Oral
in
Workshop: Differentiable Programming Workshop

A Complete Axiomatization of Forward Differentiation

Gordon Plotkin

2021 Oral
in
Workshop: Differentiable Programming Workshop

Project Page [ OpenReview]

Abstract

We give a complete decidable second-order equational axiomatisation of the forward differentiation of smooth multivariate functions. Differentiation is expressed using the binding structures available in second-order equational logic. The main mathematical theorem used is Severi’s multivariate Hermite interpolation theorem.

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