Question about grad() from Deep Learning by Chollet

On page 58 of the second edition of Deep Learning with Python, Chollet is illustrating an example of a forward and backward pass of a computation graph. The computation graph is given by:

$$ x\to w\cdot x := x_1 \to b + x_1 := x_2 \to \text{loss}:=|y_\text{true}-x_2|. $$

We are given that $x=2$, $w=3$, $b=1$, $y_{\text{true}}=4$. When running the backward pass, he calculates $$ grad(\text{loss},x_2) = grad(|4-x_2|,x_2) = 1. $$

Why is the following not true: $$ grad(\text{loss},x_2) = \begin{cases} 1 x_24 \\ -1 x_2 4 \end{cases} $$

Topic gradient backpropagation

Category Data Science

About

Geeks Mental is a community that publishes articles and tutorials about Web, Android, Data Science, new techniques and Linux security.