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I am new to AI and currently studying how backpropagation works.

Refer to the diagram below, it seems derivative $\frac{\partial f}{\partial w}$ can be expressed as $\left ( \sigma(\sigma (wx)) (1-\sigma(\sigma(wx) ) \right )$.

Can anyone please tell me how that expression can be expressed as $f(x)(1-f(x))$?

Thank you for your help.

Backpropagation Example Diagram

thom
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1 Answers1

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Let $f(x) = \sigma(\sigma (wx))$. This is a function of $x$, and indeed: $f(x)(1-f(x)) = (\sigma(\sigma (wx)))(1-\sigma(\sigma (wx)))$.

Conrad Crowley
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