The output of neuron \( i \) in layer 2 is thus, $$ \begin{align} y_i^2 &= f_2\left(\sum_{j=1}^3 w_{ij}^2 y_j^1 + b_i^2\right) \tag{6}\\ &= f_2\left[\sum_{j=1}^3 w_{ij}^2f_1\left(\sum_{k=1}^2 w_{jk}^1 x_k + b_j^1\right) + b_i^2\right] \tag{7} \end{align} $$ where we have substituted \( y_m^1 \) with. Finally, the NN output yields, $$ \begin{align} y_1^3 &= f_3\left(\sum_{j=1}^3 w_{1m}^3 y_j^2 + b_1^3\right) \tag{8}\\ &= f_3\left[\sum_{j=1}^3 w_{1j}^3 f_2\left(\sum_{k=1}^3 w_{jk}^2 f_1\left(\sum_{m=1}^2 w_{km}^1 x_m + b_k^1\right) + b_j^2\right) + b_1^3\right] \tag{9} \end{align} $$