Correction of AI systems by linear discriminants: Probabilistic foundations

We prove that this separability property holds for a wide class of distributions including log-concave distributions and distributions with a special 'SMeared Absolute Continuity' (SmAC) property defined through relations between the volume and probability of sets of vanishing volume. These classes are much wider than the Gaussian distributions. The requirement of independence and identical distribution of data is significantly relaxed. The results are supported by computational analysis of empirical data sets.