I did not understand the initial assumption that a Conv2d with 1x1 filter size would act as a fully connected layer. I thought these were very different. Thinking in a single image: a fc layer would treat the image as an 1d vector and hece assign different weights for each pixel, while a 1x1 convolution would use the same filter in the whole image, corresponding to multiply all of the pixels for a same value. So this is not that the way things work?