FedTHE (Test-Time Robust Personalized Federated Learning with Two-Head Ensemble)

A test-time adaptive personalized federated learning framework (Jiang & Lin 2023, Sections 4.1-4.2, Algorithm 1) that equips a shared feature extractor g with both an aggregated global classifier head h_g and a local personalized classifier head h_{p_m}, maintains a local training feature history h_hat_m = beta h_hat_m + (1 - beta) z_bar_m where z_bar_m is the batch average of L2-normalized penultimate features g(x) / ||g(x)||_2, and adapts per-sample ensemble weights (e, 1 - e) in the simplex Delta^1 at test time for each single test input x' by (1) updating a test-sample EMA feature tracker z'_t = alpha z'_{t-1} + (1 - alpha) z_norm(x') to compute cosine similarity lambda_s = cos(z'_t, h_hat_m) clipped to [0, 1] as a feature-space interpolator between global and personalized heads, (2) taking a one-step gradient descent update on the prediction Shannon entropy L_e(Y_hat) = -sum_c y_hat_c log y_hat_c of Y_hat = softmax(e h_g(g(x')) + (1 - e) h_{p_m}(g(x'))) projected onto Delta^1 to obtain entropy-minimized weights (e^*, 1 - e^*), and (3) combining both signals via feature-space temperature scaling Y_hat_final = softmax(e^* h_g(g(x')) / tau_g + (1 - e^*) h_{p_m}(g(x')) / tau_l) with adaptive temperatures tau_g = 1 - lambda_s + epsilon and tau_l = lambda_s + epsilon (Algorithm 1, Lines 12-13).