BibTeX
@ARTICLE{
         Despres2025Aff,
       title = "A functional framework for nonsmooth autodiff with \emph{maxpooling} functions",
       author = "Bruno Despr{\'e}s",
       journal = "Transactions on Machine Learning Research",
       issn = "2835-8856",
       year = "2025",
       url = "https://openreview.net/forum?id=qahoztvThX",
       abstract = "We make a comment on the recent contribution by Boustany (2024), by showing that
         the Murat-Trombetti Theorem provides a simple and efficient mathematical framework for nonsmooth
         automatic differentiation of \emph{maxpooling} functions. In particular it gives a the chain
         rule formula which correctly defines the composition of Lipschitz-continuous functions which are
         piecewise-$C^1$. The formalism is applied to four basic examples, with some tests in PyTorch. A self
         contained proof of an important Stampacchia formula is in the appendix.",
       ad_theotech = "Nonsmooth"
}