ByzaSpline-Fed: Gram-Weighted Functional Aggregation for Byzantine-Robust Federated Kolmogorov–Arnold Networks in Industrial IoT

Federated learning enables industrial sites to train shared condition-monitoring models without exchanging raw vibration, acoustic, or sensor data, but its openness admits Byzantine clients that submit corrupted updates. Existing robust aggregation rules—Krum, trimmed mean, median, and their variants—operate in Euclidean parameter space and implicitly assume that a malicious update must be far from honest updates to do harm. We show that this assumption fails for models with Kolmogorov–Arnold (KAN) spline heads: an adversary can hold the spline coefficients close to the honest consensus in the L2 sense while distorting the functional shape the spline encodes, an attack we term functional spline-poisoning. We propose ByzaSpline-Fed, a Byzantine-robust aggregation rule that scores clients by Gram-weighted functional B-spline distance on a consensus knot grid and rejects functional outliers. The rule reduces exactly to spline-aware federated averaging under honest participation, admits a breakdown bound of f < K/2 under the standard honest-majority assumption, and supports optional differential privacy. We evaluate across four industrial benchmarks spanning classification, unsupervised acoustic anomaly detection, and remaining-useful-life regression—CWRU, Paderborn, MIMII, and C-MAPSS—reporting task-correct metrics under clean and adversarial conditions. Under thirty percent functional poisoning, Euclidean defenses lose up to thirty-four accuracy points while ByzaSpline-Fed remains within roughly three points of its clean performance. All reported results are averaged over eight independent random seeds, and the improvements over the strongest competing defense are statistically significant under the Wilcoxon signed-rank test (p < 0.05).