the averaging method provides a more balanced approach, effectively generalizing across diverse datasets without being overly influenced by specific dataset characteristics. In contrast, PAINT exhibited the highest accuracy on ImageNet, which was used as the reference dataset. This can be attributed to the weighted averaging strategy of PAINT, which incorporates model parameters before and after fine-tuning. This allows the parameters of the updated model to be retained because they are not significantly different from the parameters of the pretrained model. Consequently, PAINT probably mitigates the catastrophic forgetting of knowledge obtained through pretraining. These results highlight the importance of explicitly incorporating mechanisms that preserve pretraining knowledge when continuously updating FMs via model merging. Conventional model merging methods often fail to sufficiently retain the knowledge acquired during pretraining, leading to degraded performance or forgetting of foundational capabilities. In addition, the sparsity-based model merging methods, such as DARE and Breadcrumbs, also exhibit high accuracy. This suggests that task vectors derived from fine-tuning contain many redundant parameters, which may introduce interference during aggregation in our settings. Figure 2 shows the accuracy trends over multiple rounds as the scaling factor in task arithmetic is varied. When the scaling factor is set to 0.1 or lower, accuracy increases monotonically with each round. Conversely, when the scaling factor is 0.2, the accuracy curve exhibits a convex shape. In addition, when the scaling factor exceeds 0.3, the accuracy peaks before round 10 and subsequently decreases. However, with a scaling factor of 0.5, accuracy increases after round 5. In this experiment, the number of clients is set to 9, and averaging the task vectors corresponds to scaling by \(\frac{1}{9}\simeq 0.11\). The strong performance observed at a scaling factor of approximately 0.1 further reinforces the effectiveness of the averaging process, which is also shown to yield high accuracy in Table 3.  
Figure 3 depicts the cosine similarity of the task vectors between the initial and final rounds of task arithmetic. A similarity value of 0 indicates that the task vectors are orthogonal, which implies minimal interference between them.