Machine learning the breakdown of tame effective theories

Effective field theories endowed with a nontrivial moduli space may be broken down by several, distinct effects as the energy scales that are probed increase. These may include the appearance of a finite number of new states, or the emergence of an infinite tower of states, as predicted by the Distance Conjecture. Consequently, the moduli space can be partitioned according to which kind of state first breaks down the effective description, and the effective-theory cutoff has to be regarded as a function of the moduli that may abruptly vary in form across the components of the partition. In this work we characterize such a slicing of the moduli space, induced by the diverse breakdown mechanisms, in a two-fold way. Firstly, employing the recently formulated Tameness Conjecture, we show that the partition of the moduli space so constructed is composed only of a finite number of distinct components. Secondly, we illustrate how this partition can be concretely constructed by means of supervised machine learning techniques, with minimal bottom-up information.