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Why Backpropagation

Why do we use Backpropagation?

For example, consider the expression  {\color{Magenta} e=(a+b)\times (b+1)}

{\color{Orange} \begin{matrix} c=a+b\\ d=b+1\\ e=c\times d \end{matrix}}

Fig. 1

 

Fig. 2

Fig. 3

Fig. 4

 

In Fig. 4, Backpropagation gives us the derivative of e with respect to every node (c, d) and input variables (a, b), but Forwardpropagation ONLY gives us the derivative of our output with respect to a single input in Fig. 3 (with respect b only).

 

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