With our definition of the targets \boldsymbol{y} , the outputs of the network \boldsymbol{\tilde{y}} and the inputs \boldsymbol{x} we define now the activation z_j^l of node/neuron/unit j of the l -th layer as a function of the bias, the weights which add up from the previous layer l-1 and the forward passes/outputs \boldsymbol{a}^{l-1} from the previous layer as
z_j^l = \sum_{i=1}^{M_{l-1}}w_{ij}^la_i^{l-1}+b_j^l,where b_k^l are the biases from layer l . Here M_{l-1} represents the total number of nodes/neurons/units of layer l-1 . The figure in the whiteboard notes illustrates this equation. We can rewrite this in a more compact form as the matrix-vector products we discussed earlier,
\boldsymbol{z}^l = \left(\boldsymbol{W}^l\right)^T\boldsymbol{a}^{l-1}+\boldsymbol{b}^l.