Formal Models and Convergence Analysis for Context-Aware Security Verification

Abstract: We present a formal framework for context-aware security verification that establishes provable guarantees for ML-enhanced adaptive systems. We introduce context-completeness - a new security property - and prove: (1) sample complexity bounds showing when adaptive verification succeeds, (2) information-theoretic limits relating context richness to detection capability, (3) convergence guarantees for ML-based payload generators, and (4) compositional soundness bounds. We further provide a formal separation between static context-blind verifiers and context-aware adaptive verifiers: for a natural family of targets, any static verifier with finite payload budget achieves completeness at most alpha, while a context-aware verifier with sufficient information achieves completeness greater than alpha. We validate our theoretical predictions through controlled experiments on 97,224 exploit samples, demonstrating: detection accuracy improving from 58% to 69.93% with dataset growth, success probability increasing from 51% to 82% with context enrichment, training loss converging at O(1/sqrt(T)) rate, and false positive rate (10.19%) within theoretical bounds (12%). Our results show that theoretically-grounded adaptive verification achieves provable improvements over static approaches under stated assumptions while maintaining soundness guarantees.