Update on "[WIP] Compute forward grads for saved_mean and saved_var when input requires grad"

We want to avoid having to recompute saved_mean and saved_invstd in batch_norm_backward's decomposition in functorch (see pytorch/functorch#877), but also avoid unnecessarily computing forward grads for saved_mean and saved_invstd when they are not needed.

Tested locally with: `python test/test_ops.py -k test_jvpvjp_nn_functional_batch_norm`

Issues:
- not sure if gradgrad in core is missing something, but it is able to pass while the fwgrad_bwgrad comparison fails in functorch


[ghstack-poisoned]

Author: soulitzer

torch/autograd/function.py

@@ -22,15 +22,16 @@ def save_for_backward(self, *tensors: torch.Tensor):
         incorrect gradients and memory leaks, and enable the application of saved
         tensor hooks. See :class:`torch.autograd.graph.saved_tensors_hooks`.
 
-        Note that if intermediary tensors (i.e., tensors that are neither input
-        nor output) are saved for backward, your custom Function may not support
-        `double backward <https://pytorch.org/tutorials/intermediate/custom_function_double_backward_tutorial.html>`_.
+        Note that if intermediary tensors (tensors that are neither input
+        nor output of :func:`forward`) are saved for backward, your custom Function
+        may not support double backward.
         Custom Functions that do not support double backward should decorate their
-        :func:`backward` method with `@once_differentiable` so that performing
-        double backward raises an error. If you'd like to support double backawrd
+        :func:`backward` method with ``@once_differentiable`` so that performing
+        double backward raises an error. If you'd like to support double backward
         you can either recompute intermediaries based on the inputs during backward
-        or return the intermediaries as the outputs of the custom Function. See
-        the tutorial linked above for more details.
+        or return the intermediaries as the outputs of the custom Function. See the
+        `double backward tutorial <https://pytorch.org/tutorials/intermediate/custom_function_double_backward_tutorial.html>`_.
+        for more details.
 
         In :func:`backward`, saved tensors can be accessed through the :attr:`saved_tensors`
         attribute. Before returning them to the user, a check is made to ensure