We want to train a neural network once to imitate formula_1 and another time to imitate formula_2. The goal is to observe how the parameters within the neural network are transformed through the training process.

Other task to perform includes:

1. Implement the feed-forward pass method feed_forward of the neural network and store the outcome values in the corresponding members.
2. Implement the back-propagation pass method back_prop of the neural network. Update the parameters (weights and bias) of the neural network accordingly with a learning rate of 0.01.
3. Implement stochastic gradient descent to be performed in each epoch.