Deep Discriminative Neural Networks 1. Give brief definitions of the following terms:
a. Feature map
b. Sub-sampling
c. Adversarial example d. Data augmentation e. Transfer learning
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f. Dropout
g. Regularization
2. Define what is meant by, and explain the causes of, the “vanishing gradient problem”. Briefly describe four methods that can be used to reduce its effects.
3. Mathematically define the following activation functions:
a. ReLU b. LReLU c. PReLU
4. The following array show the output produced by a mask in a convolutional layer of a CNN.
1 0.5 0.2 netj = −1 −0.5 −0.2
0.1 −0.1 0
Calculate the values produced by the application of the following activation functions:
b. LReLU when a=0.1,
d. Heaviside function where each neuron has a threshold of 0.1 (define H(0) as 0.5).
1 5. The following arrays show the output produced by a convolutional layer to all 4 samples in a batch. X1 = −1
0.5 0.2 −0.5 −0.2 ,
0.1 −0.1 0
1 −1 0.1 0.5 −0.5 −0.1 0.2 1 −0.2
X2 = 0.5 −0.5 −0.1 , X3 = 0 −0.4 0 , X4 = −1 −0.6 −0.1 . Calculatethecorrespond-
0.2 −0.2 0 0.5 0.5 0.2 0.1 0 0.1
ing outputs produced after the application of batch normalisation, assuming the following parameter values β = 0, γ = 1, and ε = 0.1 which are the same for all neurons.
6. The following arrays show the feature maps that provide the input to a convolutional layer of a CNN.
0.2 1 0 1 0.5 0.2 X1=−1 0 −0.1,X2=−1 −0.5 −0.2
0.1 −0.1 0
If a mask, H, has two channels defined as:
1 −0.1 0.5 0.5 H1= 1 −0.1 ,H2= −0.5 −0.5
Calculate the output produced by mask H when using:
a. padding=0, stride=1
b. padding=1, stride=1
c. padding=1, stride=2
d. padding=0, stride=1, dilation=2
7. The following arrays show the feature maps that provide the input to a convolutional layer of a CNN.
0.2 1 0 1 0.5 0.2 0.5 −0.5 −0.1 X1=−1 0 −0.1,X2=−1 −0.5 −0.2,X3= 0 −0.4 0
0.1 0 0.1 0.1 −0.1 0 0.5 0.5 0.2 Calculate the output produced by 1×1 convolution when the 3 channels of the 1×1 mask are: [1, −1, 0.5].
8. The following array shows the input to a pooling layer of a CNN.
0.2 1 0 0.4 X1=−1 0−0.1−0.1 0.1 0 −1 −0.5
0.4 −0.7 −0.5 1 Calculate the output produced by the pooling when using:
a. average pooling with a pooling region of 2×2 and stride=2 b. max pooling with a pooling region of 2×2 and stride=2
c. max pooling with a pooling region of 3×3 and stride=1
9. The input to a convolutional layer of a CNN consists of 6 feature maps each of which has a height of 11 and width of 15 (i.e., input is 11 × 15 × 6). What size will the output produced by a single mask with 6 channels and a width of 3 and a height of 3 (i.e., 3×3×6) when using a stride of 2 and padding of 0.
10. A CNN processes an image of size 200x200x3 using the following sequence of layers:
• convolution with 40 masks of size 5x5x3 with stride=1, padding=0 • pooling with 2×2 pooling regions stride=2
• convolution with 80 masks of size 4×4 with stride=2, padding=1
• 1×1 convolution with 20 masks
What is the size of the output once it has been flattened?
11. The following images show exemplars from two datasets:
Each dataset is to be expanded using data augmentation. Which of the following transformations are appropriate:
a. rescaling
b. horizontal flip c. rotation
d. cropping
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