Convolutionally Implementation of Sliding window

Course Q&A Deep Learning Specialization Convolutional Neural Networks
1

Hi Sir,

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Statement at 2:46 minute: Mathematically, this is the same as a fully connected layer because each of these 400 nodes has a filter of dimension 5 by 5 by 16. So each of those 400 values is some arbitrary linear function of these 5 by 5 by 16 activations from the previous layer.

Doubt 1: Can u please explain it , unable to understand the statement same as fully connected layer? Because only two Fully connected layer combines together equivalent to 11400 right, but in the lecture first fully connected layer pointed to first 11400 volume and second fully connected layer points to second 11400 volume. How it become valid ? or before first FC, nodes are flatten out then connected densely to first FC ?

Doubt 2: what is arbitrary linear function here ?

Doubt 3: This statement is unclear. So each of those 400 values is some arbitrary linear function of these 5 by 5 by 16 activations from the previous layer. can u pleease explain it ?

2

Hi Anbu,

Note that filters have dimensions height x width x number of channels. Using a 5 x 5 filter on a 5 x 5 x 16 volume therefore means applying a filter volume of size 5 x 5 x 16 on the 5 x 5 x 16 volume. In other words, all elements of the 5 x 5 x 16 volume are used in the calculations using one filter.

If you use 400 filters, this implies that all of the channels of the resulting 1 x 1 x 400 volume are connected to all of the values in the 5 x 5 x 16 volume. So every channel/node of the 1 x 1 x 400 volume is connected to every value of the 5 x 5 x 16 layer - with the resulting values depending on the parameters in the 400 filters using a linear function. In other words, it is equivalent to a fully connected layer.

I hope this clarifies.