This exercise asks you to implement the beginnings of a simple deep learning package.

a. Implement a data structure for general computation graphs, as described in Section 21.1, and define the node types required to support feed-forward neural networks with a variety of activation functions. 

b. Write a function that computes the outputs of the computation graph given the inputs. 

c. Now write a function that computes the error for a labelled example. 

d. Finally, implement the local back-propagation algorithm based on Equations (21.11) and (21.12) and use it to create a stochastic gradient descent learning algorithm for a set of examples.