Forward pass and backpropagation

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Problem

A scalar network has $h=\operatorname{ReLU}(wx)$ , $\hat{y}=vh$ , and loss

$L=\frac{1}{2}(\hat{y}-y)^2.$

At $x=2$ , $w=1$ , $v=3$ , and $y=4$ , compute $h$ , $\hat{y}$ , $L$ , $\frac{\partial L}{\partial v}$ , and $\frac{\partial L}{\partial w}$ .

Reveal answer or reference solution

$h=2$ , $\hat{y}=6$ , and $L=2$ . The derivatives are

$\frac{\partial L}{\partial v}=(6-4)h=4$

and

$\frac{\partial L}{\partial w}=(6-4)vx=12,$

because the ReLU input is positive.

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Appears in

Neural Networks