# CSCI 5525: Machine Learning Homework 3 solution

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## Description

1. (10 points) Consider the convolutional neural network architecture given in Figure 1 for
classifying MNIST digits. Assume that the input images are reduced to size 10 × 10 with
only 1 channel (represented as a matrix in R
10×10). In this architecture, the convolutional
layer uses a 3 × 3 filter, Wconv, with stride 2 and zero padding stride 3 and zero padding of
size 1. The dimensions of the outputs of each layer are shown below.
Figure 1: A toy CNN
(a) (5 points) What are the values of n, m, k in the graph?
(b) (5 points) What are the sizes of Wconv, Wfc, and b?
Programming Problems: The next two problems are programming problems and will focus on
implementing neural networks for handwritten digits classification. We will use the MNIST dataset
where each sample is an image of a hand-written digit and has a corresponding label indicating the
value of the digit written (0, 1, . . . , 9). This makes it a multi-class classification problem.
You must use Tensorflow 2 to implement your neural networks. The implementation must be
for the CPU version only (no GPUs or MPI parallel programming is required for this assignment).
Follow the installation instructions at https://www.tensorflow.org/install in case you want to
use your local machine (we recommend using anaconda); you may also use colab to this assignment.
You can load the MNIST dataset directly in Tensorflow with the following code:
import tensorflow as tf
mnist = tf.keras.datasets.mnist
(x train, y train), (x test, y test) = mnist.load data()
2. (40 points) Implement a multi-layer fully connected neural network:
• Input: 1-channel input, size 28×28
• Fully connected layer 1: input with bias; output – 128 nodes
• ReLU activation function
• Fully connected layer 2: input – 128 nodes; output – 10 nodes
• Softmax activation function
• Use cross entropy as the loss function
• Use SGD as optimizer
• Set mini batch size as 32
Train using mini batches of the given batch size. Plot the cumulative training loss and
accuracy for every epoch. Once training is complete, apply the learned model to the test set
and report the testing accuracy.
Epoch: An epoch is a single pass through all the training data. Typically many epochs will
be run when training a neural network before it converges.
Please submit (a) summary of methods and results report and (b) code:
(a) Summary of methods and results: Briefly describe the approaches used above, along
with relevant equations. Report the cumulative training loss and accuracy for every epoch
as plots. Also report the testing accuracy (a single number).
(b) Code: Submit the file neural net.py which contains the function def neural net()
-> None:. The function does not have any inputs and does not return anything but must
print out to the terminal (stdout) the cumulative training loss and accuracy per epoch
as well as the testing accuracy.
3. (50 points) Implement a convolutional neural network with the following specifications.
• Input: 1-channel input, size 28×28
• Convolution layer: Convolution kernel size is (3, 3) with stride as 1. Input channels – 1;
Output channels – 20 nodes
• ReLU activation function
• Max-pool: 2×2 max pool
• Dropout layer with probability p = 0.50
• Flatten input for feed to fully connected layers
• Fully connected layer 1: flattened input with bias; output – 128 nodes
• ReLU activation function
• Dropout layer with probability p = 0.50
• Fully connected layer 2: input – 128 nodes; output – 10 nodes
• Softmax activation function
• Use cross entropy as loss function
For this problem, we will be experimenting with a variety of parameters.
First, train using SGD as the optimizer and mini batches of size 32. Plot the cumulative
training loss and accuracy for every epoch. Once training is complete, apply the learned
model to the test set and report the testing accuracy.
Second, train your network using mini batch sizes of [32, 64, 96, 128] and plot the convergence
You should report 3 figures, one for each optimizer where each figure has mini batch size on
the x-axis and the convergence run time on the y-axis.
Please submit (a) summary of methods and results report and (b) code:
(a) Summary of methods and results: Briefly describe the approaches used above, along
with relevant equations. Report the cumulative training loss and accuracy for every epoch
as plots. Also report the testing accuracy (a single number). Also report the convergence
run time vs mini batch sizes for each mini batch size and optimizer above (3 plots).
(b) Code: Submit the file cnn.py which contains the function def cnn() -> None:. The
function does not have any inputs and does not return anything but must print out to
the terminal (stdout) the cumulative training loss and accuracy as well as the testing
accuracy (for the first part above). It must also print out the batch size and convergence
run time for each mini batch size and optimizer (for the second part above).
Additional instructions: Code can only be written in Python 3.6+; no other programming
languages will be accepted. One should be able to execute all programs from the Python command
Each function must take the inputs in the order specified in the problem and display the textual
output via the terminal and plots/figures should be included in the report.
For each part, you can submit additional files/functions (as needed) which will be used by the
main file. In your code, you cannot use machine learning libraries such as those available from
scikit-learn for learning the models – exception being that you must use Tensoflow 2 for your neural
network implementations. You may also use libraries for basic matrix computations and plotting
such as numpy, pandas, and matplotlib. Put comments in your code so that one can follow the key
parts and steps in your code.
Your code must be runnable on a CSE lab machine (e.g., csel-kh1260-01.cselabs.umn.edu).
One option is to SSH into a machine. Learn about SSH at these links: https://cseit.umn.edu/
and https://cseit.umn.edu/knowledge-help/remote-linux-applications-over-ssh.
Instructions
Follow the rules strictly. If we cannot run your code, you will not get any credit.
• Things to submit
1. hw3.pdf: The report that contains the solutions to Problems 1, 2, and 3 including the
summary of methods and results.
2. neural net.py: Code for Problem 2.
3. cnn.py: Code for Problem 3.