Thank you for your response. We'd like to address your concerns.
> Q1: As a natural follow-up to the responses to Q1 under clarifications, have the authors observed the change in performance of baselines when switching to prompts of 16k params?
1) First, we would like to emphasize that in our algorithm, although 16k parameters (8k global + 8k local) are used, only the 8k parameters corresponding to the global prompt are shared across clients in federated learning. Thus, our comunication cost is exact the same as baselines with 8k parameters. Using baselines with 16k parameters will double the communication cost, resulting in an unfair comparison.
2) To further alleivate your concerns, we have added experiments by increasing the parameters of baselines from 8k to 16k. From the following table, we can obsesrve that: 1) increasing the parameters will not always increase the performance; 2) PromptFolio still has the advantage even under this unfair comparsion benefit from the prompt portfolio mechanism.
| | Cifar100 | DomainNet | Caltech10 | OxfordPets | DTD |
| -------------------- | -------------------- | -------------------- | -------------------- | -------------------- | -------------------- |
| CoOp (8k param) | 76.88 $\pm$ 0.07 | 91.83 $\pm$ 0.13 | 97.10 $\pm$ 0.20 | 87.85 $\pm$ 0.32 | 56.39 $\pm$ 0.48 |
| CoOp (16k param) | 77.74 $\pm$ 0.21 | 91.92 $\pm$ 0.18 | 96.41 $\pm$ 0.43 | 87.68 $\pm$ 0.44 | 58.33 $\pm$ 0.41 |
| PromptFL (8k param) | 78.16 $\pm$ 0.16 | 92.72 $\pm$ 0.16 | 95.51 $\pm$ 2.62 | 88.91 $\pm$ 0.72 | 70.99 $\pm$ 0.32 |
| PromptFL (16k param) | 78.53 $\pm$ 0.33 | 92.88 $\pm$ 0.29 | 96.23 $\pm$ 1.41 | 91.81 $\pm$ 0.64 | **71.73 $\pm$ 0.31** |
| PromptFolio (8k + 8k param) | **80.17 $\pm$ 0.05** | **93.04 $\pm$ 0.09** | **97.24 $\pm$ 0.11** | **92.17 $\pm$ 0.32** | 71.32 $\pm$ 0.49 |
> Q2: Could the authors provide more context for the selection of $\alpha = 1$ and discuss the impact of lower $\alpha$ on the algorithm? (if possible also provide results) I am specifically interested in the lower $\alpha$ setting since it would allow for more in-depth and interesting analyses given the theoretical framework outlines in the manuscript.
We conducted experiments with multiple different $\alpha$ values instead of using only $\alpha = 1$. For instance, in Table 2, we used $\alpha = 0.3$ to compare our result with baseline methods. In Figure 2(a), we conducted parameter analysis for $\alpha$ by implementing PromptFolio with different $\alpha$ values (0.01, 0.1, 1, 10). Here, we observe that a lower $\alpha$ indicates a more non-i.i.d. data distribution, requiring a larger mixing coefficient $\theta$ to retain more local information.
Our theoretical analysis also supports this result. In our framework, $\Chi_k$ measures the heterogeneity across clients. A lower $\alpha$ leads to more data heterogeneity, meaning $\Chi_k$ will be lower as well. As described in Theorem 5.2 on Line 279, a lower $\Chi_k$ (lower $\alpha$) corresponds to a higher $\theta^\star$, also aligning with the experimental results in Figure 2. Further analysis on how different levels of data heterogeneity affect learning dynamics can be found in Theorem D.2.