Repository: pytorch/functorch (language: python)

Issue:
Actually actionable list of batching rules to write
For each of the items here, we should make sure all compositions (vmap, vmap x vjp) have a batching rule. All of these items should be actionable (in that it is possible to write a batching rule and we are not blocked on functionalization, which is coming soon).

Note: you may need to write an OpInfo for the operator if it doesn't exist already or wait for one to be added. A lot of folks are adding OpInfos right now, so if the OpInfo doesn't exist please ask first to see if someone is working on it.

Note: if any of the operations decompose into in-place operations, then we need functionalization to handle them. I think I've already filtered out all of those, but please check me on that.

Parcel 1: top nn.functional.* and top torch.* foo
- [x] torch.nn.functional.interpolate (this involves adding batching rules for adaptive_avg_pool1d, but we might as well do `adaptive_avg_pool{1, 2, 3}d` as well as their backward variants while we're at it)
- [x] nn.functional.unfold. Involves writing a batching rule for im2col im2col_backward (https://github.com/pytorch/functorch/pull/262)
- [x] nn.functional.grid_sample. Involves writing a batching rule for the backward operator. @vfdev-5 
- [x] torch.pow. The backward needs batching rule for logical_and ; use this as an opportunity to write the batching rules for `logical_{and, or, xor}` if those don't exist yet. We may need to also add a change to PyTorch core to make the logical_* functions primitives w.r.t. autograd

Parcel 2: new_blah
- [x] new_empty, new_full, new_ones, new_zeros, empty_like, zeros_like, ones_like, full_like
- [x] `adaptive_max_pool{1, 2, 3}d` as well as the backward variants
- [x] diagonal_scatter, select_scatter, slice_scatter @kshitij12345 
- [ ] linalg.householder_product (forward pass only)
- [x] pixel_shuffle, pixel_unshuffle (these might just be OP_DECOMPOSE)
- [x] isinf, isfinite, isnan
- [x] _cdist_forward, _cdist_backward (try to write a batching rule if possible. If not possible, we may need to write a decomposition) @vfdev-5 

Parcel 3: linalg things
- [x] _lu_with_info (forward pass only) @vfdev-5 
- [x] linalg.eig (forward pass only) @vfdev-5 
- [x] torch.addr @vfdev-5 
- [x] cholesky_solve (forward pass only) @vfdev-5 

Parcel 4:
- [x] ~~index_select, index_copy, etc, all need a backward formula in pytorch/pytorch https://github.com/pytorch/functorch/issues/260~~


Discussion / hints:
@zou3519 `nn.functional.pad` with circular option requires to do a copy: `out[..., out_d0:out_d1] = input[..., in_d0:in_d1]` and thus there is the following error is raised:
```
>           out[..., out_d0:out_d1] = input[..., in_d0:in_d1]                                                                                                                               
E           RuntimeError: vmap: aten::copy_(self, *extra_args) is not possible because there exists a Tensor `other` in extra_args that has more elements than `self`. This happened due to `other` being vmapped over but `self` not being vmapped over at level 2. Please try to use out-of-place operators instead of aten::copy_. If said operator is being called inside the PyTorch framework, please file a bug report instead. 
```
Can we do something with that ?
Aha. Nope, we can't do anything about that until functionalization is in, good catch.

Fix patch:
diff --git a/functorch/csrc/BatchRulesModules.cpp b/functorch/csrc/BatchRulesModules.cpp
index aa733fa1c..03cfd9f09 100644
--- a/functorch/csrc/BatchRulesModules.cpp
+++ b/functorch/csrc/BatchRulesModules.cpp
@@ -409,6 +409,14 @@ TORCH_LIBRARY_IMPL(aten, FT_BATCHED_KEY, m) {
   EXISTING_BDIM(replication_pad2d);
   EXISTING_BDIM(replication_pad3d);
 
+  EXISTING_BDIM_ALL_BOXED(replication_pad1d_backward);
+  EXISTING_BDIM_ALL_BOXED(replication_pad2d_backward);
+  EXISTING_BDIM_ALL_BOXED(replication_pad3d_backward);
+
+  EXISTING_BDIM_ALL_BOXED(reflection_pad1d_backward);
+  EXISTING_BDIM_ALL_BOXED(reflection_pad2d_backward);
+  EXISTING_BDIM_ALL_BOXED(reflection_pad3d_backward);
+
   UPSAMPLE_BATCH(upsample_bicubic2d);
   UPSAMPLE_BATCH(upsample_bilinear2d);
   UPSAMPLE_BATCH(upsample_linear1d);


Test patch:
diff --git a/test/test_ops.py b/test/test_ops.py
index d55603579..1f6874f7c 100644
--- a/test/test_ops.py
+++ b/test/test_ops.py
@@ -467,8 +467,6 @@ def test_vmapvjp(self, device, dtype, op):
         xfail('nn.functional.grid_sample'),
         xfail('nn.functional.interpolate', 'area'),
         xfail('nn.functional.pad', 'circular'),
-        xfail('nn.functional.pad', 'reflect'),
-        xfail('nn.functional.pad', 'replicate'),
         xfail('nn.functional.unfold'),
         xfail('norm', 'fro'),
         xfail('norm', 'inf'),