FoolsGold Cosine-Similarity Sybil Defense for Federated Learning

A sybil-resilient federated learning aggregation algorithm that tracks each client's cumulative historical gradient vector H_i = sum_{t=1}^T Delta_{i,t}, computes pairwise indicative-feature weighted cosine similarities cs_{ij} between historical updates, applies a ratio-based pardoning rule cs_{ij} *= v_i / v_j whenever v_j > v_i (where v_i = max_{k != i} cs_{ik}) to avoid penalizing honest clients, inverts and max-normalizes the row-wise maximum similarities into alpha_i = (1 - max_j cs_{ij}) / max_k(1 - max_j cs_{kj}), and rescales client learning rates via a centered logit function alpha_i = clip_{[0,1]}(kappa * (ln(alpha_i / (1 - alpha_i)) + 0.5)) before updating w_{t+1} = w_t + sum_i alpha_i Delta_{i,t}.