A Appendix 483 A.1 Theoretical Proofs

Proposition A.2. Assume filter atoms D Theorem A.4. Suppose the forward of decomposed convolution layer for the According to Lemma A.5, we have, Based on Lemma A.5, we have, Based on Lemma A.7, we have, Theorem A.9. Suppose the forward of decomposed convolution layer for the As Assumption 2.6 holds, it becomes As shown in Table 3, our method achieves comparable performance among different methods. The fully-connected layer of each model is fine-tuned on the user's local data with 100 The fine-tuning takes about 12 hours on Nvidia RTX A5000. All the points are below the line which is the bound provided by Proposition 2.1, reflecting that the Figure 6: The shared coefficients and user-specific atoms represent common knowledge and personalized information. The filter subspace similarity is used to calculate the relations among users. And the correlation can reach 0.985 with CIFAR-100) are similar among themselves, but they differ from untrained models.