Fixed-Point Guided ADS Scenario Generation via Multi-modal LLM Reasoning and Software Testing

Robust scenario generation is essential for systematically testing Autonomous Driving Systems (ADSs) under rare and safety-critical conditions. However, search-based approaches often lack semantic guidance, whereas specification-based approaches rely heavily on manually constructed rules. Existing LLM-assisted techniques primarily translate accident artifacts into scene descriptions without producing executable behavioral specifications that guide subsequent testing. We present InvarGen , a framework that uses a multi-modal LLM as a parametric specification generator. InvarGen organizes safety requirements into a predefined taxonomy of Scenario Fixed Points while dynamically instantiating their predicates, thresholds, and temporal bounds from each accident context. These fixed points serve as executable test oracles and optimization objectives. Unlike static templates, these fixed points adaptively constrain the search space, guiding a hybrid evolutionary process: Intelligent Fuzzing exploits boundary parameters to trigger specific violations, while Structural Mutation ensures the global exploration of diverse environmental contexts. Evaluation using 200 real-world accidents and 1,400 synthesized scenarios shows that InvarGen discovers 37.8% more critical scenario types than the best baseline, achieves a 30% fixed-point violation rate, and achieves the highest semantic-diversity score. The scenarios also achieve high physical plausibility and cross-simulator executability, with 100% syntactic compliance with the evaluated OpenX formats. These results highlight the promise of fixed-point semantics as a principled bridge between unstructured LLM reasoning and rigorous robustness testing.