code: def clip_and_aggregate_gradients(
      tape: tf.GradientTape,
      target: tf.Tensor,
      sources: Nested[tf.Tensor],
      unconnected_gradients: tf.UnconnectedGradients = tf.UnconnectedGradients.NONE,
      normalize: bool = False,
      l2_norm_clip: Optional[float] = None,
      aggregate_method: str = "mean",
      keep_sparse_threshold: int = 10000,
  ) -> Nested[GradientTensor]:
      """Clips (per-example) and aggregates gradients.
  
      This procedure computes the Jacobian with respect to a vectorized loss,
      i.e. the `target` argument, clips the gradient with repsect to each
      individual output, and sums the clipped gradients. This is correct as
      per-example gradient if there is a one to one mapping from the input example
      to the output loss.
  
      Args:
        tape: a persistent tape.
        target: Tensor to be differentiated. It is assumed that each value in
          `target` is associated with an example so the gradient clipping would be
          applied to the vectorized target.
        sources: a list or nested structure of Tensors or Variables. `target` will
          be differentiated against elements in `sources`.
        unconnected_gradients: a value which can either hold 'none' or 'zero' and
          alters the value which will be returned if the `target` and `sources` are
          unconnected. The possible values and effects are detailed in
          'UnconnectedGradients' and it defaults to 'none'.
        normalize: whether to normalize each gradient.
        l2_norm_clip: when `normalize` is `True`, every gradient is scaled to
          `l2_norm_clip` (which can be set to None, understood as 1). When
          `normalize` is `False`, it performs the regular clipping, i.e. scaling the
          gradient to `l2_norm_clip` only if the gradient's L2 norm is larger than
          `l2_norm_clip`. When `l2_norm_clip` is `None`, do nothing.
        aggregate_method: the method for aggregating the gradients. Currently only
          supports `sum` and `mean`, default to `mean`.
        keep_sparse_threshold: when the gradient is a `tf.IndexedSlices`,
          `keep_sparse_threshold` is used to determine if we should keep it in its
          sparse representation (when the number of embedding items, i.e. vocabulary
          size >= `keep_sparse_threshold`) or convert it into a dense tensor (when <
          `keep_sparse_threshold`). The reason for this parameter is that the
          current implementation of embedding lookup merges all the indices in a
          batch, hence the sparse representation has input size the same as the
          number of indices. When it is larger than the embedding size, it would be
          more efficient to convert the sparse representation to a dense tensor. So
          this threshold should be set around the number of indices in a typical
          batch. When it is -1, always convert the sparse tensor to a dense tensor.
  
      Returns:
        Gradients stored in the same structure as `sources` with a one to one
        mapping to the variables in `sources`. Each gradients may be a dense
        tensor or a `tf.IndexedSlices`.
  
      Raises:
        RuntimeError: if `tape` is not persistent.
        ValueError: if aggregate_method is not 'mean' or 'sum'.
      """
  
      if tape._tape is None:  # pylint: disable=protected-access
          raise RuntimeError(
              "A non-persistent GradientTape can only be used to "
              "compute one set of gradients (or jacobians)"
          )
  
      if aggregate_method not in ["mean", "sum"]:
          raise ValueError(
              "Only mean and sum methods are supported. But got "
              f"{aggregate_method}"
          )
  
      flat_sources = tf.nest.flatten(sources)
      # Note that we push and pop the tape here and below. This is needed since we
      # need gradients through the enclosed operations.
      with tape._ensure_recording():  # pylint: disable=protected-access
          target = tf.reshape(target, [-1])
      target_shape = target.shape
  
      convert_to_dense_indicator = [True for _ in flat_sources]
      if keep_sparse_threshold >= 0:
          convert_to_dense_indicator = [
              s.shape[0] < keep_sparse_threshold for s in flat_sources
          ]
  
      def _unpack_indexed_slices(x, convert_to_dense):
          """Optionally unpacks `tf.IndexedSlices` to dict of three dense tensors."""
          if convert_to_dense or not isinstance(x, tf.IndexedSlices):
              # If x is kept as a tf.IndexedSlices, it will be converted to a dense
              # tensor in pfor.
              return x
          return {
              "indices": x.indices,
              "values": x.values,
              "dense_shape": x.dense_shape,
          }
  
      def loop_fn(i):
          with tape._ensure_recording():  # pylint: disable=protected-access
              y = tf.gather(target, i)
          g = tape.gradient(
              y,
              flat_sources,
              unconnected_gradients=unconnected_gradients,
          )
          g = tf.nest.map_structure(
              _unpack_indexed_slices, g, convert_to_dense_indicator
          )
          return g
  
      try:
          target_size = int(target.shape[0])
      except TypeError:
          # When the shape is unavailable, fall back to the tensor op.
          target_size = tf.shape(target)[0]
  
      try:
          output = control_flow_ops.pfor(loop_fn, target_size)
      except ValueError as err:
          raise ValueError(
              "Encountered an exception while vectorizing the jacobian computation. "
              "Consider using a non-vectorized optimizer instead."
          ) from err
      grads = []
      for i, out in enumerate(output):
          if out is not None:
              # Determines if the output is a unpacked tf.IndexedSlices. Since `sources`
              # has been flattened, it is only when the output is a dictionary (of three
              # dense tensors).
              if not isinstance(out, dict):
                  if tf.executing_eagerly():
                      out.set_shape(
                          target_shape.concatenate(
                              flat_sources[i].shape
                          )
                      )
                  grads.append((out, None, None))
              else:
                  # Remove duplicates at per-example level. This is for both correctness
                  # (when the same index gets gathered more than once in the same example)
                  # and efficiency (for the subsequent clipping). All the examples in
                  # the batch should have the same indices so it suffices to take the
                  # first row.
                  values, indices = _deduplicate_batch_indexed_slices(
                      out["values"], out["indices"][0]
                  )
                  # The `dense_shape` of all the examples are the same so we take the
                  # first row.
                  grads.append((values, indices, out["dense_shape"][0]))
          else:
              grads.append((None, None, None))
  
      if normalize or l2_norm_clip is not None:
          values, indices, dense_shape = zip(*grads)
          values = _batch_clip_by_global_norm(
              values, normalize, l2_norm_clip
          )
          grads = zip(values, indices, dense_shape)
  
      new_output = []
      for values, indices, dense_shape in grads:
          if values is None:
              new_output.append(None)
              continue
          if aggregate_method == "sum":
              values = tf.reduce_sum(values, axis=0)
          else:
              values = tf.reduce_mean(values, axis=0)
          if indices is None:
              new_output.append(values)
          else:
              new_output.append(
                  tf.IndexedSlices(
                      values=values,
                      indices=indices,
                      dense_shape=dense_shape,
                  )
              )
      return tf.nest.pack_sequence_as(sources, new_output)
  
imports: from typing import Any, Dict, List, Optional, Tuple, TypeVar, Union
  import tensorflow
  from tensorflow.python.ops.parallel_for import control_flow_ops
label_desc: Use image node_id 4 for calling a global function with example usage: clip_and_aggregate_gradients(tape, target, sources, unconnected_gradients, normalize, l2_norm_clip, aggregate_method, keep_sparse_threshold) and returns: tf, dict, g, x