After reading the documents for register_full_backward_hook here 1 and register_forward_pre_hook here. I was wondering if I could ask a few clarification questions that aren’t clear within the documents?
From my understanding, register_full_backward_hook returns the grad_output and grad_input variables which are the gradient of the loss with respect to the output and input respectively. And, for register_forward_pre_hook returns the input of a given layer.
For example, I use a nn.Linear module like Linear(in_features=2, out_features=32, bias=True). where the input data has shape [B, A, 2] where B is the batch and A is another dimension to the input shape. When applying a forward_pre_hook the input shape is the same as my input which makes sense (it’s shape [B, A, 2]). When applying a backward_full_hook the grad_output shape is [B, 32, A] which makes sense. Is it right to assume that this Tensor is the individial gradients of the loss with respect to the layer output for all inputs? I.e. each element here represent the gradient of the loss for a given input before any kind of reduction operation like torch.mean?
Also, is it possible to reconstruct the gradient of the layer from its grad_output variables? For example, with a nn.Linear layer, its gradient of the loss can be decomposed into the gradient of the loss with respect to the output of the layer (aka grad_output) and the gradient of the output of the layer with respect to the weights of the layer (which for a Linear layer is just the input features, which are returned by forward_pre_hook). I tried doing the following to reconstruct the gradients but it’s not always the same as getting nn.Linear.weight.grad,
grad_output  #has shape [B,32,A]
input #has shape [B,2,A]

grad_from_hooks = torch.einsum("bia,boa->io", grad_output, input)
grad_from_module = nn.Linear.weight.grad

ratio = grad_from_hooks / grad_from_modules #should be 1 if equal. 

In my case this ratio value is near 1 for nearly all elements of the Tensor (in range of 0.95 to 1.05). Although, some elements differ by a factor of 2 or 3, and I was wondering why exactly doesn’t this formula work when reconstructing the gradients from the grad_ouput and input Tensors? The expression I saw was the outer-product of the grad_output and input should give the gradient (which is what I’ve done within the torch.einsum expression).
Is it at all possible to reconstruct the gradient of the layer by using the layers grad_output and input values from register_backward_full_hook and register_forward_pre_hook?
Apologizes for this being quite an in-depth question but I’d appreciate any clarification on this issue!
Thank you!