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COMP9444 Neural Networks and Deep Learning

Term 2, 2022 >Assignment 1 - Network Structures and Hidden Unit Dynamics

Due: Friday 1 July, 5pm

Marks: 20% of final assessment

In this assignment, you will be implementing and training various neural network models

for three different tasks, and analysing the results.

You are to submit two python files cross.py and encoder.py, as well as a written report hw1.pdf

(in pdf format).

Provided Files

Copy the archive hw1.zip into your own filespace and unzip it. This should create a directory

hw1 with the data file cross.csv, subdirectories plot and net, as well as ten python files cross.py,

encoder.py, cross_main.py, encoder_main.py, encoder_model.py, seq_train.py, seq_models.py, seq_plot.py,

reber.py and anbn.py.

Your task is to complete the skeleton files cross.py, encoder.py and submit them, along with

your report.

Part 1: Fractal Classification Task

For Part 1 you will be training a network to distinguish dots in the fractal pattern shown

above. The supplied code cross_main.py loads the training data from cross.csv, applies the

specified neural network 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. [1 mark] Provide code for a pytorch module called Full3Net which implements a 3-layer

fully connected neural network with two hidden layers using tanh activation, followed

by the output layer with one node using sigmoid activation. Your network should have

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the same number of hidden nodes in each layer, specified by the variable hid. The

hidden layer activations (after applying tanh) should be stored into self.hid1 and

self.hid2 so they can be graphed afterwards.

2. [1 mark] Train your network by typing

python3 cross_main.py --net full3 --hid ⟨hid⟩

Try to determine a number of hidden nodes close to the mininum required for the

network to be trained successfully (although, it need not be the absolute minimum).

You may need to run the network several times before hitting on a set of initial

weights which allows it to converge. (If it trains for a couple of minutes and seems to

be stuck in a local minimum, kill it with ⟨cntrl⟩-c and run it again). You are free to

adjust the learning rate and initial weight size, if you want to. The graph_output()

method will generate a picture of the function computed by your network and store it

in the plot subdirectory with a name like out_full3_?.png. You should include this picture

in your report, as well as a calculation of the total number of independent parameters

in your network (based on the number of hidden nodes you have chosen).

3. [1 mark] Provide code for a pytorch module called Full4Net which implements a 4-layer

network, the same as Full3Net but with an additional hidden layer. All three hidden

layers should have the same number of nodes (hid). The hidden layer activations (after

applying tanh) should be stored into self.hid1, self.hid2 and self.hid3.

4. [1 mark] Train your 4-layer network by typing

python3 cross_main.py --net full4 --hid ⟨hid⟩

Try to determine a number of hidden nodes close to the mininum required for the

network to be trained successfully. Keep in mind that the loss function might decline

initially, appear to stall for several epochs, but then continue to decline. The

graph_output() method will generate a picture of the function computed by your

network and store it in the plot subdirectory with a name like out_full4_?.png, and the

graph_hidden() method should generate plots of all the hidden nodes in all three hidden

layers, with names like hid_full4_?_?_?.png. You should include the plot of the output

and the plots of all the hidden units in all three layers in your report, as well as a

calculation of the total number of independent parameters in your network.

5. [1 mark] Provide code for a pytorch module called DenseNet which implements a 3-layer

densely connected neural network. Your network should be the same as Full3Net

except that it should also include shortcut connections from the input to the second

hidden layer and output layer, and from the first hidden layer to the second hidden

layer and output layer. Each hidden layer should have hid units and tanh activation, and

the output node should have sigmoid activation. The hidden layer activations (after

applying tanh) should be stored into self.hid1 and self.hid2. Specifically, the hidden and

output activations should be calculated according to the following equations. (Note

that there are various ways to implement these equations in pytorch; for example,

using a separate nn.Parameter for each individual bias and weight matrix, or combining

several of them into nn.Linear and making use of torch.cat()).

h1j = tanh( b1j + Σk w10jkxk )

h2i = tanh( b2i + Σk w20ikxk + Σj w21ij h1j )

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out = sigmoid( bout + Σk w30kxk + Σj w31j h1j + Σi w32i h2i )

6. [1 mark] Train your Dense Network by typing

python3 cross_main.py --net dense --hid ⟨hid⟩

As before, try to determine a number of hidden nodes close to the mininum required

for the network to be trained successfully. You should include the graphs of the

output and all the hidden nodes in both layers in your report, as well as a calculation

of the total number of independent parameters in your network.

7. [3 marks] Briefly discuss the following points:

a. the total number of independent parameters in each of the three networks

(using the number of hidden nodes determined by your experiments) and the

approximate number of epochs required to train each type of network,

b. a qualitative description of the functions computed by the different layers of

Full4Net and DenseNet,

c. the qualitative difference, if any, between the overall function (i.e. output as a

function of input) computed by the three networks.

Part 2: Encoder Networks

In Part 2 you will be editing the file encoder.py to create a dataset which, when run in

combination with encoder_main.py, produces the following image (which is intended to be a

stylized map of Antarctica).

You should first run the code by typing

python3 encoder_main.py --target star16

Note that target is determined by the tensor star16 in encoder.py, which has 16 rows and 8

columns, indicating that there are 16 inputs and 8 outputs. The inputs use a one-hot

encoding and are generated in the form of an identity matrix using torch.eye()

1. [2 marks] Create by hand a dataset in the form of a tensor called ant35 in the file

encoder.py which, when run with the following command, will produce an image

essentially the same as the one shown above (but possibly rotated or reflected).

python3 encoder_main.py --target ant35

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The pattern of dots and lines must be identical, except for the possible rotation or

reflection. Note in particular the four "anchor points" in the corners of the figure.

Your tensor should have 35 rows and 23 columns. Include the final image in your

report, and include the tensor ant35 in your file encoder.py

Part 3: Hidden Unit Dynamics for Recurrent Networks

In Part 3 you will be investigating the hidden unit dynamics of recurrent networks trained

on language prediction tasks, using the supplied code seq_train.py and seq_plot.py.

1. [2 marks] Train a Simple Recurrent Network (SRN) on the Reber Grammar prediction

task by typing

python3 seq_train.py --lang reber

This SRN has 7 inputs, 2 hidden units and 7 outputs. The trained networks are stored

every 10000 epochs, in the net subdirectory. After the training finishes, plot the hidden

unit activations at epoch 50000 by typing

python3 seq_plot.py --lang reber --epoch 50

The dots should be arranged in discernable clusters by color. If they are not, run the

code again until the training is successful. The hidden unit activations are printed

according to their "state", using the colormap "jet":

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Based on this colormap, annotate your figure (either electronically, or with a pen on a

printout) by drawing a circle around the cluster of points corresponding to each state

in the state machine, and drawing arrows between the states, with each arrow labeled

with its corresponding symbol. Include the annotated figure in your report.

2. [1 mark] Train an SRN on the anbn language prediction task by typing

python3 seq_train.py --lang anbn

The anbn language is a concatenation of a random number of A's followed by an

equal number of B's. The SRN has 2 inputs, 2 hidden units and 2 outputs.

Look at the predicted probabilities of A and B as the training progresses. The first B in

each sequence and all A's after the first A are not deterministic and can only be

predicted in a probabilistic sense. But, if the training is successful, all other symbols

should be correctly predicted. In particular, the network should predict the last B in

each sequence as well as the subsequent A. The error should be consistently below

0.01. If the network appears to have learned the task successfully, you can stop it at

any time using ⟨cntrl⟩-c. If it appears to be stuck in a local minimum, you can stop it

and run the code again until it is successful.

After the training finishes, plot the hidden unit activations by typing

python3 seq_plot.py --lang anbn --epoch 100

Include the resulting figure in your report. The states are again printed according to

the colormap "jet". Note, however, that these "states" are not unique but are instead

used to count either the number of A's we have seen or the number of B's we are still

expecting to see.

3. [1 mark] Briefly explain how the anbn prediction task is achieved by the network,

based on the figure you generated in Question 2. Specifically, you should describe

how the hidden unit activations change as the string is processed, and how it is able

to correctly predict the last B in each sequence as well as the following A.

4. [1 mark] Train an SRN on the anbncn language prediction task by typing

python3 seq_train.py --lang anbncn

The SRN now has 3 inputs, 3 hidden units and 3 outputs. Again, the "state" is used to

count up the A's and count down the B's and C's. Continue training (re-starting, if

necessary) for 200k epochs, or until the network is able to reliably predict all the C's as

well as the subsequent A, and the error is consistently in the range of 0.01 or 0.02.

After the training finishes, plot the hidden unit activations by typing

python3 seq_plot.py --lang anbncn --epoch 200

Rotate the figure in 3 dimensions to get one or more good view(s) of the points in

hidden unit space.

5. [1 mark] Briefly explain how the anbncn prediction task is achieved by the network,

based on the figure you generated in Question 4. Specifically, you should describe

how the hidden unit activations change as the string is processed, and how it is able

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to correctly predict the last B in each sequence as well as all of the C's and the

following A.

6. [3 marks] This question is intended to be more challenging. Train an LSTM network to

predict the Embedded Reber Grammar, by typing

python3 seq_train.py --lang reber --embed True --model lstm --hid 4

You can adjust the number of hidden nodes if you wish. Once the training is

successful, try to analyse the behavior of the LSTM and explain how the task is

accomplished (this might involve modifying the code so that it returns and prints out

the context units as well as the hidden units).

Submission

You should submit by typing

give cs9444 hw1 cross.py encoder.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 hw1

The submission deadline is Friday 1 July, 5pm. In accordance with new UNSW-wide policies,

5% penalty will be applied for every 24 hours late after the deadline, up to a maximum of 5

days, after which submissions will not be accepted.

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

Group submissions will not be allowed for this assignment. Your code and report must be

entirely your own work. Plagiarism detection software will be used to compare all

submissions pairwise (including submissions for similar assignments from previous

offering, if appropriate) and serious penalties will be applied, particularly in the case of

repeat offences.

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

Please refer to the UNSW Policy on Academic Integrity and Plagiarism if you require further

clarification on this matter.

Good luck!

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