Why Use ?
They are just looking at a pixel of the image rather than a patch . In case of a traditional convolution, its a classifier but only a linear classifier over the patch of the image, however with 1 by 1 ConvNets, we suddenly have a mini-neural network over the patch. Plus, it’s cheap, it’s more deep and relatively few parameters. Plus the underlying basics are just the matrix multiplications.
Fig : Advanced ConvNets with average pooling and 1 by 1 ConvNets Ref : Udacity
General , Very Successful Convolution network strategy :
1 by 1 Convolutions + Average Pooling = Smaller , Better ConvNets than traditional ones