How to update weights in backpropagation algorithm (a numerical example)?

Question

Assume we have the following neural network and all activation functions are $f(z)=z$. If the weights are initialized with the values you see in table below, what will be new updated weights after one step if learning rate, $\alpha = 0.05$?

Assume the input values are [$i_1$,$i_2$] = [2,3] and target value $out = 1$.

Hint:
$w_{new} = w_{old} - \alpha \frac{\partial E}{\partial w}$

$E_{\text {total}}=\sum \frac{1}{2}(\text {target}-\text {output})^{2}$

Updating weights in backpropagation algorithm

Weights	Initialization	New weights after one step
$w1$	0.11	?
$w2$	0.21	?
$w3$	0.12	?
$w4$	0.08	?
$w5$	0.14	?
$w6$	0.15	?

Comments

w6 = 0.15 and not 0.1 with respect to the posted solution.

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i1, i2, and target value  should be given! or else not possible to update w1,w2,w3, & w4.

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Thanks for your note Yoga. It is added.

Answer 1

A detailed solution is provided in this URL.

The updated weights are as follows:

Comments

In this solution, they solve using Error = 1/2 (output - target)^2, however the question above gives a hint Error = 1/2 (target - output)^2

Although, I don't think it makes a difference to our solution, as the delta is squared in calculating the error, so the sign goes away, and in the derivative, the minuses would cancel out in chain rule.

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It does make a difference, because after taking the derivative it should be (target - output) but in the solution it's (output - target)