Question

Let's design a convolutional neural network together. Suppose the size of the input image is 32-by-32-by-1 a) The first layer is a convolutional layer. The size of a filter is 7-by-7-by-X. What is the number for X? b) Given a., what is the size of the one feature map (activation map)? Note that we do not pad zeros around the input image and stride -1. c) Suppose we use 32 filters in a. How many feature maps are there after we apply the filters? d) Given the output of a., we would like to apply a nonlinear stage. Write down the name of a nonlinear function (activation function), and draw its curve in an XY axis. e) After c. suppose we would like to have another convolutional layer. Please suggest a size for the filter in the format of?-by-?-by-?. f) Given a feature map shown below, you are asked to apply a pooling stage over it. In particular, the pooling stage is done by max pooling with 2-by-2 filters and a stride of 2. Write down the output of this pooling stage. Also, what's the purpose of the pooling stage? 123 4 56 510 4 10 3 47 2110 |2

Answer 1

Solution :-

a) Size of the filter is 7-by-7-by-X. Number X is the number of convolutional layers we would like to apply in the first stage. Suppose we take X as 30 filters. So we are going to convolve 30 number of 7x7 filters on the given input. X = 30

b) Size of the feature map can be given by

Size of the filter is 7-by-7-by-X. Number X is the number of convolutional layers we would like to apply in the first stage. Suppose we take X as 30 filters. So we are going to convolve 30 number of 7x7 filters on the given input. X = 30 Size of the feature map can be given by (W - F + 2P)/S + 1 where W = input size and F = filter size and P = zero padding size and S = Stride. Here W = 32 , F = 7 and P = 0 , S = 1. So size of one feature map is 26 times 26 If we have 32 filters, then we will have 32 feature maps after applying first layer. We can apply Rectified Linear Unit (ReLU) as a non linear stage. Another convolutional layer's filter size can be 3-by-3-by-15. f) We will use 2 times 2

where W = input size and F = filter size and P = zero padding size and S = Stride.

Here W = 32 , F = 7 and P = 0 , S = 1.

So size of one feature map is 26x26

c) If we have 32 filters, then we will have 32 feature maps after applying first layer.

d) We can apply Rectified Linear Unit (ReLU) as a non linear stage.

e) Another convolutional layer's filter size can be 3-by-3-by-15.

f) We will use 2x2 pooling with stride = 2... So matrix will look like after applying pooing as..

(Here we apply max-pooling operation )

5	4	10
7	4	10

By applying pooling we will have reduced feature size without loosing the important information. Reduced feature size will help us to have further Network with less required computation and feasible to train in certain time.