# Backpropgation for a single parameter on a rather simple network

Given the following network:

I'm asked to write the backpropagation process for the $$b_3$$ parameter, where the loss function is $$L(y,z_3)=(z_3-y)^2$$

I'm not supposed to calculate any of the weights or expressions, rather write a general term in terms of $$\frac{\partial \alpha}{\partial \beta}$$

I'm also given that the starting term is $$\frac{\partial L}{\partial b_3}$$

I've thought about doing the following, which is basically: $$\frac{\partial L}{\partial b_3}=\frac{\partial L(b_3,z_3)}{\partial b_3}=\frac{\partial (z_3-b_3)^2}{\partial b_3}=2(b_3-z_3)$$ yet this feels off to me.

• $y$ is not $b_3$. $\frac{\partial (z_3 - y)^2}{\partial b_3}$ is what you need to compute.
– noe
Apr 3 at 13:12
• @noe in this, case, what is $y$? Apr 3 at 13:13
• $y$ is the expected output of the network.
– noe
Apr 3 at 13:14
• I see, how can I use that to complete what needs to be done? Apr 3 at 13:17
• I guess that you should use backpropagation: apply the chain rule until you reach something where $b_3$ appears
– noe
Apr 3 at 13:20