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.

翻译：针对（局部）唯一可逆分类器、广义线性模型（GLM）及熵AI（EAI），本文提出并证明了最小对抗路径（MAP）与最小对抗距离（MAD）的存在性、唯一性及显式解析计算的可简单验证数学条件。通过通用合成基准（双瑞士卷螺旋及其扩展）以及两个生物医学数据问题（健康保险索赔预测与心脏病致死性分类），展示了各类AI工具（神经网络、提升随机森林、GLM与EAI）中MAP与MAD的实际计算、比较与解读。在生物医学应用中，证明了MAP如何在预定义的可控变量子集中提供唯一的、针对患者的极小风险干预措施。