You can find the backward definitions in this file: https://github.com/pytorch/pytorch/blob/master/tools/autograd/derivatives.yaml#L1680-L1681 7
What is saved for backward is anything that is used in the formula these that correspond to an argument/output in the forward.
In particular you can see that all the convs there are defined in a special way to leverage these libraries (and re-use buffers I think?).
I have to admit I didn’t dive into these in a long time so there might be details I’m missing.