# Reverse-Mode Automatic Differentiation **Domain:** Numerical Analysis / Optimization / Machine Learning **Doc Type:** Canonical Method Node **Maturity:** Foundational ## Definition **Reverse-mode automatic differentiation** computes derivatives of an output with respect to many earlier variables by recording a composed computation and propagating sensitivities backward through it. ## Historical Context [[wiki/Seppo Linnainmaa|Seppo Linnainmaa]] provided an early general formulation and implementation in 1970. [[wiki/Paul Werbos|Paul Werbos]] independently described backward derivative accumulation through ordered nonlinear operations in his 1974 dissertation. Histories of the method identify multiple independent lineages. ## Neural-Network Relation [[wiki/Backpropagation|Backpropagation]] applies reverse accumulation to [[wiki/Credit Assignment|credit assignment]] in trainable networks. The general differentiation method and its explicit neural-network application are related but historically distinct questions. ## See Also [[wiki/Gradient Descent|Gradient Descent]], [[wiki/Stochastic Gradient Descent|Stochastic Gradient Descent]]