Consider a CNN with several convolutional layers followed by a fully$-$connected layer as the output. Suppose you mistakenly initialize the fully$-$connected layer with all weights to be equal. Additionally, in every individual convolutional layer, all filters have been mistakenly initialized identically, i$.$e$.,$ every filter in a layer is initialized such that it is identical to every other filter in that layer. $($a$)$ Show or explain why it is the equivalent of having a single filter in each convolutional layer. $($b$)$ Show or explain why no filter will ever learn any new pattern except for the random pattern inherent in its initialization. $($Hint: It is sufficient to show or explain that all weights in any filter will always be updated by the same amount.$)$