Get Global Guarantees: On the Probabilistic Nature of Perturbation Robustness

Robustness is a critical requirement for deploying machine learning models in safety-sensitive domains, where even imperceptible input perturbations can lead to hazardous outcomes. However, existing robustness assessment techniques prior to deployment often face a trade-off between computational feasibility and measurement precision, limiting their effectiveness in practice. To address these limitations, we provide a systematic comparative study of prevailing robustness definitions and their corresponding evaluation methodologies. Building on this analysis, we propose tower robustness, which is a novel and practical concept setting out from a global perspective. Further, we provide upper and lower bounds of tower robustness, based on hypothesis testing, for quantitative evaluation, enabling more rigorous and efficient pre-deployment assessments. Through empirical investigation, we demonstrate that our approach provides reliable robustness assessments. These findings advance the systematic understanding of robustness and contribute a practical framework for enhancing the safety of machine learning models in safety-critical applications.