2017/11/28 by Brendan Fong, David I. Spivak, Rémy Tuyéras · 2 voices · 1 citation
Mathematics · Computer Science · #math.CT #cs.AI #cs.LG
arxiv published 2017/11/28 · arxiv updated 2019/05/01
A supervised learning algorithm searches over a set of functions A → B parametrised by a space P to find the best approximation to some ideal function f\colon A → B. It does this by taking examples (a,f(a)) ∈ A× 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 from a category of parametrised functions to this category of update rules. This provides a structural perspective on backpropagation, as well as a broad generalisation of neural networks.