Lab 7: Neural Networks
Due April 3 by midnight

Starting point code

Use Teammaker to form your team. You can log in to that site to indicate your partner preference. Once you and your partner have specified each other, a GitHub repository will be created for your team.

Introduction

There are many good sofware packages that you can use to experiment with neural networks, such as tensorflow, keras, or conx. However, before using these packages we want you to first understand how backpropagation works at a detailed level. Therefore, in this lab you will implement your own neural network from scratch.

Your neural network will be made up of a number of classes:

• Network
  A network stores a list of layers.
  A layer stores of a list of nodes.
• Node
  A node stores a list of incoming edges, a list of outgoing edges, an activation value, and a delta.
  There are several specialized types of nodes:
  • InputNode
  • BiasNode
  • SigmoidNode
• Edge
  An edge stores a source node, destination node, and weight.

Neural Network Implementation

As you are working on your implementation, you should frequently try the unit tests we have provided:

  python3 nn_test.py

Below is a short summary of the tasks you need to complete. Note that much more detail about all of these methods can be found in the comments within the file neural_net.py.

1. Initially you will focus on implementing the SigmoidNode class methods:

   • compute_activation: weighted sum of inputs passed through a sigmoid function
   • compute_output_deltas: (output)(1 - output)(target - output)
   • compute_hidden_deltas: (output)(1 - output)(weighted sum of next-layer deltas)
   • update_weights: weight += (learning_rate)(delta)(input activation)

   The first three functions store their results in the node's self.activation and self.delta fields. update_weights changes the weights of the edges stored in self.in_edges.

2. Next you will work on completing the Network class. It is already set up to initialize a neural network with input, bias, and sigmoid nodes. You must implement the following functions for the neural network:

   • predict: computes the network's output for a given input, by calling compute activation on each successive layer
   • backpropagation: updates the network's weights using the error between the most recent output and the target
   • train: calls predict then backpropagation on each example in the (shuffled) training set until convergence or max epochs
   • test: computes the fraction of inputs for which the output matches the target

The main function sets up a network with a single two-neuron hidden layer and trains it to represent the function XOR.

Once you can successfully learn XOR, move on to the next section.

Explaining your XOR network

In the latex document provided (called nn.tex), fill in the diagram of the XOR network with the specific weights that were found by your program. Then explain how your network has solved the XOR problem. In particular, you need to clearly articulate when each hidden node will be active, and how the activity of the hidden nodes combined with the weights from the hidden nodes to the output nodes produces the correct output activations.

To compile your latex document into a pdf, run the following command:

pdflatex nn.tex

evince nn.pdf

Be sure to include your name(s) in the title of the document.

Submitting

You should submit the files neural_net.py and nn.tex. As usual, use git add, git commit and git push before the deadline to submit your work.