Multi-Level Distributional Entropy for Explainable Network Intrusion Detection

Abstract: Machine learning network intrusion detection systems (IDS) rely on aggregate flow statistics that discard distributional structure, while established entropy measures require raw packet sequences unavailable in pre-aggregated flow datasets. We propose Multi-Level Distributional Entropy (MDE), an analytical framework that derives interpretable entropy features directly from flow-level summary statistics at three levels: within-flow Gaussian differential entropy, cross-directional Jensen-Shannon divergence (JSD), and Transmission Control Protocol (TCP) flag-pattern Shannon entropy, without raw packet access or training data. Across four benchmarks (NSL-KDD, CICIDS-2017, CICIDS-2018, UNSW-NB15) under a leakage-free fold-local pipeline, entropy-only features achieve weighted F1 of 0.708-0.989, matching conventional features without degrading performance. Full operational metric reporting then exposes failure modes that aggregate F1 conceals. On CICIDS-2018, F1=0.74 hides a detection rate (DR) of 0.48, and on held-out attack families F1 exceeds 0.998 while DR falls to zero. Under temporal shift, a pseudo-live replay of 703K flows reveals a threshold-ranking divergence in which score ranking is preserved (AUC=0.87) but fixed thresholds collapse (DR=0.082) and recalibration offers no recovery. SHapley Additive exPlanations (SHAP) fold-stability analysis (Spearman rho=0.80-0.95) confirms that entropy attributions are reproducible and domain-coherent across heterogeneous environments.