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：本文提出并证明了（局部）唯一可逆分类器、广义线性模型（GLM）及熵AI（EAI）的最小对抗路径（MAP）与最小对抗距离（MAD）存在性、唯一性及显式解析计算的简单可验证数学条件。通过通用合成基准实验（包括双瑞士卷螺旋及其扩展形态）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率分类），展示了各类AI工具（神经网络、增强随机森林、GLM与EAI）的MAP和MAD实际计算方法、对比分析及解释。在生物医学应用中，本文验证了MAP如何在可干预控制变量的预设子集中提供具有唯一性的个体化风险最小化干预方案。