Given the following network: enter image description here

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.

  • 1
    $\begingroup$ $y$ is not $b_3$. $\frac{\partial (z_3 - y)^2}{\partial b_3}$ is what you need to compute. $\endgroup$
    – noe
    Apr 3 at 13:12
  • $\begingroup$ @noe in this, case, what is $y$? $\endgroup$
    – Aishgadol
    Apr 3 at 13:13
  • $\begingroup$ $y$ is the expected output of the network. $\endgroup$
    – noe
    Apr 3 at 13:14
  • $\begingroup$ I see, how can I use that to complete what needs to be done? $\endgroup$
    – Aishgadol
    Apr 3 at 13:17
  • 1
    $\begingroup$ I guess that you should use backpropagation: apply the chain rule until you reach something where $b_3$ appears $\endgroup$
    – noe
    Apr 3 at 13:20


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