The goal of this exercice is to modify the example from the course to perform the classification task presented in the figure above.
- Create the dataset for this task with the following classes:
- x < 0
- y < 0: Label 0
- y >= 0: Label 1
- x >= 0
- y < 0: Label 2
- y >= 0: Label 3
-
Modify the neural network architecture to be compatible with this task. Hint: What is the number of classes in this problem.
-
Add a second hidden layer to your network.
In this practical work, we will build a linear neural network that will classify MNIST digits.
Create a new notebook and, in a new cell, download the dataset using the following commands:
!rm mnist_*
!wget https://github.com/rodgzilla/teaching_public/blob/master/datasets/mnist_train.pt?raw=true -O mnist_train.pt
!wget https://github.com/rodgzilla/teaching_public/blob/master/datasets/mnist_test.pt?raw=true -O mnist_test.ptBy using ! at the beginning of the line, we can use shell commands
in the notebook.
To load the dataset, use torch.load
>>> X_train, y_train = torch.load('mnist_train.pt')
>>> X_train.shape, y_train.shape
(torch.Size([60000, 28, 28]), torch.Size([60000]))>>> X_test, y_test = torch.load('mnist_test.pt')
>>> X_test.shape, y_test.shape
(torch.Size([10000, 28, 28]), torch.Size([10000]))We can see that the dataset have two distinct parts. The training
set (X_train, y_train) composed a 60000 28x28 pixels images that we
will use to train our model and the test set (X_test, y_test)
composed of 10000 images that we will use to evaluate the
generalization capabilities of our model.
Import matplotlib using the following commands
import matplotlib.pyplot as pltVisualize a few training images using the function
plt.imshow
along with their corresponding labels.
Once the data is loaded, reshape the tensors in order to consider the
images as 1D float tensors.
The first step of the machine learning process consists in normalizing our data. We want to transform the images in a way that the pixel values such that the mean is 0 and the standard deviation is 1. We have seen this procedure in the previous practical work.
As we do not want to cheat we will standardize the test set using the mean and the standard deviation of the training set as the test set is supposed to represent new data which could not have been used to compute the mean and the standard deviation.
Create a neural network that takes the 1D representation of the images and outputs confidence levels for the the 10 digit classes. The number of layers and the number of neurons in each layer is up to you. Use the neural network presented during the course as a base.
Write a training function and an evaluation function inspired by the ones we have seen in the course.
The training function takes both the training and testing datasets as input. At regular intervals (for example every 500 batches), perform an evaluation of the model on just a few batches (for example 150) of the training set and of the testing set to check that our model is indeed learning something.
The execution of your code should display something like this:
[ 0][ 0] -> 10.208% training accuracy 10.052% testing accuracy
[ 0][ 500] -> 11.010% training accuracy 11.135% testing accuracy
[ 1][ 0] -> 15.958% training accuracy 15.937% testing accuracy
[ 1][ 500] -> 29.531% training accuracy 30.531% testing accuracy
[ 2][ 0] -> 40.302% training accuracy 40.260% testing accuracy
[ 2][ 500] -> 50.958% training accuracy 50.833% testing accuracy
[ 3][ 0] -> 54.490% training accuracy 53.885% testing accuracy
[ 3][ 500] -> 54.333% training accuracy 54.667% testing accuracy
[ 4][ 0] -> 58.396% training accuracy 59.396% testing accuracy
[ 4][ 500] -> 68.510% training accuracy 68.594% testing accuracy
[ 5][ 0] -> 73.562% training accuracy 74.042% testing accuracy
[ 5][ 500] -> 77.000% training accuracy 77.417% testing accuracy
[ 6][ 0] -> 79.167% training accuracy 79.865% testing accuracy
[ 6][ 500] -> 80.688% training accuracy 81.500% testing accuracy
[ 7][ 0] -> 82.917% training accuracy 83.042% testing accuracy
[ 7][ 500] -> 83.396% training accuracy 84.604% testing accuracy
[ 8][ 0] -> 85.458% training accuracy 85.542% testing accuracy
[ 8][ 500] -> 86.333% training accuracy 86.625% testing accuracy
[ 9][ 0] -> 86.865% training accuracy 87.094% testing accuracy
[ 9][ 500] -> 87.781% training accuracy 87.646% testing accuracy
[ 10][ 0] -> 87.802% training accuracy 88.094% testing accuracy
[ 10][ 500] -> 87.917% training accuracy 88.615% testing accuracy
[ 11][ 0] -> 88.833% training accuracy 88.812% testing accuracy
[ 11][ 500] -> 88.865% training accuracy 88.990% testing accuracy
[ 12][ 0] -> 88.771% training accuracy 89.344% testing accuracy
[ 12][ 500] -> 89.562% training accuracy 89.635% testing accuracy
[ 13][ 0] -> 89.531% training accuracy 89.740% testing accuracy
[ 13][ 500] -> 89.656% training accuracy 89.833% testing accuracy
[ 14][ 0] -> 89.458% training accuracy 89.844% testing accuracy
[ 14][ 500] -> 89.844% training accuracy 90.260% testing accuracy
[ 15][ 0] -> 90.198% training accuracy 90.385% testing accuracy
[ 15][ 500] -> 90.531% training accuracy 90.562% testing accuracy
[ 16][ 0] -> 90.552% training accuracy 90.490% testing accuracy
[ 16][ 500] -> 90.406% training accuracy 90.844% testing accuracy
[ 17][ 0] -> 90.469% training accuracy 90.844% testing accuracy
[ 17][ 500] -> 90.562% training accuracy 90.969% testing accuracy
[ 18][ 0] -> 90.906% training accuracy 91.104% testing accuracy
[ 18][ 500] -> 90.969% training accuracy 91.281% testing accuracy
[ 19][ 0] -> 91.312% training accuracy 91.260% testing accuracy
[ 19][ 500] -> 90.844% training accuracy 91.521% testing accuracy
Write a function that allows you to visualize the images on which the
model predictions were wrong. In order to visualize these images using
plt.imshow you will have to undo the normalization that we performed
earlier.