#1x1-convolution

Question 1: Single choice

mediumAI-checkedConvolutional Neural Networks

A convolutional layer with $c_i$ input and $c_o$ output channels computes $[\mathsf{H}]_{i,j,d} = \sum_{a=-\Delta}^{\Delta}\sum_{b=-\Delta}^{\Delta}\sum_{c} [\mathsf{V}]_{a,b,c,d}\,[\mathsf{X}]_{i+a,j+b,c}.$ What does the layer compute when the kernel size is $\Delta = 0$ ?

A fully connected layer over all pixels, so that every output pixel depends on the whole image1
One shared linear map from $c_i$ to $c_o$ channels, applied to each pixel separately2
A different linear map at every pixel, because with $\Delta = 0$ the weights are no longer shared across positions3
The identity map, where each output channel copies one of the input channels unchanged4

Timed test