Why, when training a neural network, can't you just calculate the error and substitute such weights for which the error will be equal to 0?

Question

Neural networks

I will give an example:

Why in this example (when calculating direction_and_amount) it is impossible to do division operation instead of multiplying by input? Then the required weight would be found already at the second iteration.

I'm new, so this might sound like a dumb question. Please do not judge strictly.

Answer 1

By substituting such weights, you tune the neural network to a "specific" instance - torn from the statistics.
It's like saying that all oranges are of the same color #fdaf21 and the colors #fdaf22 and #fdaf20 are no longer an orange, but something else.

Answer 2

In this exaggerated example, you can.
In more complex networks, the desired dependence is unknown,
so the weights are selected in small steps.

Answer 3

It is possible, but sometimes the exact calculation of the error at each iteration is comparable to the creation of another parallel neural network or analytical system.
Therefore, if the result is > 90%, they think: "And so it will do!"... :((
By the way, if you initially build the mathematical model of the neural network correctly, you can generally eliminate the appearance of errors.