Consider a convolution layer that processes an input image of size 256 × 256 × 3 and where the output has one channel. If the convolution layer contains a single 1 x 1 convolution filter, how many parameters are there including bias?

If the convolution layer processes an input image of size 256 x 256 x 3 and the output has one channel, then the output size will be 256 x 256 x 1.

If the convolution layer contains a single x 1 convolution filter, then it is a 1D convolution that slides along the height of the image. The number of parameters in a convolution layer is determined by the size of the filter, the number of input channels, and the number of output channels.

In this case, the filter size is 1 x 1, and the number of input channels is 3 (corresponding to the RGB color channels). Since the output has only one channel, the number of output channels is 1. Therefore, the number of parameters in the convolution layer is given by:

parameters = (filter width) x (filter height) x (number of input channels) x (number of output channels) + (number of output channels)

Substituting the values, we get:

parameters = (1) x (1) x (3) x (1) + (1) = 4