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Trying to understand 2D convolutions, I ran into the following image, which has me confused: link to the source

If I understood correctly:

  • the blue shape is the input
  • the orange shape is the one of the convolution filters
  • the green shape is the output

My question is: what are the calculations performed to get, from 2 tensors with shape 3x3xD (where D is the depth), a single value.

As far as I understand, the calculation of convolution would produce a 1x1xD vector, but I don't get how from this vector we get a single value. Is it just addition? Does it have normalization for the addition?

Thank you in advance!

BillTheKid
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    A convolutional kernel by default spans not only the height and the width, but also the depth of the image so the red point in your image is simply the sum of the element-wise multiplication of two `(3,3,D)` tensors, which is a scalar. – bui May 16 '22 at 09:34
  • So it's just the sum! ok thanks a lot!! – BillTheKid May 17 '22 at 10:42

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