Description
Problem 1: CNN Training on LeNet-5 (100%)
In this problem, you will learn to train a simple convolutional neural network (CNN) called the LeNet-5,
introduced by LeCun et al. [1], and apply it to three datasets MNIST [2], Fashion-MNIST [3] and
CIFAR-10 [4].
LeNet-5 is designed for handwritten and machine-printed character recognition. Its architecture is shown
in Fig. 1.
This network has two conv layers, and three fc layers. Each conv layer is followed by a max
pooling layer. Both conv layers accept an input receptive field of spatial size 5×5. The filter numbers of
the first and the second conv layers are 6 and 16 respectively. The stride parameter is 1 and no padding is
used.
The two max pooling layers take an input window size of 2×2, reduce the window size to 1×1 by
choosing the maximum value of the four responses. The first two fc layers have 120 and 84 filters,
respectively. The last fc layer, the output layer, has size of 10 to match the number of object classes in the
dataset.
Use the popular ReLU activation function [5] for all conv and all fc layers except for the output
layer, which uses softmax [6] to compute the probabilities.
Figure 1: A CNN architecture derived from LeNet-5
The following table shows statistics for different datasets:
Image type Image size # Class # training
images
# testing
images
MNIST Gray 28*28 10 60,000 10,000
FashionMNIST
Gray 28*28 10 60,000 10,000
CIFAR-10 Color 32*32 10 50,000 10,000
(a) CNN Architecture (Basic: 20%)
Explain the architecture and operational mechanism of convolutional neural networks by performing the
following tasks.
1. Describe CNN components in your own words: 1) the fully connected layer, 2) the convolutional
layer, 3) the max pooling layer, 4) the activation function, and 5) the softmax function. What are
the functions of these components?
2. What is the over-fitting issue in model learning? Explain any technique that has been used in CNN
training to avoid the over-fitting.
3. Explain the difference among different activation functions including ReLU, LeakyReLU and
ELU.
4. Read official documents of different loss functions including L1Loss, MSELoss and BCELoss.
List applications where those losses are used, and state why do you think they are used in those
specific cases?
Show your understanding as much as possible in your own words in your report.
(b) Compare classification performance on different datasets (30%)
Train the CNN given in Fig. 1 using the training images of MNIST, then test the trained network on the
testing images of MNIST. Compute and draw the accuracy performance curves (epoch-accuracy plot) on
training and test datasets on the same figure. You can adopt proper preprocessing techniques and the
random network initialization to make your training work easy.
1. Plot the performance curves under 3 different yet representative hyper-parameter settings
(optimizers, initialization of filter weights, learning rate, decay and etc.). Discuss your
observations and the effect of different settings.
2. Find the best parameter setting to achieve the highest accuracy on the test set. Then, plot the
performance curves for the test set and the training set under this setting. Your testing accuracy
should be no less than 99%.
3. Repeat 2 for Fashion-MNIST. Your best testing accuracy should be no less than 90%.
4. Repeat 2 for CIFAR-10. Your best testing accuracy should be no less than 65%.
5. Compare your best performances on three datasets. How do they differ and why do you think there
is such difference?
Note: for each setting, you need 5 runs. Report the [best test accuracy among 5 runs, mean test accuracy
of 5 runs, standard deviation of test accuracy among 5 runs] to evaluate the performance.
(c) Analysis on confusion classes and hard samples (30%)
You may achieve good recognition performance on the MNIST dataset in Problem 1(b). Now letβs dive
deeper into the classification results.
1. Generate the normalized confusion matrix for the 10 classes on the testing set. What are the top
three confused pairs of classes? Show one example for each of these three pairs. Describe your
observations and explain.
2. Repeat 1 for Fashion-MNIST.
3. Repeat 1 for CIFAR-10.
Note: you may use the best setting you found in Problem 1(b) on each dataset.
(d) Classification with noisy data (20%)
Data in real world application could be noisy with wrong labels. Symmetric Label Noise (SLN) is the type
of labeling noise where πΌ% of the data with true label of class π is labeled as other classes π β π with
uniform probability. For example, in a 3-class classification problem, the normalized confusion matrix
between the true label and the noisy label is close to the following format, where π is the noise level (say,
40%):
[
1 β π
π
2
π
2
π
2
1 β π
π
2
π
2
π
2
1 β π
]
Now youβd like to synthesize the Symmetric Label Noise on the training set of MNIST and investigate
the performance of neural networks under different noise levels.
1. Implement the Symmetric Label Noise. Describe your method and show the normalized confusion
matrix for π = 40%.
2. Train LeNet-5 with the noisy training set and measure the testing accuracy. Try π =
0%, 20%, 40%, 60%, 80%. Draw the curve of [testing accuracy vs. π]. Note that for each π, 5 runs
are needed to calculate the mean and standard deviation of the testing accuracy which then are
used to draw your plot.
3. Discuss your observations on result of 2 and analyze.
References
[1] LeCun, Yann, et al. “Gradient-based learning applied to document recognition.” Proceedings of the
IEEE 86.11 (1998): 2278-2324
[2] http://yann.lecun.com/exdb/mnist/
[3] https://github.com/zalandoresearch/fashion-mnist
[4] https://www.cs.toronto.edu/~kriz/cifar.html
[5] ReLU https://en.wikipedia.org/wiki/Rectifier_(neural_networks).
[6] Softmax https://en.wikipedia.org/wiki/Softmax_function
