How many times does the size of the input decrease (i.e. what is the value of hbd/h’b’d’ where the initial input is of size h x b x d and the output is of size h’ x b ’x d’) after passing through a 3x3 MaxPool layer with stride 3? Size of the input is defined as height x breadth x depth.(Round your answer off to the closest integer)
Question
How many times does the size of the input decrease (i.e. what is the value of hbd/h’b’d’ where the initial input is of size h x b x d and the output is of size h’ x b ’x d’) after passing through a 3x3 MaxPool layer with stride 3? Size of the input is defined as height x breadth x depth.(Round your answer off to the closest integer)
Solution
The size of the input decreases by a factor of 9 after passing through a 3x3 MaxPool layer with stride 3.
Here's the step-by-step explanation:
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The MaxPool layer with a filter size of 3x3 and stride 3 reduces the height and width of the input by a factor of 3. This is because the filter moves 3 steps at a time, so it covers the entire height and width in 1/3rd of the steps compared to a stride of 1.
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Therefore, the new height and width (h' and b') are h/3 and b/3 respectively.
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The depth (d) remains the same because MaxPooling operates independently on each depth slice. So, d' = d.
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The size of the input is defined as height x breadth x depth (h x b x d) and the size of the output is h' x b' x d'.
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Therefore, the ratio of the size of the input to the size of the output is (h x b x d) / (h' x b' x d') = (h x b x d) / ((h/3) x (b/3) x d) = 9.
So, the size of the input decreases 9 times after passing through the MaxPool layer.
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