code: def grad(
      outputs,
      inputs,
      grad_outputs=None,
      grad_inputs=None,
      set_grad=False,
      retain_grad=False,
      enable_double_backprop=False,
      loss_scale=None,
  ):
      """Computes the gradient of output variables w.r.t.\\  the input variables.
  
      This function implements the backpropagation algorithm. While
      :meth:`Variable.backward` also implements backprop, this function selects
      the smallest paths in the computational graph needed to compute the
      gradients w.r.t. inputs. The error is backpropagated only through these
      selected paths, which may reduce the overall computational cost.
  
      This function also differs from :meth:`Variable.backward` in the way to
      return the gradients; it directly returns the gradient variables as a list
      instead of setting gradients to the :attr:`Variable.grad_var` attribute of
      the original variable. It means users do not need to clear the gradient
      w.r.t. each variable before computing the gradient using this function.
      If ``set_grad`` option is set to ``True``, the computed gradient is also
      stored in the :attr:`Variable.grad_var` attribute of each variable, in
      which case any original value of :attr:`Variable.grad_var` will be updated
      even if it had already been set.
  
      Args:
          outputs (tuple or list of :class:`~chainer.Variable`):
              A sequence of output variables from which backprop starts.
          inputs (tuple or list of :class:`~chainer.Variable`):
              A sequence of input variables each of which this function computes
              the gradient w.r.t.
          grad_outputs (tuple or list of :class:`~chainer.Variable` or None):
              A sequence of variables that gives the initial value of each output
              gradient.
              If an element is set to ``None``, an array filled with 1 is used.
              If this argument itself is ``None``, it is treated as a sequence of
              ``None``\\ s.
          grad_inputs (tuple or list of :class:`~chainer.Variable` or None):
              A sequence of variables that gives the initial value of each input
              gradient. The gradients computed by the backprop
              algorithm are accumulated to them (not in-place). If an element
              is set to ``None``, the gradient is not accumulated to this value.
              If this argument itself is ``None``, it is treated as a sequence of
              ``None``\\ s.
          set_grad (bool): If it is ``True``, the :attr:`Variable.grad_var`
              attribute of each input variable is set to the corresponding
              computed gradient variable.
          retain_grad (bool): If it is ``True``, the gradients w.r.t. all the
              intermediate variables are stored in the :attr:`Variable.grad_var`
              attribute. In this case, the ``set_grad`` option is ignored.
          enable_double_backprop (bool): If it is ``True``, the computed
              gradients can be further backpropagated. Enabling it may increase
              the memory consumption (and possibly the computational time) to
              remember the intermediate gradient values for the second
              backpropagation.
          loss_scale (float): Loss scaling factor. Loss scaling is a useful
              technique to mitigate vanishing gradient issue that tends to happen
              when low precision data type like float16 is used during training.
              If you set loss scaling factor, gradients of loss values are to be
              multiplied by the factor before backprop starts. The factor is
              propagated to whole gradients in a computational graph along the
              backprop. The gradients of parameters are divided by the factor
              just before the parameters are to be updated.
  
      Returns:
          A list of gradient variables w.r.t. the inputs.
  
      """
      if not isinstance(outputs, (tuple, list)):
          raise TypeError(
              "outputs must be a tuple or a list, not {}.".format(
                  type(outputs)
              )
          )
      if not isinstance(inputs, (tuple, list)):
          raise TypeError(
              "inputs must be a tuple or a list, not {}.".format(
                  type(inputs)
              )
          )
      if grad_outputs is not None:
          if not isinstance(grad_outputs, (tuple, list)):
              raise TypeError(
                  "grad_outputs must be a tuple or a list or None, not {}.".format(
                      type(grad_outputs)
                  )
              )
          if len(outputs) != len(grad_outputs):
              raise ValueError(
                  "grad_outputs must be of the same length as outputs.\n"
                  "len(outputs) = {}, len(grad_outputs) = {}".format(
                      len(outputs), len(grad_outputs)
                  )
              )
      if grad_inputs is not None:
          if not isinstance(grad_inputs, (tuple, list)):
              raise TypeError(
                  "grad_inputs must be a tuple or a list or None, not {}.".format(
                      type(grad_inputs)
                  )
              )
          if len(inputs) != len(grad_inputs):
              raise ValueError(
                  "grad_inputs must be of the same length as inputs.\n"
                  "len(inputs) = {}, len(grad_inputs) = {}".format(
                      len(inputs), len(grad_inputs)
                  )
              )
  
      # Check if all the inputs are chainerx arrays and if so
      # Relies in chainerx.grad function
      n_chx_inputs = sum(
          [
              False if x is None else x._has_chainerx_array
              for x in inputs
          ]
      )
      if n_chx_inputs == len(inputs):
          # Need to access the arrays to invoke the chainer grad function
          if grad_outputs:
              grad_outputs_chx = [x._data[0] for x in grad_outputs]
          else:
              grad_outputs_chx = []
          outputs_chx = [x._data[0] for x in outputs]
          inputs_chx = [x._data[0] for x in inputs]
          # pybind has issues when converting opt<int> -> opt<float>
          if loss_scale is not None:
              loss_scale = float(loss_scale)
          grads = chainerx.grad(
              outputs_chx,
              inputs_chx,
              backprop_id=None,
              enable_double_backprop=enable_double_backprop,
              set_grad=set_grad,
              retain_grad=retain_grad,
              grad_outputs=grad_outputs_chx,
              loss_scale=loss_scale,
          )
  
          if grad_inputs:
              grads = [
                  g + gi._data[0] for g, gi in zip(grads, grad_inputs)
              ]
  
          return [
              variable.Variable(
                  g, requires_grad=g.is_backprop_required()
              )
              for g in grads
          ]
  
      elif n_chx_inputs > 0:
          raise TypeError(
              "Mixing chainerx and non-chainerx variables is not allowed"
          )
  
      for v in outputs:
          # Raise error here if v is created by Function.backward.
          # In such case, we don't know exact inputs of the creator.
          v.node._check_old_style_gradient()
  
      # The implementation consists of three steps.
  
      # 1. Backward enumeration: all the nodes reachable backward from the output
      #    nodes are enumerated. The forward direction links are collected in
      #    this step. Note that the variable nodes whose requires_grad is false
      #    are ignored and their creators are not searched.
      candidate_funcs = [
          v.creator_node for v in outputs if v.creator_node is not None
      ]
      visited_funcs = set()
      forward_graph = collections.defaultdict(list)
      while candidate_funcs:
          func = candidate_funcs.pop()
          if func in visited_funcs:
              continue
          visited_funcs.add(func)
          for x in func.inputs:
              # Raise error here if x is created by Function.backward.
              # In such case, we don't know exact inputs of the creator.
              x._check_old_style_gradient()
  
              if not x.requires_grad:
                  continue
              forward_graph[x].append(func)
              creator = x.creator_node
              if creator is not None and creator not in visited_funcs:
                  candidate_funcs.append(creator)
  
      # 2. Forward enumeration: all the nodes in the subgraph reachable from the
      #    input nodes are enumerated. The extracted (sub-)subgraph is the union
      #    of all paths that backpropagation will visit.
      candidate_vars = [x.node for x in inputs]
      visited_funcs = set()
      grad_required = set()
      while candidate_vars:
          x = candidate_vars.pop()
          grad_required.add(x)
          for func in forward_graph[x]:
              if func in visited_funcs:
                  continue
              visited_funcs.add(func)
              for y_ref in func.outputs:
                  y = y_ref()
                  if y is not None and y in forward_graph:
                      candidate_vars.append(y)
  
      # 3. Backpropagation: the backpropagation is executed along the
      #    (sub-)subgraph. It uses the topological order of the subgraph which is
      #    induced by the reversed order of function applications ("rank").
      grads = _backprop_utils.GradTable()
  
      # Initialize the gradient mapping.
      if grad_outputs is None:
          grad_outputs = (None,) * len(outputs)
      for y, gy in zip(outputs, grad_outputs):
          if gy is None:
              with chainer.using_device(y.device):
                  gy_data = y.device.xp.ones_like(y.array)
                  gy = variable.Variable(gy_data, requires_grad=False)
                  if loss_scale is not None:
                      gy.data *= loss_scale
          grads[y.node] = gy
  
      if grad_inputs is not None:
          for x, gx in zip(inputs, grad_inputs):
              if gx is not None:
                  grads[x.node] = gx
  
      # Backprop implementation. It edits grads which will only contain the
      # gradients w.r.t. the inputs.
      with chainer.using_config(
          "enable_backprop", enable_double_backprop
      ):
          ret_dict = _backprop(
              outputs,
              inputs,
              grad_required,
              retain_grad,
              grads,
              loss_scale,
          )
  
      # Extract the gradients w.r.t. the inputs and return them.
      ret = [ret_dict[x.node] for x in inputs]
      if set_grad:
          for x, gx in zip(inputs, ret):
              x.grad_var = gx
  
      return ret
  
imports: import collections
  import contextlib
  import heapq
  import inspect
  import traceback
  import weakref
  import six
  import chainer
  from chainer import _backprop_utils
  from chainer import backend
  from chainer.backends import cuda
  from chainer import configuration
  from chainer import function_hook
  from chainer.graph_optimizations.static_graph_utilities import static_forward_optimizations
  from chainer import utils
  from chainer.utils import type_check
  from chainer import variable
  import chainerx
label_desc: Use image node_id 2 for calling a global function with example usage: grad(outputs, inputs, grad_outputs, grad_inputs, set_grad, retain_grad, enable_double_backprop, loss_scale) and returns: ret, unknown