code: def test_module_training_with_duplicate(
      batch_shape, channels, same_layer, on_device, backend_fw
  ):
      # smoke test
      if backend_fw == "numpy":
          # NumPy does not support gradients
          return
  
      with ivy.utils.backend.ContextManager(backend_fw):
          x = ivy.astype(
              ivy.linspace(
                  ivy.zeros(batch_shape),
                  ivy.ones(batch_shape),
                  channels,
              ),
              "float32",
          )
          module = TrainableModuleWithDuplicate(
              channels, same_layer, device=on_device
          )
  
          def loss_fn(v_):
              out = module(x, v=v_)
              return ivy.mean(out)
  
          # train
          loss_tm1 = 1e12
          loss = None
          grads = None
          for i in range(10):
              loss, grads = ivy.execute_with_gradients(
                  loss_fn, module.v
              )
              module.v = ivy.gradient_descent_update(
                  module.v, grads, 1e-3
              )
              assert loss < loss_tm1
              loss_tm1 = loss
  
          # type test
          assert ivy.is_array(loss)
          assert isinstance(grads, ivy.Container)
          # cardinality test
          assert loss.shape == ()
          # value test
          assert ivy.max(ivy.abs(grads.linear0.b)) > 0
          assert ivy.max(ivy.abs(grads.linear0.w)) > 0
          if not same_layer:
              assert ivy.max(ivy.abs(grads.linear1.b)) > 0
          # tracing test
          if backend_fw == "torch":
              # pytest scripting does not support **kwargs
              return
  
imports: import os
  from hypothesis import given, strategies
  import numpy
  import ivy
  from ivy.functional.ivy.gradients import _variable
  import ivy_tests.test_ivy.helpers
label_desc: Use image node_id 5 for calling a global function with example usage: test_module_training_with_duplicate(batch_shape, channels, same_layer, on_device, backend_fw) and returns: ivy