70afbf2259b4449d8ae1429e054df1b1-Supplemental.pdf

This is the appendix for "Nonsmooth Implicit Differentiation for Machine Learning and Optimization". We recall basic definitions and results on definable sets and functions used in this work. The archetypal o-minimal structure is the collection of semialgebraic sets. R is a polynomial function. Note that the collection of semialgebraic sets verifies 3 in Definition 6 according to the Tarski-Seidenberg theorem.