General stochastic separation theorems with optimal bounds

Phenomenon of stochastic separability was revealed and used in machine learning to correct errors Artificial Intelligence (AI) systems analyze AI instabilities. In high-dimensional datasets under broad assumptions each point can be separated from the rest set by simple robust Fisher’s discriminant (is Fisher separable). Errors or clusters data. The ability an system also opens up possibility attack on it, high dimensionality induces vulnerabilities caused same that holds keys understanding fundamentals robustness adaptivity data-driven AI. To manage vulnerabilities, separation theorems should evaluate probability dataset will separable given for a class distributions. Explicit optimal estimates these probabilities are required, this problem is solved present work. general with obtained important classes distributions: log-concave distribution, their convex combinations product standard i.i.d. assumption significantly relaxed. These both correction data driven analysis vulnerabilities. third area application emergence memories ensembles neurons, phenomena grandmother’s cells sparse coding brain, explanation unexpected effectiveness small neural brain.