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Graph theorist Reinhard Diestel has a new book: Tangles, A structural approach to artificial intelligence in the empirical sciences, tangles-book.com/

If I understand it correctly, his setup involves a population (of people, states of a physical system, data points in a machine learning data set) and a collection of binary questions that each might answer (opinion poll answers, experiments, classifiers). The "tangles" of the title can be thought of as hypothetical members of the population whose answers to triples of questions are consistent, in a certain sense (Why triples? It's technical.) Consistent might mean, for instance, that there is a real population member with the same answers to that triple (but not to all the other questions). From this setup one can find a small number of questions that distinguish all tangles from each other (they will answer differently to at least one of the questions) or, if there are no tangles, an explanation for why not in the form of a small number of triples of questions that cannot all be consistently answered. This analysis can then be used both to cluster the population and to provide structure in the system of questions.

This is all a broad generalization of methods originally used in a highly technical way as part of the theory of graph minors and their extensions to matroid minors. The task Diestel has set himself is an ambitious one: describe all this readably in a book aimed at non-mathematicians. I'm not really the right reader to tell whether he is successful in this goal, but it's an interesting attempt.

(See also the post by @sioum, mathstodon.xyz/@sioum/11244573)

tangles-book.comTanglesA structural approach to artificial intelligence