Output layer

For the final output layer we have the inputs to the final activation function

$$ z^{(2)} = w_{1}^{(2)}a_1^{(1)} +w_{2}^{(2)}a_2^{(1)}+b^{(2)}, $$

resulting in the output

$$ a^{(2)}=\sigma^{(2)}(z^{(2)}). $$