FedDG Episodic Learning in Continuous Frequency Space for Federated Domain Generalization

A federated domain generalization algorithm (Liu, Chen, Qin, Dou, & Heng, 2021) that learns a shared prediction model from K decentralized source domains S = {S^1, ..., S^K} capable of generalizing directly to completely unseen target domains T without sharing raw images. Each client k decomposes local images x_i^k into Fourier amplitude spectra A_i^k (encoding low-level style distribution) and phase spectra P_i^k (encoding high-level structural semantics) via Eq. (1), shares only amplitude spectra in a distribution bank A = [A^1, ..., A^K], and synthesizes multi-source style-transferred images x_{i,lambda}^{k->n} = F^{-1}(A_{i,lambda}^{k->n}, P_i^k) via Continuous Frequency Space Interpolation (CFSI, Eqs. 2-3) with dynamically sampled interpolation ratio lambda in [0, 1] and low-frequency mask M. Local training then performs Boundary-oriented Episodic Learning (BEL, Eqs. 4-9), taking an inner-loop gradient step theta_hat^k = theta^k - beta nabla_{theta^k} L_seg(x_i^k; theta^k) on raw meta-train data and optimizing a meta-objective L_meta = L_seg(t_i^k; theta_hat^k) + gamma L_boundary(x_i^k, t_i^k; theta_hat^k) on frequency-transformed meta-test counterparts t_i^k using masked average pooling and an InfoNCE contrastive boundary loss over 2K boundary and background region-level features.