  All artificial Intelligence (AI) systems make errors. These errors are
unexpected, and differ often from the typical human mistakes ("non-human"
errors). The AI errors should be corrected without damage of existing skills
and, hopefully, avoiding direct human expertise. This paper presents an initial
summary report of project taking new and systematic approach to improving the
intellectual effectiveness of the individual AI by communities of AIs. We
combine some ideas of learning in heterogeneous multiagent systems with new and
original mathematical approaches for non-iterative corrections of errors of
legacy AI systems. The mathematical foundations of AI non-destructive
correction are presented and a series of new stochastic separation theorems is
proven. These theorems provide a new instrument for the development, analysis,
and assessment of machine learning methods and algorithms in high dimension.
They demonstrate that in high dimensions and even for exponentially large
samples, linear classifiers in their classical Fisher's form are powerful
enough to separate errors from correct responses with high probability and to
provide efficient solution to the non-destructive corrector problem. In
particular, we prove some hypotheses formulated in our paper `Stochastic
Separation Theorems' (Neural Networks, 94, 255--259, 2017), and answer one
general problem published by Donoho and Tanner in 2009.
