a(i) is the activation of the ith layer of the neural network and is the same as: $$
\begin{pmatrix}
a_{0}^{(i)} \
\vdots \
a_{n_{i}}^{(i)}
\end{pmatrix}
* Where $\displaystyle n_{i}$ is the number of nodes in the $\displaystyle i$th layer
* $\displaystyle \sigma(\cdot )$ is the [[sigmoid function]] and is applied to each entry of the vector
* $\displaystyle \boldsymbol{\Theta}^{(i)}$ is the weight matrix going from the $\displaystyle i$th layer to the $\displaystyle (i+1)$th layer (can also be represented as $\displaystyle \boldsymbol{W}$)
* The above example can be thought of as $\displaystyle \boldsymbol{a}^{(2)}=g(\Theta^{(2)}a^{(1)})$
