In this question, we will try and understand $11$ convolutional kernels and their functions:

Given that the training mini$-$batch size is $32$ images, each of dimension $128128$ pixels and $3$

channels $($Red$,$ Blue, Green$).$ Assume that we apply a single $11$ convolutional filter with stride $1.$

What will be the ratio between the size of the tensor before applying the filter and its size

after the application of the filter?

What is the interpretation of such a filter? Let us say we are designing a CNN to detect a

blue$-$colour Pepsi can. What would you expect the weights of the trained $11$

convolutional filter to be like, when each of the weights are mapped to the $0-$to$-256$

range? $($Assume the convention of Red $-$ Blue $-$ Green for writing the weights$).$ Marks: $7$

Let us say the prior layer of your network has size $3232256($i$.$e$.$ Height $x$ Width $x$

Depth, where depth denotes the number of convolutional filters used$).$ Compare the

following two scenarios in terms of the parameters that need to be trained.

Scenario A: Kernel of size $33,$ with stride of $1$ and $256$ such filters $($i$.$e$.256$ activation

maps$).$

Scenario B:

Previous Layer $-$ Size $32*32*256$

Conv $(11$ kernel$),$ stride $1,64$ such filters

Conv $(33$ kernel$),$ stride $1,64$ such filters

Conv $(1$ x $1$ kernel$),$ stride $1,256$ such filters

What will be the total number of parameters and the final size of the tensor after the

application of convolutional filters in the two scenarios?

How are these two scenarios comparable?

Marks: $10$