Concatenation of vector is a common operation in computational graph of modern day Deep Learning Networks. This post describes how to compute derivative of the output w.r.to the parameters of concatenation.

Where $C$ is concat operation. We are interested in computing $\frac{\partial z}{\partial x}$ and $\frac{\partial z}{\partial y}$

Assuming $x\in \mathbb{R}^m$ and $x\in \mathbb{R}^n$

We can rewrite the concat operation as

which implies