  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.
