Project 1 - Japanese Characters and Intertwined Spirals

In this assignment, you will be implementing and training various neural network models for two different classification tasks, and analysing the results.

You are to submit two Python files kuzu.py and spiral.py, as well as a written report hw1.pdf (in pdf format). 

Provided Files

Your task is to complete the skeleton files kuzu.py, spiral.py and submit them, along with your report. 

Part 1: Japanese Character Recognition

python3 kuzu_main.py --net conv

Your network should consistently achieve at least 93% accuracy on the test set after 10 training epochs. Copy the final accuracy and confusion matrix into your report. 

4. [7 marks] Discuss what you have learned from this exercise, including the following points:
a. the relative accuracy of the three models,
b. the confusion matrix for each model: which characters are most likely to be mistaken for which other characters, and why?
c. you may wish to experiment with other architectures and/or metaparameters for this dataset, and report on your results; the aim of this exercise is not only to achieve high accuracy but also to understand the effect of different choices on the final accuracy. 

Part 2: Twin Spirals Task

For Part 2 you will be training on the famous Two Spirals Problem (Lang and Witbrock, 1988). The supplied code spiral_main.py loads the training data from spirals.csv, applies the specified model and produces a graph of the resulting function, along with the data. For this task there is no test set as such, but we instead judge the generalization by plotting the function computed by the network and making a visual assessment. 

1. [2 marks] Provide code for a Pytorch Module called PolarNet which operates as follows: First, the input (x,y) is converted to polar co-ordinates (r,a) with r=sqrt(x*x + y*y), a=atan2(y,x). Next, (r,a) is fed into a fully connected neural network with one hidden layer using tanh activation, followed by a single output using sigmoid activation. The conversion to polar coordinates should be included in your forward() method, so that the Module performs the entire task of conversion followed by network layers. 

2. [1 mark] Run the code by typing

python3 spiral.py --net polar --hid 10

Try to find the minimum number of hidden nodes required so that this PolarNet learns to correctly classify all of the training data within 20000 epochs, on almost all runs. The graph_output() method will generate a picture of the function computed by your PolarNet called polar_out.png, which you should include in your report. 

3. [1 mark] Provide code for a Pytorch Module called RawNet which operates on the raw input (x,y) without converting to polar coordinates. Your network should consist of two fully connected hidden layers with tanh activation, plus an output layer. You should not use Sequential but should instead build the network from individual components as shown in the program xor.py from Exercises 5 (repeated in slide 4 of lecture slides 3b on PyTorch). The number of neurons in both hidden layers should be determined by the parameter num_hid. 

4. [1 mark] Run the code by typing

python3 spiral.py --net raw

Keeping the number of hidden nodes in each layer fixed at 10, try to find a value for the size of the initial weights (--init) such that this RawNet learns to correctly classify all of the training data within 20000 epochs, on almost all runs. Include in your report the number of hidden nodes, and the values of any other metaparameters. The graph_output() method will generate a picture of the function computed by your RawNet called raw_out.png, which you should include in your report. 

5. [1 mark] Provide code for a Pytorch Module called ShortNet which again operates on the raw input (x,y) without converting to polar coordinates. This network should again consist of two hidden layers plus an output layer, but this time should include short-cut connections between every pair of layers (input, hid1, hid2 and output) as depicted on slide 10 of lecture slides 3a on Hidden Unit Dynamics. The number of neurons in both hidden layers should be determined by the parameter num_hid. 

6. [1 mark] Run the code by typing

python3 spiral.py --net short 

You should experiment to find a good value for the initial weight size, and try to find the mininum number of hidden nodes per layer so that this ShortNet learns to correctly classify all of the training data within 20000 epochs, on almost all runs. Include in your report the number of hidden nodes per layer, as well as the initial weight size and any other metaparameters. The graph_output() method will generate a picture of the function computed by your ShortNet called short_out.png, which you should include in your report. 

7. [2 marks] Using graph_output() as a guide, write a method called graph_hidden(net, layer, node) which plots the activation (after applying the tanh function) of the hidden node with the specified number (node) in the specified layer (1 or 2). (Note: if net is of type PolarNet graph_output() only needs to behave correctly when layer is 1).

Hint: you might need to modify forward() so that the hidden unit activations are retained, i.e. replace hid1 = torch.tanh(...) with self.hid1 = torch.tanh(...)

Use this code to generate plots of all the hidden nodes in PolarNet, and all the hidden nodes in both layers of RawNet and ShortNet, and include them in your report. 

8. [9 marks] Discuss what you have learned from this exercise, including the following points:

a. the qualitative difference between the functions computed by the hidden layer nodes of the three models, and a brief description of how the network uses these functions to achieve the classification

b. the effect of different values for initial weight size on the speed and success of learning, for both RawNet and ShortNet

c. the relative "naturalness" of the output function computed by the three networks, and the importance of representation for deep learning tasks in general

d. you may like to also experiment with other changes and comment on the result - for example, changing batch size from 97 to 194, using SGD instead of Adam, changing tanh to relu, adding a third hidden layer, etc. 

Submission

give cs9444 hw1 kuzu.py spiral.py hw1.pdf

You can submit as many times as you like - later submissions will overwrite earlier ones. You can check that your submission has been received by using the following command:

9444 classrun -check 

Additional information may be found in the FAQ and will be considered as part of the specification for the project. You should check this page regularly. 

Plagiarism Policy

DO NOT COPY FROM OTHERS; DO NOT ALLOW ANYONE TO SEE YOUR CODE

Good luck!