Project 4 Description
CS 3600 –
In this project you will be implementing a neural network through the most common
algorithm for learning the correct weights for a neural net from examples.
Code structure is provided for a Perceptron and a multilayer NeuralNet class, and you are
responsible for filling in some missing functions in each of these classes. This includes
writing code for the feed forward processing of input, as well as the backward propagation
algorithm to update network weights.
Files you will edit:
Neural Network Implementation Section:
This project follows the same terminology as in the lectures and Ch 18.7 in your book.
Neural networks are composed of nodes called perceptrons, as well as input units. Every
perceptron has inputs with associated weights, and from this it produces an output based on
its activation function. Thus you will be implementing a feed forward multilayer neural net,
and training the neural nets to be classifiers.
Inputs will be in the form of sets of examples that have an assignment of values to various
features and corresponding class values. The datasets used for this project include a cars
dataset and a dataset of pen handwriting values. For the latter, numeric data from images is
stored to train a classifier of handwritten digits. Instead of converting the stored examples
into dictionaries as in the last project, each example will be parsed into lists of numeric
values. Each possible classification for each class corresponds to a single output perceptron,
so in addition to the list of inputs each example includes the list of outputs for the output
layer. The Pen dataset has 16 inputs and 10 output perceptrons since there are 16 different
features for the handwriting recognition data input and 10 possible classifications of the
input (corresponding to the digits 0-9). In the case of a discrete -valued examples such as in
the cars dataset, distinct arbitrary numeric values are assigned to every value of every
The code we provide you has the methods for parsing the datasets into python data
structures, and the beginning of the Perceptron and NeuralNet classes. A Perceptron merely
stores an input size and weights for all the inputs, as well as methods for computing the
output and error given an input. An object of the NeuralNet class stores lists of Perceptrons
and has methods for computing the output of an entire network and updating the network
via back propagation learning.
The network consists of inputs (just a list of inputs that is a parameter to feed forward), an
output layer, and 0 or more hidden layers. Although the structure and initialization is
written, all the actual functionalities will be implemented by you.
Questions 1-4 will be autograded, the remaining (next section) will be analyzed by a TA and
Question 1 (2 points): Feed Forward
Implement sigmoid and sigmoidActivation in the Perceptron class. Then, implement
feedForward in the NeuralNet class.
Be sure to heed the comments in particular, don’t forget to add a 1 to the input list for the
bias input! After completing this question you have a working Neural Net classifier!
However, the weights are still randomized so it needs the following questions to be able to
Question 2 (2 points): Weight Update
Implement sigmoidDeriv, sigmoidActivationDeriv, and updateWeights in Perceptron
according to the equations from lecture and in the book.
Note that delta is an input to updateWeights, and will be the appropriate delta value
regardless of whether the Perceptron is in the output or a hidden layer; its computation will
be implemented later in backPropLearning.
Question 3 (4 points): Back Propagation Learning
Implement backPropLearning in NeuralNet using the methods you implemented in
questions 1 and 2.
Note that this is a single iteration of the back propagation learning, and the loop to perform
the full learning algorithm will be implemented in the next question. You can largely follow
the pseudocode in your book, though note that you should not be updating weights until you
have computed the error delta values that use those delta values. You code does not have to
exactly follow our suggestions in the comments, so long as it correctly implements back
propagation. To debug, you may use the following:
For test backprop0.test, the deltas for the first iteration are:
0.13274639952200898, 0.11272791158412912, 0.0627102923404577,
Question 4 (4 points): Learning Loop
Lastly, implement buildNeuralNet to actually train a good neural network classifier.
The stopping condition for training should be the average weight modification of all edges
going below the passed in threshold, or the iteration going above the maximum number of
iterations also passed in. See the comments in the code for more detail.
You should now have a working neural net classifier! If your solutions are right, then calling
testPenData in Testing.py should result in output similar (since we are starting from random
weights, the numbers will not be exactly the same) to:
Starting training at time 01:17:58.806009 with 16 inputs, 10 outputs, hidden layers , size
training set 7494, and size of test set 3498
. . . . . . . . . ! on iteration 10; training error 0.006085 and weight change 0.000272
. . . . . . . . . ! on iteration 20; training error 0.004340 and weight change 0.000188
. . . . . . . . . ! on iteration 30; training error 0.003674 and weight change 0.000144
. . . . . . . . . ! on iteration 40; training error 0.003342 and weight change 0.000119
. . . . . . . . . ! on iteration 50; training error 0.003142 and weight change 0.000102
. . . . . . . . . ! on iteration 60; training error 0.003006 and weight change 0.000091
. . . . . . . . . ! on iteration 70; training error 0.002902 and weight change 0.000083
. . . . . . . . . ! on iteration 74; training error 0.002865 and weight change 0.000080
Finished after 74 iterations at time 01:25:13.266676 with training error 0.002865 and
Feed Forward Test correctly classified 3118, incorrectly classified 380, test accuracy
Apart from the code implementation section from this project, we also ask you to write an
analysis of results for the following questions.
The analysis can be concise, you do not need to go over details of the algorithms
implementation, we are primarily interested in a report of the performance statistics
alongside a short explanation of the results.
Your analysis for Questions 5-6 (or 5-7 for extra credit) including all writing, plots, and tables
should be included into a PDF file named Analysis.pdf
Because of the nature of neural networks, training and running the model for the analysis
questions below can take up to a few hours! For this reason we recommend that you use
PyPy (more on it on the section below) to speed up the computations. Using PyPy can be the
difference between your code taking 3-4 hours to run and taking 15-20 minutes to run.
Question 5 (4 points): Learning with Restarts
Neural Networks as you have implemented them work by gradient descent from a random
starting point. This is a form of local search, so we have the typical local search problem of
landing in a local minima point that may or may not be close to the global minima.
To show the effects of random initialization on the performance of a neural net run 5
iterations of testPenData and testCarData with default parameters and report the max,
average, and standard deviation of the accuracy.
You should write your own code that uses the functions of Testing.py and NeuralNet.py to
run the model and obtain results
Question 6 (4 points): Varying the Hidden Layer
Vary the amount of perceptrons in the hidden layer from 0 to 40 inclusive in increments of
5, and get the max, average, and standard deviation of 5 runs of testPenData and testCarData
for each number of perceptrons.
Report the results in a table. Additionally, produce a learning curve with the number of
hidden layer perceptrons being the independent variable and the average accuracy being the
dependent variable. Briefly discuss any notable trends you noticed related to increasing the
size of the hidden layer has in your neural net.
Again you should write your own code that uses the functions of Testing.py and
NeuralNet.py to do this.
Question 7 (2 points Extra Credit): Learning XOR
As you’ve learned in class, adding the hidden layer allows Neural Nets to learn nonlinear
functions such as XOR. To show this in effect, produce the set of examples needed to train a
neural net to compute a 2 variable XOR function.
Train a neural net without a hidden layer in it and report the behavior. Then, run it on neural
nets starting with 1 perceptron in the hidden layer and increasing until the performance
begins to fall. The expected behavior is the performance to increase until a certain point and
then begin to fall.
Report the performance statistics of each run and write any conclusions and observations
you can draw.
If you choose to complete Question 7 you should include all the extra code needed in
Testing.py (and maybe NeuralNet.py but this shouldn’t be needed) and explain its
functionality in the Analysis PDF. You are free to use screenshots, pseudocode, comments,
and any other ways to explain how you build your network and why. Additionally, you must
submit the data you used to train your model as xor_data.txt
• xor_data.txt (if you completed the extra credit Q7)
“If you want your code to run faster you should probably just use PyPy.”
– Guido van Rossum (creator of Python)
What is PyPy?
PyPy is an implementation of Python different than the “default” implementation you have
been using all this time, which is CPython, this means that PyPy has a different way of
interpreting your .py source code and executing it.
The specific reasons why PyPy is so much faster than CPython is beyond the scope of this
class so we won’t get much in detail apart from saying Pypy uses “just-in-time compilation”,
meaning it compiles the code as it is executing it instead of simply interpreting the
instructions on a script as it goes. If you’re interested in understanding more about the
backend reasons for this difference the Wikipedia page for PyPy is a good stating point for
you to start poking around the hyperlinks to all these concepts.
How do I use Pypy?
First install it directly from the source: https://www.pypy.org/download.html
Once you install PyPy for your OS you can use it to run Python source code by typing:
instead of the usual:
Note that to use PyPy to run the code for your analysis questions you do not have to change
anything in NeuralNet.py or Testing.py, and you don’t have to write code any differently than
“regular” Python for this to work!
Just write the code for your project like you would normally do, and run the PyPy command
for your files!
Do I have to use PyPy for this project?
No! We are not mandating that students download PyPy and use it to run their code, however
the TAs strongly advise that you do, otherwise be prepared to potentially have to wait for up
to 3-4 hours each time you want to run your code for questions 5 to 7.