FedAwS (Federated Averaging with Spreadout for Positive-Only Labels)

A federated multi-class and extreme-classification training algorithm (Yu, Rawat, Menon, & Kumar 2020, Section 3, Equations 7-8, Algorithm 1) for settings where each client i holds only positive examples of its own class(es) and cannot share data or other clients' class embeddings: clients locally minimize only the positive alignment loss l_pos(f(x), y) = d(w_y, g_theta(x))^2 on the shared input encoder g_theta and local class embedding w_y, while the central server prevents trivial embedding collapse after averaging by applying a geometric spreadout regularizer reg_sp(W) = sum_{c in [C]} sum_{c' != c} (max(0, nu - d(w_c, w_{c'})))^2 (Equation 7) or its top-k closest-negative variant reg_sp^top(W) (Equation 8) to the class embedding matrix W.