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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def serialize_training_step(features, model_fn, batch_dim, num_splits):
 """Break the training batch into multiple microbatches. Returns two structures: grads - a list of Tensors corresponding to the gradients on graph.trainable_variables. These are summed across all microbatches outputs - a dictionary of Tensors corresponding to the output dictionary of model_fn. Each value is either summed across all microbatches (if it has no batch-dimension), or concatenated across all microbatches to represent the original batch (if it does have a batch-dimension). Args: features: a dictionary of Tensors, each with a batch_dim dimension model_fn: a function from feature dictionary to output dictionary output_dictionary must contain "loss" batch_dim: a Dimension num_splits: an integer dividing batch_dim.size Returns: grads: a list of Tensors corresponding to the gradients on graph.trainable_variables outputs: dictionary of output Tensors summed across microbatches """

  for v in features.values():
    mesh = v.mesh
    graph = v.graph
  microbatch_dim = Dimension("microbatch", num_splits)
  smaller_batch_dim = Dimension(batch_dim.name, batch_dim.size // num_splits)
  cache = {}
  def select(t, microbatch_num):
    return gather(
        replace_dimensions(t, batch_dim, [smaller_batch_dim, microbatch_dim]),
        microbatch_num, microbatch_dim)
  def cond_fn(microbatch_num):
    return less(microbatch_num, num_splits)
  def body_fn(microbatch_num):
    """Body function for mtf.while_loop.

    Args:
      microbatch_num: a mtf Scalar
    Returns:
      a list of mtf Tensors
    """
    my_features = {}
    for k, v in six.iteritems(features):
      my_features[k] = select(v, microbatch_num)
    outputs = model_fn(my_features)
    grads = gradients(
        [outputs["loss"]], [v.outputs[0] for v in graph.trainable_variables])
    output_keys = outputs.keys()
    cache["output_keys"] = output_keys
    ret = []
    ret.append(microbatch_num + 1)
    # The rest of the returned values are "accumulators" that get summed
    # across all microbatches.
    for t in outputs.values():
      if smaller_batch_dim in t.shape:
        # The output contains a batch dimension, so we want to concatenate
        # across microbatches.
        # Here we pad the tensor for each microbatch - summing will complete
        #  the concatenation.
        t = einsum(
            [t, one_hot(microbatch_num, microbatch_dim, dtype=t.dtype)],
            output_shape=replace_dimensions(
                t.shape, smaller_batch_dim,
                [smaller_batch_dim, microbatch_dim]))
        t = replace_dimensions(
            t, [smaller_batch_dim, microbatch_dim], batch_dim)
        ret.append(t)
      else:
        # There is no batch dimension.  Sum across all microbatches.
        ret.append(t)
    # we also want to sum the gradients.
    ret.extend(grads)
    return ret
  while_out = while_loop(
      cond_fn, body_fn, [constant(mesh, 0, dtype=tf.int32)],
      has_accumulators=True)
  num_outputs = len(cache["output_keys"])
  combined_outputs = {}
  for k, v in zip(cache["output_keys"], while_out[1:1 + num_outputs]):
    combined_outputs[k] = v
  combined_grads = while_out[1 + num_outputs:]
  return combined_grads, combined_outputs