Necessity of a Dual-Engine Paradigm: Resolving the Robustness-Adaptability Trade-off in Anomaly Detection

The trade-off between model-driven robustness and data-driven adaptability is a fundamental challenge in machine learning, particularly for anomaly detection in non-stationary environments. Here, we prove mathematically that no single-engine architecture can overcome a detection completeness lower bound- any monolithic model must sacrifice either robustness or adaptability (Theorem 7). This impossibility necessitates a paradigm shift: instead of seeking a single optimal model, we must architecturally integrate two complementary information sources. To realize this principle, we propose the Dual-Engine Anomaly Detection Framework (dEADF), combining a Gaussian Orthogonal Ensemble (GOE) macro-statistical engine with a Multi-granularity Liquid Neural Network (MLNN) micro-dynamic engine. The GOE engine provides a theoretically grounded neutral reference manifold that preserves normal geometry and amplifies anomalies (Theorems 1-4). The MLNN engine captures adaptive, data-driven temporal patterns. Their integration is stabilized by GOE-guided regularization, which convexifies the loss landscape and tightens generalization bounds (Theorem 6 and Corollary 6.1). Feature-space complementarity (Theorem 5) and an optimal dimension principle (Theorem 8) further ensure that the two engines operate synergistically, while universality results (Theorem 9) delineate the framework's operational boundary under heavy-tailed distributions. We validate dEADF on three benchmarks-financial transactions, credit card fraud, and network intrusion-including a proprietary dataset with 1.42 million unlabeled transactions for deployment analysis. Without domain-specific feature engineering, dEADF achieves state-of-the-art performance across multiple metrics against 13 existing methods. This work does not propose an incremental model; rather, it identifies a mathematical necessity and provides the first constructive proof-of-concept for anomaly detection systems that are both theoretically grounded and adaptively powerful.