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Backprop as Functor: A compositional perspective on supervised learning

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arxiv 1711.10455 v3 pith:BEV3NUNC submitted 2017-11-28 math.CT cs.AIcs.LG

Backprop as Functor: A compositional perspective on supervised learning

classification math.CT cs.AIcs.LG
keywords categoryfunctionfunctionsfunctorlearningparametrisedperspectiverules
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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A supervised learning algorithm searches over a set of functions $A \to B$ parametrised by a space $P$ to find the best approximation to some ideal function $f\colon A \to B$. 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 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.

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Cited by 3 Pith papers

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