Inputs to the activation function

With the activation values $\boldsymbol{z}^l$ we can in turn define the output of layer $l$ as $\boldsymbol{a}^l = \sigma(\boldsymbol{z}^l)$ where $\sigma$ is our activation function. In the examples here we will use the sigmoid function discussed in our logistic regression lectures. We will also use the same activation function $\sigma$ for all layers and their nodes. It means we have

$$a_j^l = \sigma(z_j^l) = \frac{1}{1+\exp{-(z_j^l)}}.$$

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