FedCP (Federated Conditional Policy for Sample-Wise Feature Information Separation)

A personalized federated learning algorithm (Zhang et al. 2023, Section 3.2, Equations 2-8, Algorithm 1) that separates each input sample's K-dimensional representation h_i = f(x_i; W_i^{fe}) in R^K into global feature information r_i odot h_i and personalized feature information s_i odot h_i using a client-specific Conditional Policy Network (CPN, parameterized by Theta_i) that takes the head-conditioned vector C_i = (v_i / ||v_i||_2) odot h_i (with v_i = sum_{c=1}^C w_c^T summed over the rows of the personalized head W_i^{hd}) and outputs complementary per-dimension soft routing gates r_i^k = exp(a_{i,1}^k) / (exp(a_{i,1}^k) + exp(a_{i,2}^k)) and s_i^k = exp(a_{i,2}^k) / (exp(a_{i,1}^k) + exp(a_{i,2}^k)) satisfying r_i^k + s_i^k = 1 (Equations 3-4), routes r_i odot h_i to the frozen global head W^{hd} and s_i odot h_i to the trainable personalized head W_i^{hd} to form combined logits out_i = g(r_i odot h_i; W^{hd}) + g(s_i odot h_i; W_i^{hd}) (Equation 5), regularizes h_i toward the frozen global feature extractor via RKHS Maximum Mean Discrepancy E_i^d (Equations 7-8), and uploads the averaged head W_hat_i^{hd} = (W^{hd} + W_i^{hd}) / 2 (Equation 6).