Autodiff

Autodiff, aka Automatic Differentiation, is a method to calculate Partial Derivatives through a multigraph of functions, where each node is a variable, and each edge is a constraint between said variables.

It avoids the need for symbolic differentiation, at the cost of the potential blow up of derivatives:

$$\begin{array}{ccc}\{f_i{\}}_i& \stackrel{\text{Automatic differentiation}}{\to }& \{\frac{\partial }{\partial w_j}{f}_i{\}}_{ij}\\ \downarrow \text{Single expression}& & \uparrow {\varphi }_t\\ y=f(x)& \stackrel{\text{Symbolic differentiation}}{\to }& y^{\prime }=f^{\prime }(x)\end{array}$$