# Calculation of backpropagation of a NN with skip nodes

Assume this neural net.

In our course we had to provide the forward and backward pass for this net. This is the solution we received:

Even with the solutions provided I still have problems understanding the steps taken to get through the backward pass. Especially the step $$\frac{\partial L}{\partial z_0}$$ where the partial derivative of the skip node comes together is a mystery to me. Our Profs do not go in detail of the algorithm. Especially if the partial is shortened it yields a contradiction, right? Or does this simply not matter since the gradient is a vector?

\begin{align} \frac{\partial L}{\partial z_0}&= \frac{\partial L}{\partial a_1}\cdot\frac{\partial a_1}{\partial z_0}+ \frac{\partial L}{\partial a_2}\cdot\frac{\partial a_2}{\partial z_0}\\ \frac{\partial L}{\partial z_0}&= \frac{\partial L}{\partial z_0}+\frac{\partial L}{\partial z_0}\\ \frac{\partial L}{\partial z_0}&\stackrel{!}{=}2\cdot\frac{\partial L}{\partial z_0}\\ \end{align}

Wheres my fallacy?

• Hi, welcome. Where are these pictures from? – Jim Feb 8 '19 at 19:08
• Thank you. From our exercises. Is this not allowed? – ManuelSchneid3r Feb 8 '19 at 19:55
• It is allowed, but could you post a link. – Jim Feb 8 '19 at 20:10
• The exercises are on a closed platform of our university. – ManuelSchneid3r Feb 11 '19 at 11:13
• Why the downvotes? – ManuelSchneid3r Feb 11 '19 at 11:13