Hierarchical Universe of data and Braverman Compactness

According to a modern deep learning textbook, “the goal of machine learning research is not to seek a universal learning algorithm or the absolute best learning algorithm. Instead, our goal is to understand what kinds of distributions are relevant to the ’real world’ that an AI agent experiences and what kinds of machine learning algorithms perform well on data drawn from the kinds of data generating distributions we care about”. The first formalization of the “real world properties for machine learning was Braverman compactness. Now, this idea is developed to hierarchical universe od data with compact granules. The distributions in real data world are rather mixtures of clusters (“patterns”) than regular distributions. In high-dimensional asymptotics this structure allows us to analyse reality and create effective methods for one- and few-shot learning.