Backprop as Functor: A compositional perspective on supervised learning

@article{Fong2017BackpropAF,
  title={Backprop as Functor: A compositional perspective on supervised learning},
  author={Brendan Fong and David I. Spivak and R{\'e}my Tuy{\'e}ras},
  journal={2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)},
  year={2017},
  pages={1-13}
}
A supervised learning algorithm searches over a set of functions $A\rightarrow B$ parametrised by a space $P$ to find the best approximation to some ideal function $f:A\rightarrow B$. It does this by taking examples $(a, f(a))\in A\times B$, and updating the parameter according to some rule. We define a category where these update rules may be composed, and show that gradient descent-with respect to a fixed step size and an error function satisfying a certain property-defines a monoidal functor… 

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