CS3600 Solution

Project 4: Neural Nets
Introduction

In this project you will be implementing neural nets, and in particular the most common algorithm for learning the correct weights for a neural net from examples. Code structure is provided for a Perceptron and a multi layer 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

NeuralNet.py: Your entire Neural Net implementation will be within this file
Testing.py: Helper functions for learning a neural net from data
NeuralNet_report.pptx: Your answers to the analysis questions go into this file. Convert this file to a pdf and then submit it to Gradescope. You must submit your written answers in this format. Do not remove or add slides.
(optional) xor.txt: Your training examples for q7 (extra credit)
(optional) NeuralNetUtil.py: Functions for converting the datasets into python data structures Testing.py Helper functions for learning a neural net from data. Note: if you decide to do question 8 for extra credit, you will have to add a method to this file.

Evaluation

Your code will be autograded for technical correctness, using the same autograder and test cases you are provided with. Please do not change the names of any provided functions or classes within the code, or you will wreak havoc on the autograder. You should ensure your code passes all the test cases before submitting the solution, as we will not give any points for a question if not all the test cases for it pass. However, the correctness of your implementation, not the autograder's judgments, will be the final judge of your score. Even if your code passes the autograder, we reserve the right to check it for mistakes in implementation, though this should only be a problem if your code takes too long or you disregarded announcements regarding the project. The short answer grading guidelines are explained below.



Getting Help


Neural Network Learning Implementation

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 multi layer neural net.

We will be 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.


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 functionality will be implemented by you.
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. You now have a Neural Net classifier! However, the weights are still randomized so it is rather useless…

File you’ll edit: NeuralNet.py
Question 2 (2 points): Weight Update

Implement sigmoidDeriv, sigmoidActivationDeriv, and updateWeights in Perceptron according to the equation 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.

File you’ll edit: NeuralNet.py
Question 3 (4 points): Back Propagation Learning


For test backprop0.test, the deltas for the first iteration are:

[[0.030793495980775746, 0.015482381603395969, 0.011581614293905421,
0.004449919337742824, 0.02164433012587241, 0.02929895427882054,
0.009128354470904964, 0.002752718694772222, 0.0136716072376759,
0.015406354991598608, 0.013100536741508734, 0.0041637660666657295,
0.00017176192932002172, 0.010111421606106267, 0.036790975475881824,
0.007334760193359876, 0.00698074822965782, 0.029598447675293165,
0.010824328898999185, 0.03097345080247739, 0.007777081314307609,
0.0023536881454502725, 0.01345707648774709, 0.007920771403715898], [
0.026000590890107898, 0.06031387251323732, 0.03958313495848832,
0.07355044647726003, 0.06973954192905674, 0.10235871158610363,
0.13274639952200898, 0.11272791158412912, 0.0627102923404577,
0.03676930932503297]]

File you’ll edit: NeuralNet.py
Question 4 (4 points): Back Propagation 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 this:

Starting training at time 01:17:58.806009 with 16 inputs, 10 outputs, hidden layers [24], size of 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 weight change 0.000080

Feed Forward Test correctly classified 3118, incorrectly classified 380, test accuracy 0.891366

File you’ll edit: NeuralNet.py

Analysis

Put your answers to questions 5-8 in NeuralNet_report.pptx with data tables and plots, with a short and concise written analysis for each question. We primarily care that you report the performance statistics asked for accurately. You will convert your slides to PDF later on for submission.

Question 5 (4 points): Learning with Restarts


File you’ll edit: NeuralNet_report.pptx
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 (you’ll want just let your computer run this one for a while) 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. You should write your own code that uses the functions of Testing.py and NeuralNet.py to do this.

File you’ll edit: NeuralNet_report.pptx

Extra Credit
Question 7 (2 points Extra Credit): Learning XOR

As you’ve learned in class, adding the hidden layer allows Neural Nets to learn non linear 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. Put your examples in a text file called xor.txt. Train a neural net without a hidden layer with it and report the behavior. Then, run it on neural nets starting with 1 perceptron in the hidden layer and increasing until you get a
neural net that works well. Are the results what you expected?
File you’ll edit: NeuralNet_report.pptx
Question 8 (2 points Extra Credit): Novel Dataset

Explore the UCI Machine Learning Repository or other ML datasets found online, and select a new dataset to try your Neural Network with. Write a method in NeuralNetUtil.py called buildExamplesFromExtraData that is akin to the other get methods we wrote. Answer question 5 for this dataset, and submit your NeuralNetUtil.py in addition to NeuralNet.py for the option of extra credit. Also include your code to set up training and a description on how to run this code.

File you’ll edit: NeuralNet_report.pptx, NeuralNetUtil.py

Submission


Make sure to convert NeuralNet_report.pptx to a PDF. Do NOT add or remove slides.

Programming Files:
• NeuralNet.py
• xor.txt (optional for question 7)
• NeuralNetUtil.py (optional for question 8)

Non-programming Files:
• NerualNet_report.pdf

PyPy

"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 starting 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:
pypy filename.py

instead of the usual:
py filename.py

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?