Simply-verifiable mathematical conditions for existence, uniqueness and explicit analytical computation of minimal adversarial paths (MAP) and minimal adversarial distances (MAD) for (locally) uniquely-invertible classifiers, for generalized linear models (GLM), and for entropic AI (EAI) are formulated and proven. Practical computation of MAP and MAD, their comparison and interpretations for various classes of AI tools (for neuronal networks, boosted random forests, GLM and EAI) are demonstrated on the common synthetic benchmarks: on a double Swiss roll spiral and its extensions, as well as on the two biomedical data problems (for the health insurance claim predictions, and for the heart attack lethality classification). On biomedical applications it is demonstrated how MAP provides unique minimal patient-specific risk-mitigating interventions in the predefined subsets of accessible control variables.

简单可验证的数学条件用于存在性、唯一性和明确的最小对抗路径 (MAP) 和最小对抗距离 (MAD) 的分析计算，适用于 (局部) 唯一可逆分类器，常规化线性模型 (GLM)，以及熵 AI (EAI)。通过在常见的合成基准测试上展示 MAP 和 MAD 的实际计算、比较和解释，为各类 AI 工具 (如神经网络、提升随机森林、GLM 和 EAI) 提供了证明。在两个生物医学数据问题上 (医疗保险理赔预测和心脏病发作致死率分类) 展示了 MAP 在预定义可控变量子集中为每位患者提供独特的最小风险干预措施。

关于人工智能分类器的对抗鲁棒性度量存在性、唯一性和可扩展性