Statistical Runtime Verification for LLMs via Robustness Estimation

Adversarial robustness verification is essential for ensuring the safe deployment of Large Language Models (LLMs) in runtime-critical applications. However, formal verification techniques remain computationally infeasible for modern LLMs due to their exponential runtime and white-box access requirements. This paper presents a case study adapting and extending the RoMA statistical verification framework to assess its feasibility as an online runtime robustness monitor for LLMs in black-box deployment settings. Our adaptation of RoMA analyzes confidence score distributions under semantic perturbations to provide quantitative robustness assessments with statistically validated bounds. Our empirical validation against formal verification baselines demonstrates that RoMA achieves comparable accuracy (within 1\% deviation), and reduces verification times from hours to minutes. We evaluate this framework across semantic, categorial, and orthographic perturbation domains. Our results demonstrate RoMA's effectiveness for robustness monitoring in operational LLM deployments. These findings point to RoMA as a potentially scalable alternative when formal methods are infeasible, with promising implications for runtime verification in LLM-based systems.