  The categories of open learners (due to Fong, Spivak and Tuy\'eras) and open
games (due to the present author, Ghani, Winschel and Zahn) bear a very
striking and unexpected similarity. The purpose of this short note is to prove
that there is a faithful symmetric monoidal functor from the former to the
latter, which means that any supervised neural network (without feedback or
other complicating features) can be seen as an open game in a canonical way.
Roughly, each parameter is controlled by a different player, and the game's
best response relation encodes the dynamics of gradient descent. We suggest
paths for further work exploiting the link.
