Backprop as Functor: A compositional perspective on supervised learning
Backprop as Functor: A compositional perspective on supervised learning
A supervised learning algorithm searches over a set of functions <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$A\rightarrow B$</tex> parametrised by a space <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$P$</tex> to find the best approximation to some ideal function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$f:A\rightarrow B$</tex> . It does this by taking examples <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(a, f(a))\in A\times B$</tex> , and updating …