Exercise IV AMTH/CPSC 663b 


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Exercise IV
Compress your solutions into a single zip file titled <lastname and
initials>, e.g. for a student named Tom Marvolo Riddle, riddletm Include a single PDF titled
<lastname and initials> assignment4.pdf and any Python scripts
specified. If you complete your assignment in a Jupyter notebook, submit
the notebook file along with a PDF of the notebook contents. Any requested
plots should be sufficiently labeled for full points. Your homework should
be submitted to Canvas before Monday, May 3rd at 11:59 PM.
Programming assignments should use built-in functions in Python
and PyTorch; In general, you may use the scipy stack [1]; however,
exercises are designed to emphasize the nuances of machine learning and
deep learning algorithms – if a function exists that trivially solves an entire
problem, please consult with the TA before using it.
Problem 1
In this problem, you will review some of the unique parameters involved in the construction of convolutional
neural networks (CNNs). Then you will train a CNN on MNIST using the code provided in and
visualize a sample of the learned filters of the network.
1. Tracking the dimensionality of representations as they pass through the CNN is slightly different than
for fully-connected networks. For the following, give the final output dimensions in terms of height
h and width w if the size of the input image is 50×50 (hxw). Here k, s, and p refer to kernel size,
stride and padding, respectively. For a) and b), assume the image is passing through a convolutional
layer while for c) and d), assume a max-pooling layer. Assume a square kernel. (This is a helpful
(a) k=4, s=1, p=1
(b) k=8, s=5, p=0
(c) k=10, s=2, p=2
(d) k=2, s=1, p=0
2. The following questions can be answered by looking at the provided code in
(a) Train the model for 5 epochs. Visualize filters from the first convolutional layer (40 filters total).
Include this image in your report.
(b) Produce a confusion matrix using the test split and comment on any noticeable class confusion
(one class is commonly mislabeled as the other). You may use the sklearn for this. Include the
plot in your report.
Problem 2
1. Principal Component Analysis (PCA) is a very common method for dimensionality reduction. Conceptually, describe how the principal components in PCA are chosen. If PCA is to implemented in
PyTorch, the function torch.svd() will play an important role in the algorithm. Please briefly describe
what this function does, and why the results will be useful in implementing PCA.
2. Describe the similarity between PCA and an autoencoder.
3. What is the difference between a convolutional autoencoder and linear autoencoder? Implement a
convolutional autoencoder and save it as Compare the results of your autoencoder with the
original images. Include in your report both the original images and the reconstructed images (there
should be 8 images in total). You may reuse parts of
4. What similarities and differences are there between a denoising autoencoder and a variational autoencoder?
Problem 3
In this problem, you’ll learn word embeddings of a text corpus of your choosing – not via the famous
Word2Vec, but through an alternate strategy consisting of two parts. First, you’ll vectorize your words
via an embedding matrix. You’ll then feed sequences of these vectorized words (i.e., sentences) into an
sequence-to-sequence LSTM model. If all goes according to plan, as your LSTM model learns to reconstruct
sentences, it will reshape the word embeddings to imbue their spatial position with semantic meaning.
1. Follow the todos in to build a seq-to-seq LSTM model. This model will include four parts,
which should be unified under a single class:
• A word embedding layer that converts word indices into vectors in the embedding space. You can
use nn.Embedding for this.
• An LSTM encoder, which takes a sequence of words and outputs a sentence embedding.
Figure 1: Illustration of the LSTM Seq-to-Seq Model
• An LSTM decoder, which reconstructs the sentence from the above embedding. To achieve this,
we must apply the LSTM iteratively to its own output. Initially, it will take a start of sequence
token coupled with the sentence embedding, and will output a predicted word and a new hidden
state. Next, it will take the previously predicted word and outputted hidden state, and will
produce a new word prediction and hidden state. This will be repeated for the desired sequence
• A decoder which translates from the LSTM output space into the vocabulary space. A single
nn.Linear layer will suffice here.
2. Fill in the loss and backpropogation operations in, and train your model. To assess progress,
you can translate your model’s reconstructions of the input sequences back into actual words. Watch
out for the local minimum that reconstructs every sentence to ”the the the the the”! You may aid
your model in the training task by reducing the sequence length to a small number like 5. By tuning
hyperparameters and increasing model capacity, try to raise the sequence length as high as you can
while maintaining good reconstruction accuracy.
3. Plot these word embeddings with the given code. You are able to adjust the plotting parameters to
suit your needs for making a compelling visualization. Discuss what you notice in your embeddings.
For example, using the introduction to Charles Darwin’s On the Origin of Species as a text file, we
obtain the embeddings in Figure 2.
4. Since this is too crowded to interpret, we’ve provided code to randomly select words to plot as long
as there is space as shown in Figure 3. Either use this code multiple times or create your own code to
obtain a visualization(s) that facilitates allows you to learn something about your data. Include this
visualization in your report
Figure 2: word embeddings from the introduction to Charles Darwin’s On the Origin of Species
Figure 3: subsampled word embeddings
Problem 4
1. Graph convolutional networks are modeled explicitly after classical CNNs. The graph domain, however,
poses unique challenges: whereas every pixel in an image is connected to its neighbors in the same way,
nodes in a graph exhibit a range of local structures that make it impossible to define a convolutional
operator as a dot product with a filter. How does the GCN of Kipf and Welling draw upon spectral
graph theory to overcome these difficulties? Are there any problems with this approach? (Bonus: what
alternate ways exist of defining convolutions in the graph domain?)
For reference, see the paper that introduced the first GCN,“Kipf2017: Semi-Supervised Classification
with Graph Convolutional Networks”. You may also enjoy this article, which reviews Kipf and Welling’s
approach: “How Powerful are Graph Convolutional Networks?”.
2. PyTorch Geometric is a powerful library that makes building GNNs as easy as building CNNs with
PyTorch. Follow the (rather involved) installation instructions to set it up on your machine. (Tip: You
can set the variables TORCH and CUDA by running TORCH=”1.8.0″ and CUDA=”cpu” in the command
line.) While you wait for the packages to download, I suggest reading through the brief Introduction
by Example to familiarize yourself with PyTorch Geometric’s conventions of graph usage.
3. Fill out the skeleton code in to build a more powerful variant of Kipf and Welling’s GCN, as
proposed in Xu et al’s “How Powerful Are Graph Neural Networks?”. You can follow the Pytorch
Geometric tutorial on Creating Message Passing Networks, but please make these modifications to the
tutorial’s baseline:
• For γ, use a multi-layer perceptron network.
• Do not perform any normalization in the aggregation step, φ.
4. Put your newly-hewn GCN to work by running This script imports the
GCN you built in the previous section, and trains it on the CORA citation network. Each node in the
CORA graph is an academic paper, linked to those nodes it cites (or is cited by), and accompanied
by a bag-of-words feature vector. Your network’s task is to predict the category of each paper. After
training your modified version of the GCN on CORA, train a clone of your model that uses the original
GCNConv layers (of Kipf and Welling). How does its performance compare to our modified version?
5. Using, train your hand-built GCN on the REDDIT-BINARY dataset for
100 epochs. Each graph in this dataset depicts a single discussion thread on Reddit, with edges
connecting those users who replied to each other’s comments. The task is to predict which community
the thread comes from. After you have trained your modified GCN on the dataset, once again replace
the BetterGCNConv layers in the GraphClassifier class with standard GCNConv layers and train the
original Kipf and Welling GCN on the Reddit dataset (again, for a full 100 epochs). Report the
accuracies for each. How do you explain any differences?
[1] “The scipy stack specification¶.” [Online]. Available:

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