I don't think I fully understand what's going on here. There are a bunch of checks in the engine for if we are invoking legacy autograd functions -- it's looking for stuff like are there staticmethod forwards/backwards, etc. Is it "fine" to have non-staticmethods as long as you call apply? Does it invoke the legacy path in that case?

@gchanan I think the biggest concern about legacy autograd function is clobbering between different function calls: #22983 (comment). I adapt the test case that shows clobbering to use apply(), and got the following result:

# `test_call_legacy_twice` is currently in test_autograd.py
def test_call_legacy_twice(self):
    class Id(Function):
        def forward(self, x):
            self.save_for_backward(x)
            return x

        def backward(self, grad_x):
            x = self.saved_tensors
            return x

    x1 = torch.zeros(1, requires_grad=True)
    x2 = torch.ones(1, requires_grad=True)
    y = Id.apply(x1)
    z = Id.apply(x2)
    y.backward()
    self.assertEqual(x2.grad, x2)
    self.assertNotEqual(x1.grad, x2)  # If clobbering happens, x1.grad == x2

Running this code gives error:

Traceback (most recent call last):
  File "test_autograd.py", line 1745, in test_call_legacy_twice
    y.backward()
  File "/data/miniconda3/envs/working2/lib/python3.7/site-packages/torch/tensor.py", line 118, in backward
    torch.autograd.backward(self, gradient, retain_graph, create_graph)
  File "/data/miniconda3/envs/working2/lib/python3.7/site-packages/torch/autograd/__init__.py", line 93, in backward
    allow_unreachable=True)  # allow_unreachable flag
  File "/data/miniconda3/envs/working2/lib/python3.7/site-packages/torch/autograd/function.py", line 77, in apply
    return self._forward_cls.backward(self, *args)
  File "/data/miniconda3/envs/working2/lib/python3.7/site-packages/torch/autograd/function.py", line 181, in backward
    raise NotImplementedError
NotImplementedError

Based on this result, I think calling apply() on legacy autograd function doesn't actually work (because calling backward() on the output gives error). So I think it's okay to not print a warning in this case and close this PR.

I tested all versions from 0.4.0 to 1.1.0, and can confirm that calling backward() on the output of legacy autograd function apply() always gives NotImplementedError.