Let us now try to increase our level of ambition and attempt at setting up the equations for a neural network with two input nodes, one hidden layer with two hidden nodes and one output layer with one output node/neuron only (see graph)..
We need to define the following parameters and variables with the input layer (layer \( (0) \)) where we label the nodes \( x_1 \) and \( x_2 \)
$$ x_1 = a_1^{(0)} \wedge x_2 = a_2^{(0)}. $$The hidden layer (layer \( (1) \)) has nodes which yield the outputs \( a_1^{(1)} \) and \( a_2^{(1)} \)) with weight \( \boldsymbol{w} \) and bias \( \boldsymbol{b} \) parameters
$$ w_{ij}^{(1)}=\left\{w_{11}^{(1)},w_{12}^{(1)},w_{21}^{(1)},w_{22}^{(1)}\right\} \wedge b^{(1)}=\left\{b_1^{(1)},b_2^{(1)}\right\}. $$