In a fully convolutional network, if we forward an image of size 1000 x 1000, but only provide supervision signal for a 100 x 100 crop of the output, how are the weights of the convolution filters expected to be updated? Because the same filters were applied to all pixels.

Should they -

- update all the filters with the average of the update derived by backproping the 100x100 crop?
- Or should they take the average for all the pixels. This means the update will be scaled down by 1e-2, because the gradient from most other pixels is zero.

When computing the scalar loss, I take the average over the patch that I chose. Under the assumption that the error is evenly distributed, the scalar loss will have the same value.

But, this loss will only give gradients to a 100 x 100 patch. Say the the receptive field is x, itâ€™ll impact a max of (100 + 2x) * (100 + 2x) pixels at the shallowest layer. Since the conv filter was applied across 1000 x 1000, many of indexes will receive no grad. Does PyTorch ignore these for update calculation or consider them 0? And which is the correct way?