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The categories of open learners (due to Fong, Spivak and Tuy\'eras) and opengames (due to the present author, Ghani, Winschel and Zahn) bear a verystriking and unexpected similarity. The purpose of this short note is to provethat there is a faithful symmetric monoidal functor from the former to thelatter, which means that any supervised neural network (without feedback orother 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'sbest response relation encodes the dynamics of gradient descent. We suggestpaths for further work exploiting the link.

From open learners to open games