code: def test_nested_parallel(self, same_inputs, kernel_type):
      platform = default_backend()
      rtol = RTOL if platform != "tpu" else 0.05
  
      rng = random.PRNGKey(0)
      (
          input_key1,
          input_key2,
          input_key3,
          input_key4,
          mask_key,
          mc_key,
      ) = random.split(rng, 6)
  
      x1_1, x2_1 = _get_inputs(input_key1, same_inputs, (BATCH_SIZE, 5))
      x1_2, x2_2 = _get_inputs(
          input_key2, same_inputs, (BATCH_SIZE, 2, 2, 2)
      )
      x1_3, x2_3 = _get_inputs(
          input_key3, same_inputs, (BATCH_SIZE, 2, 2, 3)
      )
      x1_4, x2_4 = _get_inputs(
          input_key4, same_inputs, (BATCH_SIZE, 3, 4)
      )
  
      m1_key, m2_key, m3_key, m4_key = random.split(mask_key, 4)
  
      x1_1 = test_utils.mask(
          x1_1, mask_constant=-1, mask_axis=(1,), key=m1_key, p=0.5
      )
      x1_2 = test_utils.mask(
          x1_2,
          mask_constant=-1,
          mask_axis=(
              2,
              3,
          ),
          key=m2_key,
          p=0.5,
      )
      if not same_inputs:
          x2_3 = test_utils.mask(
              x2_3,
              mask_constant=-1,
              mask_axis=(
                  1,
                  3,
              ),
              key=m3_key,
              p=0.5,
          )
          x2_4 = test_utils.mask(
              x2_4, mask_constant=-1, mask_axis=(2,), key=m4_key, p=0.5
          )
  
      x1 = (((x1_1, x1_2), x1_3), x1_4)
      x2 = (((x2_1, x2_2), x2_3), x2_4) if not same_inputs else None
  
      N_in = 2**7
  
      # We only include dropout on non-TPU backends, because it takes large N to
      # converge on TPU.
      dropout_or_id = (
          stax.Dropout(0.9) if platform != "tpu" else stax.Identity()
      )
  
      init_fn, apply_fn, kernel_fn = stax.parallel(
          stax.parallel(
              stax.parallel(
                  stax.Dense(N_in),
                  stax.serial(
                      stax.Conv(N_in + 1, (2, 2)), stax.Flatten()
                  ),
              ),
              stax.serial(
                  stax.Conv(N_in + 2, (2, 2)),
                  dropout_or_id,
                  stax.GlobalAvgPool(),
              ),
          ),
          stax.Conv(N_in + 3, (2,)),
      )
  
      kernel_fn_empirical = nt.monte_carlo_kernel_fn(
          init_fn=init_fn,
          apply_fn=stax.unmask_fn(apply_fn),
          key=mc_key,
          n_samples=N_SAMPLES,
          implementation=_DEFAULT_TESTING_NTK_IMPLEMENTATION,
          vmap_axes=(
              ((((0, 0), 0), 0), (((0, 0), 0), 0), {})
              if platform == "tpu"
              else None
          ),
      )
  
      test_utils.assert_close_matrices(
          self,
          kernel_fn(x1, x2, get=kernel_type, mask_constant=-1),
          kernel_fn_empirical(
              x1, x2, get=kernel_type, mask_constant=-1
          ),
          rtol,
      )
  
imports: import functools
  import itertools
  import random
  from absl.testing import absltest
  from jax import config
  from jax import default_backend
  from jax import jit
  from jax import random
  from jax.example_libraries import stax
  import jax.numpy
  import neural_tangents
  from neural_tangents import stax
  from neural_tangents._src.empirical import _DEFAULT_TESTING_NTK_IMPLEMENTATION
  from tests import test_utils
  import numpy
label_desc: Use image node_id 4 for calling the ParallelInOutTest obj's underlying member method code with example usage: obj.test_nested_parallel(same_inputs, kernel_type) without return types