## NPTEL Deep Learning for Computer Vision Week 4 Assignment Answers 2024

1. Which one of the following statements is true:

- Weight change criterion is a method of ‘early stopping’ that checks whether or not the error is dropping over epochs to decide whether to continue training or stop.
- L
_{2}norm tends to create more sparse weights than L_{1}norm. - During the training phase, for each iteration, Dropout ignores a random fraction, p, of nodes, and accounts for it in the test phase by scaling down the activations by a factor of p.
- A single McCulloch-Pitts neuron is capable of modeling AND, OR, XOR, NOR, and NAND functions

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2.

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3. Which of the following statements are **true**? (Select all that apply)

- Sigmoid activation function σ(⋅) can be represented in terms of tanh activation function as below:

` σ(x)=(tanh(x/2)−1)/2`

- The derivative of the sigmoid activation function is symmetric around the y-axis
- Gradient of a sigmoid neuron vanishes at saturation.
- Sigmoid activation is centered around 0 whereas tanh activation is centered around 0.5

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5. Consider the following statements P and Q regarding AlexNet and choose the correct option:

(P) In AlexNet, Response Normalization Layers were introduced to emulate the competitive nature of real neurons, where highly active neurons suppress the activity of neighboring neurons, creating

competition among different kernel outputs.

(Q) Convolutional layers contain only about 5% of the total parameters hence account for the least computation.

- Only statement P is true
- Only statement Q is true
- Both statements are true
- None of the statements is true

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6. Given an input image of shape (10,10,3), you want to use one of the two following layers:

Fully connected layer with 2 neurons, with biases

Convolutional layer with three 2×2 filters (with biases) with 0 padding and a stride of 2.

If you use the fully-connected layer, the input volume is “flattened” into a column vector before being fed into the layer. What is the difference in the number of trainable parameters between these two layers?

- The fully connected layer has 566 fewer parameters
- The convolutional layer has 518 fewer parameters
- The convolutional layer has 570 fewer parameters
- None of the above

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7.

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8. Compute the value for the following expression ELU(tanh(x)) where x=−1. 3 and α=0.3 (Round decimal point till 2 places).

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9. Using RMSProp-based Gradient Descent, find the new value of parameter θ_{t+1}, given that the old value θ_{t}=1.2, aggregated gradient Δθ_{t}=0.85, gradient accumulation r_{t−1}=0.7, learning rate α=0.9, decay rate ρ=0.3 and small constant δ=10^{−7} (Round decimal point till 3 places).

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If we convolve a feature map of size 32 × 32 × 6 with a filter of size 7 × 7 × 3, with a stride of 1 across all dimensions and a padding of 0, the width of the output volume is **A**,the height of the output volume is **B** and the depth of the output volume is **C**

10. A____________

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11. B______________

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12. C_____________

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Assume that the feature map given below is generated from a convolution layer in CNN, after which a 2 × 2 Max Pooling layer with a stride 2 is applied to it.

While backpropagation, we get the following gradient for the pooling layer.

Assign the appropriate gradient value for the locations at feature map.

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13. Location (1,1):-

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14. Location (1,4):

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15. Location (2,2):

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16. Location (3,1):

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17. Location (3,3):

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18. Location (4,3):

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For the same previous question, assign the appropriate gradient value for the locations at feature map but use Average Pooling layer instead of Max Pooling layer.

19. Location (1,1):

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20. Location (1,4):

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21. Location (2,2):

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22. Location (3,1):

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23. Location (3,3):

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24. Location (4,3):

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