Is there a name for a convolution that has the same size as the input?

I have an input tensor of dimensions (C, H, W) and kernel with size (H, W).

It feels like there should be a name for this but I am unaware and can't get Google or ChatGPT to show it to me. Is there a name for this?

Turns out I am stupid, this is just a fully connected layer.

ChatGPT had me confused as to how convolutions work but yeah, it is in fact a different kernel for each input channel in every filter, making this "convolution" have one weight for every connection from an input neuron to an output neuron, which is effectively a fully connected layer in disguise.

My uni professors call it same convolution, but there is no universal accepted name for this operator in the deep-learning community.

Regarding your answer, convolutional layer and fully connected one are two different things and are not related by the "same convolution" operator. For example, you can obtain the same final shape using this convolutional layer:

• kernel of 3x3
• stride = 1
• dilation = 1
• padding = 1

Here the exact formula.

In the convolution layer, you have a different set of weights for each output channel you want and each "pixel" in the output image depends only on the neighborhood covered by the kernel.
In the fully connected layer, each unit (or neuron) has its own set of weights.

Think of the extreme case in which the kernel height and width are the same of the input image, with no stride, no padding and default dilation at 1. In this case, you obtain 1 output pixel for each output channel you want and such pixel depends on the whole image.

I know that convolution can be a little confusing, at first, but I hope that what I write can be useful for you.