CNN and NLP Quiz - Part A

What is the primary purpose of a convolutional layer in a CNN?

• To perform matrix multiplication

• To reduce the dimensions of the input

• To detect patterns in the input data

• To perform data normalization

Answer explanation

The primary purpose of a convolutional layer in a CNN is to detect patterns in the input data. It achieves this by applying filters that capture spatial hierarchies, enabling the model to recognize features like edges and textures.

Given an input image of size 64∗64∗3, kernel size of 5∗5, stride of 2, and no padding, what is the output size?

• 30∗30∗3

• 30∗30∗1

• 32∗32∗1

• 32∗32∗3

Answer explanation

To calculate the output size, use the formula: \( O = \frac{(W - K + 2P)}{S} + 1 \). Here, W=64, K=5, P=0, S=2. Thus, \( O = \frac{(64 - 5 + 0)}{2} + 1 = 30 \). The depth remains 3, so the output size is 30∗30∗3.

What is the size of the feature map produced when applying a 3∗3 filter to an input of size 28∗28∗3 with stride 1 and padding 1?

• 28∗28∗3

• 28∗28∗1

• 30∗30∗3

• 30∗30∗1

Answer explanation

With a 3x3 filter, stride 1, and padding 1, the output size remains the same as the input size. Therefore, the feature map produced is 28x28x3, matching the input dimensions.

For a convolutional layer with 32 filters, a 5∗5 kernel, and an input depth of 3, how many trainable parameters are there?

• 480

• 800

• 2400

• 400

Answer explanation

To calculate the trainable parameters: each filter has a size of 5*5*3 (kernel width * kernel height * input depth) plus 1 bias term. Thus, for 32 filters: (5*5*3 + 1) * 32 = 800. Therefore, the correct answer is 800.

Max pooling with a 2∗2 filter, stride 2, and no padding is applied to an image of size 10∗10∗3. What is the output size?

• 5∗5∗3

• 5∗5∗1

• 8∗8∗3

• 4∗4∗3

Answer explanation

Max pooling with a 2x2 filter and stride 2 reduces each dimension by half. For a 10x10 input, the output size becomes (10/2, 10/2) = 5x5. The depth remains the same at 3, resulting in an output size of 5x5x3.

If the number of filters in a CNN layer is increased, which of the following happens?

• The feature map depth decreases

• The feature map depth increases

• The spatial dimensions of the output reduce

• The input size increases

Answer explanation

Increasing the number of filters in a CNN layer results in a greater number of feature maps, which directly increases the feature map depth. Thus, the correct answer is that the feature map depth increases.

Given two vectors A=[1,2,3] and B=[4,5,6], what is the cosine similarity between them?

• 0.974

• 0.992

• 1.0

• 0.5

Answer explanation

Cosine similarity is calculated as (A·B) / (||A|| ||B||). Here, A·B = 1*4 + 2*5 + 3*6 = 32, ||A|| = sqrt(14), ||B|| = sqrt(77). Thus, cosine similarity = 32 / (sqrt(14) * sqrt(77)) ≈ 0.974, which is the correct answer.

Given the term frequency of the word "data" in document D1 as 3, and the inverse document frequency for the word "data" as 1.2, what is the TF-IDF value?

• 3.6

• 2.4

• 3.0

• 1.2

Answer explanation

The TF-IDF value is calculated as TF * IDF. Here, TF = 3 and IDF = 1.2. Thus, TF-IDF = 3 * 1.2 = 3.6. Therefore, the correct answer is 3.6.

Which of the following is a limitation of the Bag-of-Words (BoW) model?

• It captures word order and syntax

• It ignores semantics and context of the words

• It handles word frequency well

• It reduces the size of the vocabulary

Answer explanation

The Bag-of-Words model ignores semantics and context, treating words as independent tokens. This limitation means it cannot capture the meaning derived from word relationships or order, which is crucial for understanding language.

Given two vectors A=[2,3,4] and B=[1,1,1], which of the following is true?

• The cosine similarity between A and B will be 1.

• The cosine similarity will be 0.

• The cosine similarity will be negative.

• The cosine similarity will be positive but less than 1.

Answer explanation

The cosine similarity is calculated as the dot product of A and B divided by the product of their magnitudes. Since A and B are not identical and have positive components, the similarity will be positive but less than 1.