code: def test_input_hooks_same(self):
      backends = ["eager", "aot_eager", "inductor"]
      for backend in backends:
  
          def my_hook(grad, *, k=0):
              return grad + k
  
          hook = functools.partial(my_hook, k=3)
  
          class MyMod(torch.nn.Module):
              def forward(self, x):
                  x.register_hook(hook)
                  y = x.mul(2)
                  z = y.mul(3)
                  return (z,)
  
          mod = MyMod()
          x0 = torch.ones(4, requires_grad=True)
          eager_out = mod(x0)
          eager_out[0].backward(torch.ones(4))
  
          x1 = torch.ones(4, requires_grad=True)
          mod_compiled = aot_module_simplified(mod, (x1,), nop)
          aot_out = mod_compiled(x1)
          aot_out[0].backward(torch.ones(4))
  
          x2 = torch.ones(4, requires_grad=True)
          dynamo_out = torch._dynamo.optimize(backend, nopython=True)(
              mod
          )(x2)
          with compiled_autograd.enable(compiler_fn):
              dynamo_out[0].backward(torch.ones(4))
  
          self.assertEqual(dynamo_out, aot_out)
          self.assertEqual(dynamo_out, eager_out)
  
          self.assertEqual(x0.grad, x1.grad)
          self.assertEqual(x0.grad, x2.grad)
  
imports: import contextlib
  import functools
  import torch
  import torch._dynamo
  import torch._dynamo.test_case
  import torch._dynamo.testing
  from functorch.compile import nop
  from torch._dynamo import compiled_autograd
  from torch._functorch.aot_autograd import aot_module_simplified
label_desc: Use image node_id 17 for calling the HooksTests obj's underlying member method code with example usage: obj.test_input_hooks_same() and returns: unknown, z