backward.py 81.7 KB
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#   Copyright (c) 2018 PaddlePaddle Authors. All Rights Reserved.
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
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#
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#     http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

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from __future__ import print_function
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from .proto import framework_pb2
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from paddle.fluid import framework as framework
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from . import core
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import collections
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import copy
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import six
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import logging
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from .. import compat as cpt
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from . import unique_name
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from . import log_helper
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import paddle.fluid
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from .data_feeder import check_type
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__all__ = [
    'append_backward',
    'gradients',
]

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_logger = log_helper.get_logger(
    __name__, logging.INFO, fmt='%(asctime)s-%(levelname)s: %(message)s')

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class ProgramStats(object):
    def __init__(self, block, ops):
        self.block = block
        self.ops = ops
        self.op_deps = {}  # op-> in_ops, out_ops
        self.var_op_deps = {}  # var as input op, var as output op

    def get_input_nodes(self):
        input_names = []
        for name in self.var_op_deps:
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            if len(self.var_op_deps[name]["var_as_output_ops"]) == 0 and \
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                    len(self.var_op_deps[name]["var_as_input_ops"]) > 0:
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                if self.block.var(name).persistable:
                    continue
                input_names.append(name)
        for op in self.ops:
            if op.desc.type() == "read":
                input_names.extend(op.desc.output_arg_names())
        return input_names

    def get_reserved_vars(self):
        var_name = []
        for op in self.ops:
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            if op.desc.type() == "seed":
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                var_name.extend(op.desc.output_arg_names())
        return var_name

    def get_out_of_subgraph_vars(self, begin_op_idx, end_op_idx):
        var_name = []
        for i in range(begin_op_idx, end_op_idx, 1):
            for name in self.ops[i].desc.output_arg_names():
                if name in self.var_op_deps:
                    for idx in self.var_op_deps[name]["var_as_input_ops"]:
                        if idx >= end_op_idx:
                            var_name.append(name)
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            for name in self.ops[i].desc.input_arg_names():
                if name in self.var_op_deps:
                    for idx in self.var_op_deps[name]["var_as_output_ops"]:
                        if idx < begin_op_idx:
                            var_name.append(name)
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        return var_name

    def is_subgraph(self, var_group1, var_group2):
        # should traverse from var_group1 to var_group2
        # max op idx in var_group2
        # min op idx in var_group1
        min_op_idx = len(self.ops)
        max_op_idx = -1
        for name in var_group1:
            if name not in self.var_op_deps:
                return False, min_op_idx, max_op_idx
        for name in var_group2:
            if name not in self.var_op_deps:
                return False, min_op_idx, max_op_idx
        for name in var_group1:
            op_idx = self.var_op_deps[name]["var_as_input_ops"]
            for idx in op_idx:
                min_op_idx = min(min_op_idx, idx)
        for name in var_group2:
            op_idx = self.var_op_deps[name]["var_as_output_ops"]
            for idx in op_idx:
                max_op_idx = max(max_op_idx, idx)
        if min_op_idx >= max_op_idx:
            return False, min_op_idx, max_op_idx
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        return True, min_op_idx, max_op_idx

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    def _update_segment_start(self, min_idx, pre_segment_end_idx):
        """
        persist vars of amp-related cast should be included in recompute segment
        """

        def is_amp_cast(op):
            return op.desc.type() == 'cast' and self.block.var(
                op.desc.input_arg_names()[0]).persistable

        idx_ = min_idx - 1
        updated_min_idx = min_idx
        while idx_ > pre_segment_end_idx:
            if is_amp_cast(self.ops[idx_]):
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                _logger.info("found amp-cast op: {}, : {}".format(self.ops[
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                    idx_].desc.type(), self.ops[idx_].desc.input_arg_names()[
                        0]))
                updated_min_idx = idx_
                idx_ -= 1
            else:
                break

        return updated_min_idx

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    def build_stats(self):
        for i, op in enumerate(self.ops):
            self.op_deps[i] = {"in_ops": [], "out_ops": []}
            for j, name in enumerate(op.desc.input_arg_names()):
                if name in self.var_op_deps:
                    self.op_deps[i]["in_ops"].extend(self.var_op_deps[name][
                        "var_as_output_ops"])
            for j, name in enumerate(op.desc.input_arg_names()):
                if name in self.var_op_deps:
                    self.var_op_deps[name]["var_as_input_ops"].extend([i])
                else:
                    self.var_op_deps[name] = {}
                    self.var_op_deps[name]["var_as_input_ops"] = [i]
                    self.var_op_deps[name]["var_as_output_ops"] = []

            for j, name in enumerate(op.desc.output_arg_names()):
                if name in self.var_op_deps:
                    self.var_op_deps[name]["var_as_output_ops"].extend([i])
                else:
                    self.var_op_deps[name] = {}
                    self.var_op_deps[name]["var_as_input_ops"] = []
                    self.var_op_deps[name]["var_as_output_ops"] = [i]

            for op_idx in self.op_deps[i]["in_ops"]:
                self.op_deps[op_idx]["out_ops"].extend([i])

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    def sort_checkpoints(self, checkpoints_name):
        sorted_checkpoints = []
        for name in checkpoints_name:
            if name not in self.var_op_deps:
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                _logger.info(
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                    "Recompute Optimizer: deleted %s from checkpoints, because it is not used in paddle program."
                    % name)
            elif self.var_op_deps[name]["var_as_output_ops"] == []:
                # input nodes
                sorted_checkpoints.append((name, -1))
            else:
                sorted_checkpoints.append(
                    (name, max(self.var_op_deps[name]["var_as_output_ops"])))
        sorted_checkpoints = sorted(sorted_checkpoints, key=lambda x: x[1])
        return [x[0] for x in sorted_checkpoints]

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    def modify_forward_desc_for_recompute(self):
        op_types = [op.desc.type() for op in self.ops]
        if "dropout" not in op_types:
            return

        op_idx = 0
        while (op_idx < len(self.ops)):
            op = self.ops[op_idx]
            if op.desc.type() != "dropout":
                op_idx += 1
                continue
            # add a seed op so that the two dropout op can generate same output
            op_unique_name = unique_name.generate("seed")
            var_unique_name = unique_name.generate_with_ignorable_key(".".join(
                [op_unique_name, 'tmp']))
            added_var = self.block.create_var(
                name=var_unique_name,
                dtype='int32',
                type=core.VarDesc.VarType.LOD_TENSOR,
                persistable=False,
                stop_gradient=False)
            seed = 0 if op.attr("fix_seed") is False else int(op.attr("seed"))
            added_op = self.block._insert_op(
                index=op.idx,
                type='seed',
                inputs={},
                outputs={'Out': [added_var]},
                attrs={'seed': seed})
            self.ops.insert(op_idx, added_op)
            # modify dropout op desc so that it accept a seed var as input
            op.desc.set_input("Seed", [var_unique_name])
            op.desc.remove_attr("fix_seed")
            op.desc.remove_attr("seed")
            self.block._sync_with_cpp()
            op_idx += 2

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def _pretty_op_desc_(op_desc, prefix):
    out_s = "%s\tname:[%s]\n%s    \tinputs:[%s]\n%s    \toutputs:[%s]" % \
            (prefix + "_op", str(op_desc.type()), prefix + "_input", " ".join(op_desc.input_arg_names()),
             prefix + "_output", " ".join(op_desc.output_arg_names()))
    return out_s


def _add_needed_descs_to_block(descs, block, main_block, in_memory_vars):
    if len(descs) == 0:
        return []
    result_descs = []
    op_role_attr_name = \
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        core.op_proto_and_checker_maker.kOpRoleAttrName()
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    backward = core.op_proto_and_checker_maker.OpRole.Backward
    for desc in descs:
        if isinstance(desc, framework.Operator):
            desc = desc.desc
        if isinstance(desc, tuple):
            desc = desc[0]
        is_needed = False
        for name in desc.output_arg_names():
            if main_block.has_var(name) and main_block.var(name).persistable:
                continue
            if name not in in_memory_vars:
                is_needed = True
        if is_needed:
            new_op_desc = block.desc.append_op()
            new_op_desc.copy_from(desc)
            new_op_desc._set_attr(op_role_attr_name, backward)
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            if desc.has_attr('op_device'):
                new_op_desc._set_attr('op_device', desc.attr('op_device'))
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            result_descs.append(new_op_desc)
    return result_descs


def _add_descs_to_block(descs, block):
    if len(descs) == 0:
        return []
    result_descs = []
    op_role_attr_name = \
        core.op_proto_and_checker_maker.kOpRoleAttrName()
    backward = core.op_proto_and_checker_maker.OpRole.Backward
    for desc in descs:
        if isinstance(desc, framework.Operator):
            desc = desc.desc
        if isinstance(desc, tuple):
            desc = desc[0]
        new_op_desc = block.desc.append_op()
        new_op_desc.copy_from(desc)
        new_op_desc._set_attr(op_role_attr_name, backward)
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        if desc.has_attr('op_device'):
            new_op_desc._set_attr('op_device', desc.attr('op_device'))
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        result_descs.append(new_op_desc)
    return result_descs


def _find_loss_op_(loss):
    for op in reversed(loss.block.ops):
        assert isinstance(op, framework.Operator)
        if len(op.output_arg_names) == 1 and op.output_arg_names[
                0] == loss.name:
            loss.op = op
            break
    if loss.op is None:
        raise ValueError("loss.op is None. Should not happend")
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def _rename_arg_(op_descs, old_name, new_name, begin_idx=None, end_idx=None):
    """
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    Traverse all ops in op_descs[begin_idx : end_idx],
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    if any op has inputs/outputs named "old_name", rename it as 'new_name'
    """
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    if begin_idx is None:
        begin_idx = 0
    if end_idx is None:
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        end_idx = len(op_descs)
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    if isinstance(op_descs, (list, tuple)):
        for i in range(begin_idx, end_idx):
            op_desc = op_descs[i]
            if isinstance(op_desc, tuple):
                op_desc = op_desc[0]
            op_desc._rename_input(old_name, new_name)
            op_desc._rename_output(old_name, new_name)
    if isinstance(op_descs, collections.OrderedDict):
        for key, value in op_descs.items():
            if isinstance(value, (list, tuple)):
                for op_desc in value:
                    op_desc._rename_input(old_name, new_name)
                    op_desc._rename_output(old_name, new_name)
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def _create_op_desc_(op_type, inputs, outputs, attrs):
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    """
    Create a C++ OpDesc object with specified inputs, outputs and attributes.
    """
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    op_desc = core.OpDesc()
    op_desc.set_type(op_type)
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    for para, args in six.iteritems(inputs):
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        op_desc.set_input(
            para,
            list(
                map(lambda arg: arg.decode() if isinstance(arg, six.binary_type) else arg,
                    args)))
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    for para, args in six.iteritems(outputs):
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        op_desc.set_output(
            para,
            list(
                map(lambda arg: arg.decode() if isinstance(arg, six.binary_type) else arg,
                    args)))
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    op_role_attr_name = core.op_proto_and_checker_maker.kOpRoleAttrName()
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    op_device_attr_name = core.op_proto_and_checker_maker.kOpDeviceAttrName()
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    if op_role_attr_name not in attrs:
        attrs[
            op_role_attr_name] = core.op_proto_and_checker_maker.OpRole.Backward
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    if op_device_attr_name not in attrs:
        attrs[op_device_attr_name] = ""
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    for name, val in six.iteritems(attrs):
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        if isinstance(val, framework.Block):
            op_desc.set_block_attr(name, val.desc)
        else:
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            op_desc._set_attr(name, val)
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    return op_desc


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def _create_loss_op_desc_(loss):
    op_desc = _create_op_desc_(
        "fill_constant", {}, {"Out": [_append_grad_suffix_(loss.name)]}, {
            "shape": [1],
            "value": 1.0,
            "dtype": loss.dtype,
            "force_cpu": False,
            core.op_proto_and_checker_maker.kOpRoleAttrName():
            int(core.op_proto_and_checker_maker.OpRole.Backward) |
            int(core.op_proto_and_checker_maker.OpRole.Loss),
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            core.op_proto_and_checker_maker.kOpDeviceAttrName():
            loss.op.attr(core.op_proto_and_checker_maker.kOpDeviceAttrName())
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        })
    return op_desc


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def _infer_var_data_type_shape_(grad_var_name, block):
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    """
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    Infer the data type and shape of given grad variable
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    """
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    grad_var = block.desc.find_var(cpt.to_bytes(grad_var_name))
    fwd_name = _strip_grad_suffix_(grad_var_name)
    if block.desc.has_var_recursive(cpt.to_bytes(fwd_name)):
        fwd_var = block.desc.find_var_recursive(cpt.to_bytes(fwd_name))
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        grad_var.set_dtype(fwd_var.dtype())
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        grad_var.set_shape(fwd_var.shape())
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    else:
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        grad_var.set_dtype(core.VarDesc.VarType.FP32)
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def _all_in_set_(cands, s):
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    """
    Test if all elements of 'cands' are in set 's'
    """
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    if len(cands) == 0:
        return False
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    for c in cands:
        if not c in s:
            return False
    return True


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def _some_in_set_(cands, s):
    """
    Test if some elements of 'cands' are in set 's'
    """
    if len(cands) == 0:
        return False
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    literal_set = cpt.to_text(s)
    literal_cands = cpt.to_text(cands)
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    for c in literal_cands:
        if c in literal_set:
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            return True
    return False


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def _strip_grad_suffix_(name):
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    """
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    Strip the grad suffix from the given variable name
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    e.g. x@GRAD ==> x
         y@GRAD@RENAME@1 ==> y
    """
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    name = cpt.to_text(name)
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    pos = name.find(core.grad_var_suffix())
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    return name[:pos] if pos != -1 else name
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def _append_grad_suffix_(name):
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    """
    Append grad suffix to the given variable name
    e.g. x ==> x@GRAD
    """
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    return cpt.to_text(name) + core.grad_var_suffix()
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def _accumulate_gradients_by_sum_op_(var_name,
                                     renamed_vars,
                                     pending_sum_ops,
                                     op_idx,
                                     op_device=""):
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    """
    Use sum op to accumulate_gradients, the gradients are stored in renamed_vars.
    """
    if op_idx not in pending_sum_ops.keys():
        pending_sum_ops[op_idx] = []
    pending_sum_ops[op_idx].append(
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        _create_op_desc_("sum", {"X": renamed_vars[var_name]}, {
            "Out": [var_name]
        }, {"use_mkldnn": False,
            "op_device": op_device}))
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    renamed_vars[var_name] = [var_name]


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def _accumulate_gradients_by_add_ops_(var_name,
                                      renamed_vars,
                                      pending_sum_ops,
                                      op_idx,
                                      op_device=""):
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    """
    Use several inplace add op to accumulate_gradients, the gradients are stored in renamed_vars.
    """
    if op_idx not in pending_sum_ops.keys():
        pending_sum_ops[op_idx] = []
    out_name = renamed_vars[var_name][0]
    for i in range(1, len(renamed_vars[var_name])):
        x_name = out_name
        y_name = renamed_vars[var_name][i]
        if i != len(renamed_vars[var_name]) - 1:
            out_name = var_name + '@ADD@' + str(i)
        else:
            out_name = var_name
        pending_sum_ops[op_idx].append(
            _create_op_desc_("grad_add", {"X": [x_name],
                                          "Y": [y_name]}, {"Out": [out_name]},
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                             {"use_mkldnn": False,
                              "op_device": op_device}))
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    renamed_vars[var_name] = [var_name]


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def _addup_repetitive_outputs_(op_descs, block_idx):
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    """
    In backward part, an variable may be the output of more than one ops.
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    And one op may yield its multiple outputs to the same variable.
    In these cases, the variable should be the accumulation of all the outputs.
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    `sum_op`s are added to implement the accumulate.
    """
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    _MAX_ADD_NUM_ = core.globals()['FLAGS_max_inplace_grad_add']
    #pending_sum_ops = []
    pending_sum_ops = collections.OrderedDict()
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    var_rename_count = collections.defaultdict(int)
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    renamed_vars = collections.defaultdict(list)
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    renamed_var_start_idx = collections.defaultdict(list)
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    for idx, op_desc in enumerate(op_descs):
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        op_device_attr_name = core.op_proto_and_checker_maker.kOpDeviceAttrName(
        )
        op_device = ""
        if op_desc.has_attr(op_device_attr_name):
            op_device = op_desc.attr(op_device_attr_name)
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        for var_name in op_desc.input_arg_names():
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            if "@GRAD" not in var_name:
                continue
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            if len(renamed_vars[var_name]) > 1:
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                if len(renamed_vars[var_name]) > _MAX_ADD_NUM_:
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                    _accumulate_gradients_by_sum_op_(
                        var_name, renamed_vars, pending_sum_ops, idx, op_device)
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                else:
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                    _accumulate_gradients_by_add_ops_(
                        var_name, renamed_vars, pending_sum_ops, idx, op_device)
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        for param_idx, param_name in enumerate(op_desc.output_names()):
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            arg_names = op_desc.output(param_name)
            for arg_idx, var_name in enumerate(arg_names):
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                if "@GRAD" not in var_name:
                    continue
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                # if "@RENAME@" in var_name:
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                #    continue
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                if var_name == core.empty_var_name(
                ) or var_name in op_desc.input_arg_names():
                    # empty variable or inplace op
                    continue
                if len(renamed_vars[var_name]) == 0:
                    # it's the first time we get the variable
                    renamed_vars[var_name] = [var_name]
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                    renamed_var_start_idx[var_name] = idx
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                else:
                    if len(renamed_vars[var_name]) == 1:
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                        new_name = var_name + "@RENAME@block" + str(block_idx) + "@" + \
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                            str(var_rename_count[var_name])
                        var_rename_count[var_name] += 1
                        # rename original var_name
                        renamed_vars[var_name][0] = new_name
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                        # before change: _rename_arg_(op_descs, var_name,
                        #                             new_name, 0, idx)
                        # rename arg from idx of the first appearance
                        # in backward, not always from 0
                        _rename_arg_(op_descs, var_name, new_name,
                                     renamed_var_start_idx[var_name], idx)
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                        _rename_arg_(pending_sum_ops, var_name, new_name)

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                        for p in op_desc.output_names()[:param_idx]:
                            p_arg_names = op_desc.output(p)
                            if var_name in p_arg_names:
                                op_desc.set_output(p, [
                                    new_name if x == var_name else x
                                    for x in p_arg_names
                                ])

                        arg_names = [
                            new_name if x == var_name else x
                            for x in arg_names[:arg_idx]
                        ] + arg_names[arg_idx:]

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                    new_name = var_name + "@RENAME@block" + str(block_idx) + "@" + \
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                        str(var_rename_count[var_name])
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                    var_rename_count[var_name] += 1
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                    arg_names[arg_idx] = new_name
                    op_desc.set_output(param_name, arg_names)
                    renamed_vars[var_name].append(new_name)
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    for var_name, inputs in six.iteritems(renamed_vars):
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        if len(renamed_vars[var_name]) > 1:
            if len(renamed_vars[var_name]) > _MAX_ADD_NUM_:
                _accumulate_gradients_by_sum_op_(var_name, renamed_vars,
                                                 pending_sum_ops, len(op_descs))
            else:
                _accumulate_gradients_by_add_ops_(var_name, renamed_vars,
                                                  pending_sum_ops,
                                                  len(op_descs))

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    # sum_op descs are sorted according to their insert position
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    for key, value in collections.OrderedDict(
            reversed(list(pending_sum_ops.items()))).items():

        # NOTE(zhiqiu): Since reversed, the idx of op_descs to be inserted will remains correct.
        # For example, [0, 1, 2], and we want to insert 'a' at idx 1, 'b' at idx 2, and the expected result is [0, 1, 'a', 2, 'b'].
        # If reversed, we first insert 'b' at idx 2, it becomes [0, 1, 2, 'b'], and then insert 'a' at idx 1, it becomes [0, 1, 'a', 2, 'b'].
        # If not reverse, we first insert 'a' at idx 1, it becomes [0, 1, 'a', 2], and then insert 'b' at idx 2, it becomes [0, 1, 'a', 'b', 2].
        idx = key
        for i, op in enumerate(value):
            op_descs.insert(idx + i, op)
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    return op_descs


def _remove_no_grad_branch_(op_descs, no_grad_set):
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    """
    Remove unnecessary grad ops
    A grad op can be removed in two cases:
        1. all outputs of the grad op are in 'no_grad_set'
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        2. all grad inputs of the grad op are in 'no_grad_set'
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    """
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    def _op_can_be_removed_(op_desc, no_grad_set):
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        out_arg_names = op_desc.output_arg_names()
        if len(out_arg_names) == 0 or _all_in_set_(out_arg_names, no_grad_set):
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            return True
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        if _all_in_set_([
                name for name in op_desc.input_arg_names()
                if name.find(core.grad_var_suffix()) != -1
        ], no_grad_set):
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            no_grad_set.update(out_arg_names)
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            return True
        return False

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    # Remove ops whose outputs are all in no_grad_dict
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    op_descs = [
        op_desc for op_desc in op_descs
        if not _op_can_be_removed_(op_desc, no_grad_set)
    ]
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    # Insert fill_zeros_like_op
    to_insert = []
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    for idx, op_desc in enumerate(op_descs):
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        for arg in op_desc.input_arg_names():
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            # arg is a gradient var name and arg should not have gradient
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            if core.grad_var_suffix() in arg and arg in no_grad_set:
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                x_in = _strip_grad_suffix_(arg)
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                # the reason should be: arg can be input of another grad op
                # and the op is a not-to-remove op
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                to_insert.append((_create_op_desc_(
                    "fill_zeros_like", {"X": [x_in]}, {"Out": [arg]}, {}), idx))
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    list([op_descs.insert(p[1], p[0]) for p in reversed(to_insert)])
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    return op_descs


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def _find_not_need_ops(grad_op_descs, forward_ops, input_grad_names_set):
    """
    Pruning Program with Structural Analysis Method of Computational Graph.
    The nodes of the computational graph composed of backward OPS should be
    interconnected. If there are unconnected sub-graphs in the computational graph,
    these sub-graphs should be cut off.

    Args:
        grad_op_descs(list[core.OpDesc]): The candidate backward OpDescs.
        forward_ops(list[Operator]): The forward ops.
        input_grad_names_set(set): this set is used to store the gradients' name
            which is generated by backward ops, and input_grad_names_set can help
            to prune the unnecessary backward ops.

    Return:
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        (set[core.OpDesc]): A set of OpDescs which should be pruned.
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    """

    class Var(object):
        def __init__(self, var_name):
            self.var_name = var_name
            self.gen_op = None
            self.pendding_ops = []

        def set_gen_op(self, gen_op):
            assert isinstance(gen_op, Op)
            assert self.gen_op is None
            self.gen_op = gen_op

        def add_pending_op(self, op):
            assert isinstance(op, Op)
            self.pendding_ops.append(op)

    class Op(object):
        def __init__(self, op_desc):
            self.op_desc = op_desc
            self.inputs = []
            self.outputs = []

        def insert_input(self, var):
            assert isinstance(var, Var)
            self.inputs.append(var)

        def insert_output(self, var):
            assert isinstance(var, Var)
            self.outputs.append(var)

    var_versions = dict()

    def _create_node(name):
        if name not in var_versions.keys():
            var_versions[name] = [Var(name)]
        else:
            var_versions[name].append(Var(name))
        return var_versions[name][-1]

    def _create_or_get_last_version_node(name):
        if name not in var_versions.keys():
            var_versions[name] = [Var(name)]
        return var_versions[name][-1]

    def _create_op_node(op_desc):
        op_node = Op(op_desc)
        for input in op_desc.input_arg_names():
            var = _create_or_get_last_version_node(name=input)
            var.add_pending_op(op_node)
            op_node.insert_input(var)
        for output in op_desc.output_arg_names():
            var = _create_node(name=output)
            var.set_gen_op(op_node)
            op_node.insert_output(var)
        return op_node

    # Record the forward vars
    forward_vars_set = set() if input_grad_names_set is None else set(
        input_grad_names_set)
    for op in forward_ops:
        forward_vars_set.update(op.desc.input_arg_names())
        forward_vars_set.update(op.desc.output_arg_names())

    # Record the vars which are created during backward and is not generated by op.
    backward_vars_set = set()
    # special_op_nodes is the candidate sub-graph head node.
    special_op_nodes = set()
    for op_desc in grad_op_descs:
        input_set = set(op_desc.input_arg_names())
        # The new_vars are created during backward and is not generated by op.
        new_vars = input_set - forward_vars_set - backward_vars_set
        backward_vars_set.update(op_desc.output_arg_names())

        op_node = _create_op_node(op_desc)
        if len(new_vars) == len(input_set):
            special_op_nodes.add(op_node)

    not_need_op_descs = []
    # Start traversing all candidate sub-graph headers to check whether
    # they are connected to backward computational graphs, and if they are
    # not, list them in not_need_op_descs
    for special_op_node in special_op_nodes:
        op_list = [special_op_node]
        ready_vars = set(special_op_node.inputs)
        remove_ops = True
        candidate_ops = [special_op_node]
        while len(candidate_ops) > 0:
            op_node = candidate_ops.pop(0)
            if _all_in_set_(op_node.inputs, ready_vars):
                for out_var in op_node.outputs:
                    candidate_ops.extend(out_var.pendding_ops)
                    op_list.extend(out_var.pendding_ops)
                ready_vars.update(op_node.outputs)
            else:
                remove_ops = False
                break
        if remove_ops:
            not_need_op_descs.extend([node.op_desc for node in op_list])
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    not_need_op_descs_set = set(not_need_op_descs)
    grad_op_descs_set = set(grad_op_descs)
    # If a backward computational graph is simply one sub-graph header, the
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    # not_need_op_descs will be whole graph, this IF clause avoids it.
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    if grad_op_descs_set == not_need_op_descs_set:
        return set()
    return not_need_op_descs_set
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def serialize_op_decs(op_desc):
    protostr = op_desc.serialize_to_string()
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    proto = framework_pb2.OpDesc.FromString(six.binary_type(protostr))
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    return proto.__str__()


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def _append_backward_ops_with_checkpoints_(
        block, ops, target_block, no_grad_dict, grad_to_var, checkpoints):
    """
    Create grad ops with forward ops, and insert them into given block

    Args:
        block(Block): the block where forward ops are
        ops(Op): the forward operators whose forward recomputation backward ops need to be added
        target_block(Block): the block which is going to hold new generated grad ops
        no_grad_dict(dict):
            key(int) block index
            val(str): corresponding forward variable name
        checkpoints: variables that a user defined as checkpoint for forward recomputation

    Algorithms:
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        0) deal with forward recomputing program descs
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        1) find ops between checkpoints, i.e. recompute_segments
        2) go through all forward ops and induct all variables that will be hold in memory
            a. variables that are used across segments will be held in memory
            b. output of dropout op will be held in memory
            c. input variables will be held in memory
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        3) go through each recompute_segments, add backward ops with forward recomputation
            a. add ops in current recompute_segment as forward recomputation ops
            b. rename all non-checkpoint variables in recomputation ops
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            c. add backward ops of current recomputation ops
            d. add sum op for repetitive_outputs
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        4) remove no grad branch as it is in _remove_no_grad_branch_
        5) Note1: all appended ops' OpRole are Backward
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        6) Note2: all variables with new name should be returned so that _append_backward_vars_ can be called
        7) Note3: current forward recomputation backpropagation does not handle programs with subblock
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    """
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    checkpoints_name = [x.name for x in checkpoints]
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    checkpoints_name = list(set(checkpoints_name))
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    local_block = block.program._create_block()
    buffer_block = block.program._create_block()
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    # 0) deal with forward recomputing program descs
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    program_stat = ProgramStats(block, ops)
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    program_stat.modify_forward_desc_for_recompute()
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    program_stat.build_stats()
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    # 1) find ops between checkpoints, i.e. recompute_segments
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    checkpoints_name = program_stat.sort_checkpoints(checkpoints_name)
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    segments = []

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    if len(checkpoints_name) == 1:
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        # only one checkpoint
        max_op_idx = -1
        var_group = [checkpoints_name[0]]
        for name in var_group:
            if name not in program_stat.var_op_deps:
                break
            op_idx = program_stat.var_op_deps[name]["var_as_output_ops"]
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            # only count the last generate op
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            for idx in op_idx:
                max_op_idx = max(max_op_idx, idx)
        if max_op_idx > 0:
            segments.append([0, max_op_idx + 1])
    else:
        start_idx = 0
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        pre_segment_end_idx = -1
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        while True:
            if start_idx >= len(checkpoints_name) - 1:
                break
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            # min_idx: checkpoint_1' s input op
            # max_idx: checkpoint_2' s output op
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            flag, min_idx, max_idx = program_stat.is_subgraph(
                [checkpoints_name[start_idx]],
                [checkpoints_name[start_idx + 1]])
            if flag:
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                # max_idx + 1 since the exact and used segment end idx is max_idx
                min_idx = program_stat._update_segment_start(
                    min_idx, pre_segment_end_idx)
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                segments.append([min_idx, max_idx + 1])
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            else:
                _logger.info("Could not recompute op range [{}] - [{}] ".format(
                    min_idx, max_idx + 1))
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            start_idx += 1

    if segments != [] and segments[0][0] != 0:
        recompute_segments = [[0, segments[0][0]]] + segments
    else:
        recompute_segments = segments
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    for i, (idx1, idx2) in enumerate(recompute_segments):
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        _logger.info("recompute segment[{}]".format(i))
        _logger.info("segment start op: [{}]: [{}]".format(ops[idx1].desc.type(
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        ), ops[idx1].desc.input_arg_names()))
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        _logger.info("segment end op: [{}]: [{}]".format(ops[
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            idx2 - 1].desc.type(), ops[idx2 - 1].desc.input_arg_names()))
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        _logger.info("recompute segment[{}]".format(i))
        _logger.info("segment start op: [{}]: [{}]".format(ops[idx1].desc.type(
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        ), ops[idx1].desc.input_arg_names()))
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        _logger.info("segment end op: [{}]: [{}]".format(ops[
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            idx2 - 1].desc.type(), ops[idx2 - 1].desc.input_arg_names()))

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    # 2) go through all forward ops and induct all variables that will be hold in memory
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    vars_should_be_hold = []
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    # a. variables that are used across segments will be held in memory
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    for segment in recompute_segments:
        vars_should_be_hold.extend(
            program_stat.get_out_of_subgraph_vars(segment[0], segment[1]))
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    cross_vars = set(vars_should_be_hold) - set(checkpoints_name)
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    _logger.info("found [{}] vars which cross recompute segment: [{}], better checkpoints might be set to reduce those vars".format( \
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    len(cross_vars), cross_vars))

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    # b. output of seed op should be kept in memory
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    vars_should_be_hold.extend(program_stat.get_reserved_vars())
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    # c. input variables are checkpoints
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    vars_should_be_hold.extend(program_stat.get_input_nodes())
    vars_should_be_hold = list(set(vars_should_be_hold))

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    # 3) go through each recompute_segments, add backward ops with forward recomputation
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    grad_op_descs = []
    var_name_dict = {}

    vars_in_memory = vars_should_be_hold + checkpoints_name

    max_calculated_op_position = len(ops)
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    device_attr_name = core.op_proto_and_checker_maker.kOpDeviceAttrName()
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    if recompute_segments == []:
        gap_ops = ops[0:max_calculated_op_position]
        for op in reversed(gap_ops):
            if op.has_attr("sub_block"):
                raise Exception("Recompute don't support ops with sub_block"
                                "invoke op: %s" %
                                _pretty_op_desc_(op.desc, "with_sub_block"))
            grad_op_desc, op_grad_to_var = core.get_grad_op_desc(
                op.desc, cpt.to_text(no_grad_dict[block.idx]), [])
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            # Set device for grad_op according to forward Op
            if op.desc.has_attr(device_attr_name):
                op_device = op.desc.attr(device_attr_name)
                for op_desc in grad_op_desc:
                    op_desc._set_attr(device_attr_name, op_device)
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            added_descs = _add_descs_to_block(grad_op_desc, local_block)
            grad_op_descs.extend(added_descs)
            grad_to_var.update(op_grad_to_var)

    for i, segment in enumerate(recompute_segments[::-1]):
        gap_ops = ops[segment[1]:max_calculated_op_position]
        max_calculated_op_position = segment[0]
        for op in reversed(gap_ops):
            if op.has_attr("sub_block"):
                raise Exception("Recompute don't support ops with sub_block"
                                "invoke op: %s" %
                                _pretty_op_desc_(op.desc, "with_sub_block"))
            grad_op_desc, op_grad_to_var = core.get_grad_op_desc(
                op.desc, cpt.to_text(no_grad_dict[block.idx]), [])
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            # Set device for grad_op according to forward Op
            if op.desc.has_attr(device_attr_name):
                op_device = op.desc.attr(device_attr_name)
                for op_desc in grad_op_desc:
                    op_desc._set_attr(device_attr_name, op_device)
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            added_descs = _add_descs_to_block(grad_op_desc, local_block)
            grad_op_descs.extend(added_descs)
            grad_to_var.update(op_grad_to_var)

        ff_ops = ops[segment[0]:segment[1]]
        var_suffix = ".subprog_%d" % i

        for op in ff_ops:
            if op.has_attr("sub_block"):
                raise Exception("Recompute don't support ops with sub_block"
                                "invoke op: %s" %
                                _pretty_op_desc_(op.desc, "with_sub_block"))
            input_and_output_names = []
            input_and_output_names.extend(op.desc.input_arg_names())
            input_and_output_names.extend(op.desc.output_arg_names())
            for name in input_and_output_names:
                if block.var(name).persistable or name in checkpoints_name:
                    continue
                if name in vars_should_be_hold:
                    continue
                if name not in var_name_dict:
                    var_name_dict[name] = name + var_suffix
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                    # we should create the rename var in subprog, otherwise its VarType will be BOOL
                    ref_var = block.program.global_block().var(name)
                    block.create_var(
                        name=var_name_dict[name],
                        shape=ref_var.shape,
                        dtype=ref_var.dtype,
                        type=ref_var.type,
                        persistable=ref_var.persistable,
                        stop_gradient=ref_var.stop_gradient)

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        # 3.a. add ops in current recompute_segment as forward recomputation ops
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        buffer_descs = _add_needed_descs_to_block(ff_ops, buffer_block, block,
                                                  vars_in_memory)
        added_descs = _add_descs_to_block(ff_ops, local_block)

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        # 3.b. rename all non-checkpoint variables in recomputation ops
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        for key in var_name_dict:
            _rename_arg_(buffer_descs, key, var_name_dict[key])

        # added_descs should be in grad_op_descs because it is backward op desc
        grad_op_descs.extend(buffer_descs)

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        # 3.c. add backward ops for all ops in current segment 
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        for op_desc in reversed(added_descs):
            grad_op_desc, op_grad_to_var = core.get_grad_op_desc(
                op_desc, cpt.to_text(no_grad_dict[block.idx]), [])
            for key in var_name_dict:
                _rename_arg_(grad_op_desc, key, var_name_dict[key])
            grad_op_descs.extend(grad_op_desc)
            grad_to_var.update(op_grad_to_var)

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    # 3.d. add sum op for repetitive_outputs
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    grad_op_descs = _addup_repetitive_outputs_(grad_op_descs, block.idx)
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    # 4) remove no grad branch as it is in _remove_no_grad_branch_
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    grad_op_descs = _remove_no_grad_branch_(grad_op_descs,
                                            no_grad_dict[block.idx])
    added_descs = _add_descs_to_block(grad_op_descs, target_block)
    return program_stat, checkpoints_name, vars_should_be_hold, recompute_segments


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def _get_sub_block_path(sub_block,
                        sub_block_op_desc,
                        no_grad_set,
                        op_path_dict,
                        sub_block_target_names=None):
952 953
    """
    Get output vars in subblock which will be assigned to parent block.
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    It is used to find the grad path in subblock.

    Args:
        sub_block(Block): The sub-block in which to get op path.
        sub_block_op_desc: The op desc of the sub-block op such as 'while', 'conditional_block' and 'recurrent'.
        no_grad_set(set): The set of no grad var name. no_grad_set will be changed.
        op_path_dict(dict): op_path_dict will be changed.
            key(int) block index
            val(list) the op path of block(index)
        sub_block_target_names(set): Target var names of sub-block.
    Return:
        The forward op path of sub-block corresponding to backward op.
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    """
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    assert sub_block_op_desc.has_attr(
        "sub_block") and sub_block.idx == sub_block_op_desc._block_attr_id(
            "sub_block")
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    assert isinstance(sub_block_target_names, (set, type(None)))

    if sub_block_target_names is None:
        sub_block_target_names = sub_block_op_desc.output_arg_names

    # TODO(huihuangzheng): add support for recurrent op.
    if sub_block_op_desc.type in ["conditional_block", "while"]:
        # Step1: get the output vars in sub-block
        sub_outputs = [
            sub_block._var_recursive(var) for var in sub_block_target_names
        ]
        for var in sub_block_target_names:
983
            for op_desc in sub_block.ops:
984
                if var in op_desc.output_arg_names:
985
                    for name in op_desc.input_arg_names:
986
                        sub_outputs.append(sub_block._var_recursive(name))
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988 989
        # Step2: find op path of sub-block
        is_while = sub_block_op_desc.type in ["while"]
990
        sub_block_op_path = _find_op_path_(sub_block, sub_outputs, [],
991
                                           no_grad_set, op_path_dict, is_while)
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        return sub_block_op_path
    return sub_block.ops


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def _is_grad_op_(op):
    op_maker = core.op_proto_and_checker_maker
    backward = core.op_proto_and_checker_maker.OpRole.Backward
    if op_maker.kOpRoleVarAttrName() in op.attr_names and \
            int(op.all_attrs()[op_maker.kOpRoleAttrName()]) == int(backward):
        return True
    return False


def _rename_grad_name_(name, grad_order):
    return 'grad/' * grad_order + name


1009 1010
def _append_backward_ops_(block,
                          ops,
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                          target_block,
                          no_grad_dict,
                          grad_to_var,
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                          callbacks=None,
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                          input_grad_names_set=None,
                          op_path_dict=None):
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    """
    Create all grad ops, and insert them into given block

    Args:
        block(Block): the block where forward ops are
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        ops(Op): the forward operators whose backward ops need to be added
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        target_block(Block): the block which is going to hold new generated grad ops
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        no_grad_dict(dict):
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            key(int)  block index
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            val(set) a set of variable names. These variables have no gradient
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        grad_to_var(dict)(output argument):
            key(str): grad variable name
            val(str): corresponding forward variable name
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        callbacks(callable object): a callable object used to decorate new generated grad ops
        input_grad_names_set(set): this set is used to store the gradients' name which is
            generated by backward ops, and input_grad_names_set can help to prune the unnecessary
            backward ops.
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        op_path_dict(dict): op_path_dict will be changed.
            key(int) block index
            val(list) the op path of block(index)
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    """
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    if callbacks is not None:
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        assert (isinstance(callbacks, list))
        for cb in callbacks:
            if not hasattr(cb, '__call__'):
                raise ValueError("'callback' must be a callable object.")
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    # grad_op_descs holds created grad_op, and will be appended to target_block
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    grad_op_descs = []
    program = block.program
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    rename_var_map = {}

1050
    # add grad_op_desc by reversed ops
1051
    for op in reversed(ops):
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        grad_sub_block_list = []
        # If the op has its own sub-block, deal with the sub-block first
        if op.has_attr("sub_block"):
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            sub_block = program.block(op._block_attr_id("sub_block"))
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            grad_sub_block = program._create_block()
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            grad_sub_block._set_forward_block_idx(sub_block.idx)
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            # see follwing comments for why set None here.
            pre_input_grad_names_set = copy.copy(input_grad_names_set)
            input_grad_names_set = None
1061
            sub_block_path = op_path_dict[op._block_attr_id("sub_block")]
1062
            _append_backward_ops_(sub_block, sub_block_path, grad_sub_block,
1063
                                  no_grad_dict, grad_to_var, callbacks,
1064
                                  input_grad_names_set, op_path_dict)
1065
            input_grad_names_set = pre_input_grad_names_set
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            program._rollback()
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            grad_sub_block_list.append(grad_sub_block.desc)

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        # Getting op's corresponding grad_op
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        grad_op_desc, op_grad_to_var = core.get_grad_op_desc(
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            op.desc, cpt.to_text(no_grad_dict[block.idx]), grad_sub_block_list)
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        # Set device for grad_op according to forward Op
        device_attr_name = core.op_proto_and_checker_maker.kOpDeviceAttrName()
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        if op.desc.has_attr(device_attr_name):
            op_device = op.desc.attr(device_attr_name)
            for op_desc in grad_op_desc:
                op_desc._set_attr(device_attr_name, op_device)
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        # Rename internal gradient variables in multiple backward
        # so that they have different names with previous backward.
        # For example:
        #  y = x * x, grad = fluid.gradients(fluid.gradients(y, x) + y * y, x)
        # In second-time backward, gradient variable names of partial
        # forward network (y * y) may be have same names with first-time
        # fluid.gradients(y, x).
        # So rename here before _addup_repetitive_outputs_.
        if program._appending_grad_times > 1:
            for op_desc in grad_op_desc:
                if not _is_grad_op_(op):
                    for name in op_desc.input_arg_names():
                        if name in rename_var_map:
                            op_desc._rename_input(name, rename_var_map[name])
                for name in op_desc.output_arg_names():
                    if "@GRAD" not in name:
                        continue
                    if block.desc.find_var(name.encode("ascii")):
                        new_name = _rename_grad_name_(
                            name, program._appending_grad_times)
                        op_desc._rename_output(name, new_name)
                        rename_var_map[name] = new_name

                        if name in op_grad_to_var:
                            op_grad_to_var[new_name] = op_grad_to_var[name]
                            op_grad_to_var.pop(name)

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        # If input_grad_names_set is not None, extend grad_op_descs only when
        # any input grad in outputs of previous grad ops.
        # But this strategy is not suited for while op for some control flow,
        # for example, for while op, the grads maybe generated in next loop.
        if input_grad_names_set is not None:
            is_append_grad = False
            for op_desc in grad_op_desc:
                input_grad_names = [
                    name for name in op_desc.input_arg_names()
                    if name.find(core.grad_var_suffix()) != -1
                ]
                # some code of gradient ops, like increment, are not very
                # standard, there is no @GRAD in these ops' inputs.
                if len(input_grad_names) == 0:
                    is_append_grad = True
                    break

                if _some_in_set_(input_grad_names, input_grad_names_set):
                    grad_op_descs.append(op_desc)
                    is_append_grad = True
                    for name in op_desc.output_arg_names():
                        input_grad_names_set.add(name)
            if is_append_grad:
                grad_to_var.update(op_grad_to_var)
        else:
            grad_op_descs.extend(grad_op_desc)
            grad_to_var.update(op_grad_to_var)
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    # sum parameter's gradients' var given multiple var gradient
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    grad_op_descs = _addup_repetitive_outputs_(grad_op_descs, block.idx)
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    # if all outputs of the grad op are in no_grad_set, then just remove and fill zero
    # if all inputs of the grad op are in no_grad_set, just remove this op
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    grad_op_descs = _remove_no_grad_branch_(grad_op_descs,
                                            no_grad_dict[block.idx])
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    # remove some backward ops
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    not_need_ops = _find_not_need_ops(grad_op_descs, ops, input_grad_names_set)
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    grad_op_descs = [
        op_desc for op_desc in grad_op_descs if op_desc not in not_need_ops
    ]
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    # append op_desc in grad_op_descs to target_block
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    op_role_attr_name = core.op_proto_and_checker_maker.kOpRoleAttrName()
    backward = core.op_proto_and_checker_maker.OpRole.Backward
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    for op_desc in grad_op_descs:
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        new_op_desc = target_block.desc.append_op()
        new_op_desc.copy_from(op_desc)
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        new_op_desc._set_attr(op_role_attr_name, backward)
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        grad_to_var["__current_op_desc__"] = new_op_desc
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        if callbacks is not None:
            assert (isinstance(callbacks, list))
            for cb in callbacks:
                cb(block=target_block, context=grad_to_var)
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def _is_grad_var_(var_name):
    return core.grad_var_suffix() in var_name


# Find the op who holds the sub_block as its "sub_block" attr
def _find_parent_op_(sub_block):
    sub_block_id = sub_block.idx

    if sub_block_id == 0:
        return None

    program = sub_block.program
    for block_id in six.moves.range(program.num_blocks):
        block_desc = program.block(block_id).desc
        for op_idx in six.moves.range(block_desc.op_size()):
            op = block_desc.op(op_idx)
            if op.has_attr("sub_block") and op._block_attr_id(
                    "sub_block") == sub_block_id:
                return op

1185
    # NOTE(paddle-dev): When optimizer is added in conditional block,
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    # sub_block may not be found.
    return None


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def _append_backward_vars_(block, start_op_idx, grad_to_var, grad_info_map):
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    """
    Create new variables required by backward pass.

    Args:
        block(Block): the block where new variables will be created
        start_op_idx(int): Only variables required by ops in block.ops[start_op_idx : ] will be created
        grad_to_var(dict):
            key(str): grad variable name
            val(str): corresponding forward variable name
            In most cases, this dict is generated by _append_backward_ops_()
        grad_info_map(dict)(output argument):
            key(str): forward variable name
1203
            val(tuple): a tuple of (str, Block), str is the corresponding grad name, Block is the block containing grad variable
1204
    """
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    ops_to_remove = []
    '''
    NOTE(paddle-dev): while_grad op may hold some inputs which are not found 
    in the parent/forward block, and they are also the outputs of while_grad 
    op. These kinds of inputs are the recursive outputs inside while_grad op. 
    They should be considered as "already created" when scanning the inner 
    ops of while_grad ops.  
    '''
    parent_op = _find_parent_op_(block)
    parent_op_vars = []
    if parent_op is not None:
        input_args = parent_op.input_arg_names()
        output_args = parent_op.output_arg_names()
        for in_arg in input_args:
            if in_arg in output_args:
                parent_op_vars.append(in_arg)

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    for op_idx in range(start_op_idx, block.desc.op_size()):
        op_desc = block.desc.op(op_idx)
        if op_desc.has_attr("sub_block"):
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            sub_block = block.program.block(op_desc._block_attr_id("sub_block"))
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            _append_backward_vars_(sub_block, 0, grad_to_var, grad_info_map)
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        grad_var_ins = [
            var for var in op_desc.input_arg_names() if _is_grad_var_(var)
        ]
        grad_var_outs = [
            var for var in op_desc.output_arg_names() if _is_grad_var_(var)
        ]

        inputs = [
            var for var in op_desc.input_arg_names()
            if var != core.empty_var_name()
        ]
        outputs = [
            var for var in op_desc.output_arg_names()
            if var != core.empty_var_name()
        ]

1244
        # If the outputs of grad op is empty, just remove it
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        if not outputs:
            ops_to_remove.append(op_idx)
            continue
        else:
            '''
            If the output is not empty and there is any grad input, find 
            whether there is any existing input. If not, just remove it.
            '''
            if grad_var_ins:
                existing_grad_var_ins = [
                    var for var in grad_var_ins
                    if block.desc.has_var_recursive(cpt.to_bytes(var)) or var in
                    parent_op_vars
                ]
                if not existing_grad_var_ins:
                    '''
                    FIXME(paddle-dev, zengjinle): rnn_memory_helper_grad is used
                    in recurrent op. The input of this op does not even exist in 
                    the program! Therefore, any dependency analysis would not 
                    work to this op! If I do not add the following code, this op
                    would be pruned, and the calculation result would be wrong. 
                    Maybe we should re-design this op later...  
                    '''
                    if op_desc.type() not in ['rnn_memory_helper_grad']:
                        ops_to_remove.append(op_idx)
1270
                        continue
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        new_vars = set()
        # create new gradient variables
        for grad_var_name in op_desc.output_arg_names():
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            if block.desc.has_var_recursive(cpt.to_bytes(
                    grad_var_name)) or grad_var_name == core.empty_var_name():
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                continue
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            block.desc.var(cpt.to_bytes(grad_var_name))
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            new_vars.add(grad_var_name)
1280
            if grad_var_name not in grad_to_var:
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                continue
            grad_info_map[grad_to_var[grad_var_name]] = (grad_var_name, block)
        # infer_shape and infer_type
        op_desc.infer_var_type(block.desc)
        op_desc.infer_shape(block.desc)
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        for arg in op_desc.output_arg_names():
            if arg in new_vars:
1289
                _infer_var_data_type_shape_(arg, block)
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    for op_idx in reversed(ops_to_remove):
        block.desc._remove_op(op_idx, op_idx + 1)

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def _rename_grad_(block, start_op_idx, grad_to_var, target_grad_map):
    var_map = copy.copy(target_grad_map)
    for op_idx in range(start_op_idx, block.desc.op_size()):
        op_desc = block.desc.op(op_idx)
        for name in op_desc.input_arg_names():
            if name in var_map:
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                op_desc._rename_input(name, var_map[name])
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        for name in op_desc.output_arg_names():
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            if "@GRAD" not in name:
                continue
1306
            if block.desc.find_var(name.encode("ascii")):
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                new_name = unique_name.generate(name)
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                op_desc._rename_output(name, new_name)
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                var_map[name] = new_name

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    for g, ng in six.iteritems(var_map):
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        if g in grad_to_var:
            grad_to_var[ng] = grad_to_var[g]
            grad_to_var.pop(g)


def _get_stop_gradients_(program):
    no_grad_dict = dict()
    assert isinstance(program, framework.Program)
    for block in program.blocks:
        assert isinstance(block, framework.Block)
        block_no_grad_set = set()
1323
        for var in list(block.vars.values()):
1324 1325 1326 1327 1328 1329 1330
            assert isinstance(var, framework.Variable)
            if var.stop_gradient:
                block_no_grad_set.add(_append_grad_suffix_(var.name))
        no_grad_dict[block.idx] = block_no_grad_set
    return no_grad_dict


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def _get_son_parent_block_idx_dict(program, current_block_idx):

    son_parent_block_idx_dict = collections.OrderedDict()
    while current_block_idx >= 0:
        parent_block_idx = program.block(current_block_idx).parent_idx
        son_parent_block_idx_dict[current_block_idx] = parent_block_idx
        current_block_idx = parent_block_idx

    return son_parent_block_idx_dict


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def _get_no_grad_set_name(no_grad_set):
    no_grad_set_name = set()
    if no_grad_set is not None:
        if isinstance(no_grad_set, (set, list, tuple)):
            for i, no_grad_var in enumerate(no_grad_set):
                if isinstance(no_grad_var, framework.Variable):
                    no_grad_set_name.add(no_grad_var.name)
                elif isinstance(no_grad_var, six.string_types):
                    no_grad_set_name.add(no_grad_var)
                else:
                    raise TypeError(
                        "The type of no_grad_set's member must be paddle.fluid.Variable or str, but received %s."
                        % (type(no_grad_var)))
        else:
            raise TypeError(
                "The type of no_grad_set should be set or list or tuple, but received {}".
                format(type(no_grad_set)))
    return no_grad_set_name


1362
@framework.static_only
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def append_backward(loss,
                    parameter_list=None,
                    no_grad_set=None,
                    callbacks=None,
                    checkpoints=None):
1368
    """
1369 1370
    :api_attr: Static Graph

1371
    This function appends backward part to main_program.
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1373 1374
    A complete neural network training is made up of forward and backward
    propagation. However, when we configure a network, we only need to
1375 1376
    specify its forward part. This function uses the chain rule to automatically
    generate the backward part according to the forward part.
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1378 1379
    In most cases, users do not need to invoke this function manually.
    It will be automatically invoked by the optimizer's `minimize` function.
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1381
    Parameters:
1382 1383
        loss(Tensor): The loss Tensor of the network.
        parameter_list(list[Tensor|str], optional): List of Parameters or Parameter.names
1384
                                           that need to be updated by optimizers.
1385
                                           If it is None, all parameters
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                                           will be updated.
1387
                                           Default: None.
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        no_grad_set(set[Tensor|str], optional): Set of Tensors or Tensor.names in the :ref:`api_guide_Block_en` 0 whose gradients
                               should be ignored. All Tensors with
1390
                               `stop_gradient=True` from all blocks will
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                               be automatically added into this set.
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                               If this parameter is not None, the Tensors or Tensor.names in this set will be added to the default set.
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                               Default: None.
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        callbacks(list[callable object], optional): List of callback functions.
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                                               The callbacks are used for
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                                               doing some custom jobs during
                                               backward part building. All
                                               callable objects in it will
                                               be invoked once each time a
                                               new gradient operator is added
                                               into the program. The callable
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                                               object must have two input
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                                               parameters: ``block`` and ``context`` .
                                               The ``block`` is the :ref:`api_guide_Block_en` which
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                                               the new gradient operator will
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                                               be added to. The ``context`` is a
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                                               map, whose keys are gradient
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                                               Tensor names and values are
                                               corresponding original :ref:`api_guide_tensor_en` .
                                               In addition to this, the ``context``
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                                               has another special key-value pair:
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                                               the key is string ``__current_op_desc__``
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                                               and the value is the op_desc of the
                                               gradient operator who has just
                                               triggered the callable object.
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                                               Default: None.
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    Returns:
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        list of tuple ( :ref:`api_guide_tensor_en` , :ref:`api_guide_tensor_en` ): Pairs of parameter and its corresponding gradients.
        The key is the parameter and the value is gradient Tensor.
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    Raises:
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        AssertionError: If ``loss`` is not an instance of Tensor.
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    Examples:
        .. code-block:: python

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            import paddle
            import paddle.nn.functional as F
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            paddle.enable_static()

            x = paddle.static.data(name='x', shape=[None, 13], dtype='int64')
            y = paddle.static.data(name='y', shape=[None, 1], dtype='float32')
            x_emb = paddle.static.nn.embedding(x, size=[100, 256])
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            y_predict = paddle.static.nn.fc(x=x_emb, size=1, activation=None, name='my_fc')
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            loss = F.square_error_cost(input=y_predict, label=y)
            avg_loss = paddle.mean(loss)
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            # Get all weights in main_program, not include bias.
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            all_weights = [param for param in paddle.static.default_main_program().block(0).all_parameters() if 'w_' in param.name]
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            all_weights_name = [w.name for w in all_weights]

            # return all param_grads needed to be updated if parameter_list set default None.
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            p_g_list1 = paddle.static.append_backward(loss=avg_loss)
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            # output: [(embedding_0.w_0, embedding_0.w_0@GRAD), (my_fc.w_0, my_fc.w_0@GRAD), (my_fc.b_0, my_fc.b_0@GRAD)]

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            # return the param_grads corresponding to parameter_list that can be list of param (Tensor).
            p_g_list2 = paddle.static.append_backward(loss=avg_loss, parameter_list=all_weights)
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            # output: [(embedding_0.w_0, embedding_0.w_0@GRAD), (my_fc.w_0, my_fc.w_0@GRAD)]

            # parameter_list can be list of param.name (str).
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            p_g_list3 = paddle.static.append_backward(loss=avg_loss, parameter_list=all_weights_name)
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            # output: [(embedding_0.w_0, embedding_0.w_0@GRAD), (my_fc.w_0, my_fc.w_0@GRAD)]

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            # no_grad_set can be set of Tensors that means grad will be cut off from these Tensors.
            p_g_list4 = paddle.static.append_backward(loss=avg_loss, no_grad_set=set([x_emb]))
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            # output: [(my_fc.w_0, my_fc.w_0@GRAD), (my_fc.b_0, my_fc.b_0@GRAD)]

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            # no_grad_set can be set of Tensor.name when the Tensor is created inside layers and can't be specified explicitly.
            p_g_list5 = paddle.static.append_backward(loss=avg_loss, no_grad_set=set(['my_fc.b_0']))
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            # output: [(embedding_0.w_0, embedding_0.w_0@GRAD), (my_fc.w_0, my_fc.w_0@GRAD)]

            # return [] because all param_grads are filtered by no_grad_set.
1465
            p_g_list6 = paddle.static.append_backward(loss=avg_loss, parameter_list=all_weights, no_grad_set=set(all_weights))
1466

1467
    """
1468
    check_type(loss, 'loss', framework.Variable,
1469
               'paddle.static.append_backward')
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    if loss.op is None:
        # the loss is from a cloned program. Find loss op manually.
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        _find_loss_op_(loss)
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    loss.op._set_attr(core.op_proto_and_checker_maker.kOpRoleAttrName(),
                      int(core.op_proto_and_checker_maker.OpRole.Forward) |
                      int(core.op_proto_and_checker_maker.OpRole.Loss))
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    if callbacks is not None:
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        check_type(callbacks, 'callbacks', list,
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                   'paddle.static.append_backward')
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    program = loss.block.program
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    root_block = program.block(0)
    current_block_idx = program.current_block_idx
    current_block = program.block(current_block_idx)

    is_in_control_flow = current_block_idx != 0

    # Double grad is not supported in sub-block (control flow)
    if not is_in_control_flow:
        # _appending_grad_times used for double grad
        program._appending_grad_times += 1
1494

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    if no_grad_set is None:
1496
        no_grad_set = set()
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    else:
        no_grad_set = _get_no_grad_set_name(copy.copy(no_grad_set))
1499
    no_grad_dict = _get_stop_gradients_(program)
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    # no_grad_set only contains vars in block 0
    # Todo(liym27): support vars in sub block
1502
    no_grad_dict[0].update(list(map(_append_grad_suffix_, no_grad_set)))
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    # Currently it is only to support the optimizer.minimize
    # in a switch branch, which can append_backward in a sub_block.
    # Note: while_loop is in control flow, but it makes no sense to call optimizer in while.
    # Todo: report error when it is in while_loop
    if is_in_control_flow:
        # create grad block if in switch control flow.
        target_grad_block = program._create_block(
            parent_idx=current_block.parent_idx)
        target_grad_block._set_forward_block_idx(current_block_idx)
        # after _create_block, program.current_block changes
    else:
        target_grad_block = root_block

    son_parent_block_idx_dict = _get_son_parent_block_idx_dict(
        program, current_block_idx)

    block_fwd_op_num_dict = {}  # block_id: fwd_op_num
    for idx in son_parent_block_idx_dict:
        block_fwd_op_num_dict[idx] = program.block(idx).desc.op_size()
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    grad_to_var = dict()

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    op_desc = _create_loss_op_desc_(loss)
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    target_grad_block.desc.append_op().copy_from(op_desc)

    for block_idx in son_parent_block_idx_dict:
        block = program.block(block_idx)

        block_no_grad_set = set(
            map(_strip_grad_suffix_, no_grad_dict[block_idx]))
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        op_path_dict = dict()
        op_path = _find_op_path_(block, [loss], [], block_no_grad_set,
                                 op_path_dict)
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        no_grad_vars = _find_no_grad_vars(block, op_path, [loss],
                                          block_no_grad_set)

        block_no_grad_set.update(no_grad_vars)
        no_grad_dict[block_idx].update(
            list(map(_append_grad_suffix_, block_no_grad_set)))

        input_grad_names_set = None
        # For double backward, input_grad_names is used for filtering
        # some non-used gradients op(s).

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        # TODO(liym27): need a better design.
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        # not support double grad in control flow sub-block now.
        if not is_in_control_flow:
            if program._appending_grad_times > 1:
                input_grad_names_set = set([_append_grad_suffix_(loss.name)])

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        # TODO: support _append_backward_ops_with_checkpoints_ in
1557
        #  sub-block (control flow)
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        is_recompute = False
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        if checkpoints != None and \
                isinstance(checkpoints, list) and \
                len(checkpoints) > 0:
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            is_recompute = True
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            program_stat, checkpoint_names, \
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                vars_should_be_hold, \
                recompute_segments = \
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                _append_backward_ops_with_checkpoints_(
                    root_block,
                    op_path,
                    root_block,
                    no_grad_dict,
                    grad_to_var,
                    checkpoints)
        else:
            _append_backward_ops_(
                block,  # the block where forward ops are in
                op_path,
                target_grad_block,
                no_grad_dict,
                grad_to_var,
                callbacks,
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                input_grad_names_set=input_grad_names_set,
                op_path_dict=op_path_dict)
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    grad_info_map = dict()

    # if in control flow, target_grad_block is a created new block which only contains grad ops,
    # so fwd_op_num is set to 0.
    fwd_op_num = block_fwd_op_num_dict[
        current_block_idx] if not is_in_control_flow else 0

    # Because append_backward may be called multiple times,
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    # we need rename the internal gradient variables so that they have
    # different names.
1594
    _rename_grad_(target_grad_block, fwd_op_num, grad_to_var, {})
1595

1596 1597
    _append_backward_vars_(target_grad_block, fwd_op_num, grad_to_var,
                           grad_info_map)
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    program.current_block_idx = current_block_idx
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    program._sync_with_cpp()
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    if parameter_list is not None:
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        check_type(parameter_list, 'parameter_list', (list, tuple, set),
                   'fluid.backward.append_backward')
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        parameters = []
        for i, param in enumerate(parameter_list):
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            check_type(param, 'parameter_list[%s]' % i, (framework.Variable,
                                                         six.string_types),
                       'fluid.backward.append_backward')
1610 1611 1612 1613
            if isinstance(param, framework.Variable):
                parameters.append(param.name)
            elif isinstance(param, six.string_types):
                parameters.append(param)
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    else:
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        params = program.global_block().all_parameters()
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        parameters = [param.name for param in params if param.trainable]
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1618
    params_and_grads = []
1619
    op_role_var_attr_name = core.op_proto_and_checker_maker.kOpRoleVarAttrName()
1620
    for param in parameters:
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        if cpt.to_text(param) not in grad_info_map:
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            continue
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        grad_info = grad_info_map[param]
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        grad_block = grad_info[1]
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        if not grad_block.has_var(grad_info[0]):
            raise ValueError("grad block[{0}] did not have grad var {1}".format(
                grad_info[1], grad_info[0]))
        # Get the param var from the global block
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        param_var = program.global_block().var(param)
1630
        grad_var = grad_block.var(grad_info[0])
1631 1632 1633 1634 1635
        if not is_in_control_flow:
            if loss.block.has_var(grad_info[0]):
                params_and_grads.append((param_var, grad_var))
            else:
                params_and_grads.append((param_var, None))
1636
        else:
1637
            params_and_grads.append((param_var, grad_var))
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    for p, g in params_and_grads:
        if g is None:
            continue
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        ops = grad_block.ops if is_in_control_flow else program.global_block(
        ).ops
        for op in reversed(ops):
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            assert isinstance(op, framework.Operator)
            if g.name in op.output_arg_names:
                g.op = op
                break

        if g.op is None:
            raise ValueError("Unexpected branch")
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        attr_val = [p.name, g.name]
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        if g.op.has_attr(op_role_var_attr_name):
            attr_val.extend(g.op.attr(op_role_var_attr_name))
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        g.op._set_attr(op_role_var_attr_name, attr_val)
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    if is_recompute:
        return params_and_grads, checkpoint_names
    else:
        return params_and_grads
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def _as_list(x):
    if x is None:
        return []
    return list(x) if isinstance(x, collections.Sequence) else [x]


1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694
def _is_ancestor_block(ancestor_block, block):
    prog = block.program
    ancestor_idx = ancestor_block.idx
    parent_idx = block.parent_idx

    while parent_idx != -1:
        if parent_idx == ancestor_idx:
            return True
        parent_idx = prog.block(parent_idx).parent_idx

    return False


def _get_output_names(cur_block, targets):
    """
    In `cur_block`, get output names those linked to targets.
    NOTE:
    1. `targets` can be in `cur_block`;
    Usually, `targets` is in `cur_block`. However, considering control flow,
    2. `targets` may be in sub-block but `cur_block` is an ancestor of `targets[0].block`;
    3. `targets` may be in the block which is ancestor of `cur_block`.
    """

    block = targets[0].block if targets else cur_block
    current_output_names = set([out.name for out in targets])

1695 1696 1697 1698 1699 1700
    # 1. If `targets` in cur_block or the ancestral block of `cur_block`
    if block.idx == cur_block.idx or _is_ancestor_block(block, cur_block):
        return current_output_names

    # 2. If `cur_block` is an ancestor of `targets[0].block`, run while loop
    prog = cur_block.program
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    while block.idx != cur_block.idx:
        assert block.parent_idx != -1
        parent_block = prog.block(block.parent_idx)

        parent_block_output_names = set()
        for op in reversed(block.ops):
            if _some_in_set_(op.desc.output_arg_names(), current_output_names):
                for name in op.desc.input_arg_names():
                    current_output_names.add(name)
                    if not block.desc.find_var(cpt.to_bytes(name)) \
                            and parent_block.desc.find_var(cpt.to_bytes(name)):
                        parent_block_output_names.add(name)

        block = parent_block
        current_output_names = parent_block_output_names

    return current_output_names


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def _find_no_grad_vars(block, op_path, targets, no_grad_set):
    """
    Find the vars which is not used in the program, and
1723
    those vars belong to no_grad_var.
1724
    """
1725
    output_names = _get_output_names(block, targets)
1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739
    no_grad_var = []
    for i, op in reversed(list(enumerate(op_path))):
        # If the op has sub_block, it is too complicated to find the correct no_grad_var.
        if not op.has_attr("sub_block"):
            for out_var in op.desc.output_arg_names():
                if out_var not in output_names and out_var not in op.desc.input_arg_names(
                ) and not block.vars[out_var].stop_gradient:
                    no_grad_var.append(out_var)
        for name in op.desc.input_arg_names():
            if name not in no_grad_set:
                output_names.add(name)
    return set(no_grad_var)


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def _find_op_path_(block,
                   targets,
                   inputs,
                   no_grad_set,
                   op_path_dict=None,
                   is_while=False):
1746
    """
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    It is used to find the grad path in `block`.

    Args:
        block(Block): The block in which to get op path.
        targets(list[Variable]): The target variables.
        inputs(list[Variable]): The input variables.
        no_grad_set(set): The set of no grad var name. no_grad_set will be changed.
        op_path_dict(dict): op_path_dict will be changed. op_path_dict will be changed.
            key(int) block index
            val(list) the op path of block(index)
        is_while(bool): Whether or not `block` is while block
    Return:
        The forward op path of block corresponding to backward op.
1760
    """
1761

1762
    input_names = set([inp.name for inp in inputs])
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    output_names = _get_output_names(block, targets)
    if op_path_dict is None:
        op_path_dict = dict()
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    relevant_op_flags = [True] * len(block.ops)

    # All the inputs of the block are used if inputs is empty,
    if inputs:
        for i, op in enumerate(block.ops):
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            if _some_in_set_(
                    op.desc.input_arg_names(),
                    input_names) and core.has_non_empty_grad_op_maker(op.type):
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                for name in op.desc.output_arg_names():
                    if name not in no_grad_set:
                        input_names.add(name)
            else:
                relevant_op_flags[i] = False

    for i, op in reversed(list(enumerate(block.ops))):
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        if op.has_attr("sub_block"):
            sub_block_id = op._block_attr_id("sub_block")
            sub_block = block.program.block(sub_block_id)
            sub_block_target_names = output_names & set(op.output_arg_names)
            sub_block_path = _get_sub_block_path(sub_block, op,
                                                 set(), op_path_dict,
                                                 sub_block_target_names)
            op_path_dict[sub_block_id] = sub_block_path

1791 1792 1793
        if _some_in_set_(
                op.desc.output_arg_names(),
                output_names) and core.has_non_empty_grad_op_maker(op.type):
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            for name in op.desc.input_arg_names():
                if name not in no_grad_set:
                    output_names.add(name)
        else:
            relevant_op_flags[i] = False

1800 1801 1802 1803 1804
    if is_while:
        # If block is while block, dealing with op specifically again.
        # TODO(liym27): Consider special types of ops.
        for i, op in reversed(list(enumerate(block.ops))):
            if relevant_op_flags[i] == False \
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                    and _some_in_set_(op.desc.output_arg_names(), output_names):
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                relevant_op_flags[i] = True

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    op_path = [
        block.ops[i] for i in range(len(block.ops)) if relevant_op_flags[i]
    ]

    if inputs:
        for op in op_path:
            for name in op.desc.input_arg_names():
1815
                if name not in input_names and block.vars[name].stop_gradient:
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                    no_grad_set.add(name)

    return op_path


def calc_gradient(targets, inputs, target_gradients=None, no_grad_set=None):
    """
1823
    Backpropagate the gradients of targets to inputs.
1824 1825

    Args:
1826 1827 1828
        targets(Tensor|list[Tensor]): The target Tensors
        inputs(Tensor|list[Tensor]): The input Tensors
        target_gradients (Tensor|list[Tensor], optional): The gradient Tensors
1829 1830
            of targets which has the same shape with targets, If None, ones will
            be created for them.
1831 1832
        no_grad_set(set[Tensor|str], optional): Set of Tensors or Tensor.names in the :ref:`api_guide_Block_en` 0 whose gradients
                               should be ignored. All Tensors with
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                               `stop_gradient=True` from all blocks will
                               be automatically added into this set.
1835
                               If this parameter is not None, the Tensors or Tensor.names in this set will be added to the default set.
1836
                               Default: None.
1837 1838

    Return:
1839 1840
        (list[Tensor]): A list of gradients for inputs
        If an input does not affect targets, the corresponding gradient Tensor
1841 1842 1843 1844 1845 1846 1847 1848
        will be None
    """
    targets = _as_list(targets)
    inputs = _as_list(inputs)
    target_gradients = _as_list(target_gradients)

    block = targets[0].block
    prog = block.program
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    # increase appending gradients times
    prog._appending_grad_times += 1
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    block_idx = block.idx

    if not target_gradients:
        target_gradients = [None] * len(targets)

    if len(targets) != len(target_gradients):
        raise ValueError(
            "Should have the same number of target_gradients as targets")

    if no_grad_set is None:
        no_grad_set = set()
1862 1863
    else:
        no_grad_set = _get_no_grad_set_name(copy.copy(no_grad_set))
1864
    no_grad_dict = _get_stop_gradients_(prog)
1865
    no_grad_dict[0].update(list(map(_append_grad_suffix_, no_grad_set)))
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    fwd_op_num = block.desc.op_size()

1869 1870
    input_grad_names_set = set()

1871 1872 1873 1874 1875
    target_grad_map = {}
    for i, grad in enumerate(target_gradients):
        target = targets[i]
        if grad is None:
            grad_name = _append_grad_suffix_(target.name)
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            target_shape = target.name + '_shape'
            block.desc.append_op().copy_from(
                _create_op_desc_("shape", {'Input': [target.name]},
                                 {"Out": [target_shape]}, {}))
            input_grad_names_set.add(target_shape)
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            op_desc = _create_op_desc_("fill_constant",
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                                       {"ShapeTensor": [target_shape]},
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                                       {"Out": [grad_name]}, {
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                                           "shape": target.shape,
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                                           "value": 1.0,
                                           "dtype": target.dtype,
                                       })
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            block.desc.append_op().copy_from(op_desc)
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            input_grad_names_set.add(grad_name)
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        else:
            if target.block.idx != block_idx or target.block.program != prog:
                raise ValueError("all targets must be in the same block")
            if target.shape != grad.shape:
                raise ValueError(
                    "The shapes of target and grad are different: %s %s" % (
                        target.name, grad.name))
            target_grad_map[_append_grad_suffix_(target.name)] = grad.name
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            input_grad_names_set.add(grad.name)

    # For double backward, input_grad_names is used for filter
    # some non-used gradients op.
    if prog._appending_grad_times == 1:
        input_grad_names_set = None
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    for input in inputs:
        if input.block.program != prog:
            raise "input must be in the same program as targets"

    block_no_grad_set = set(map(_strip_grad_suffix_, no_grad_dict[0]))
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    op_path_dict = dict()
    op_path = _find_op_path_(block, targets, inputs, block_no_grad_set,
                             op_path_dict)
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    # find no grad var by op_path
    no_grad_vars = _find_no_grad_vars(block, op_path, targets,
                                      block_no_grad_set)
    block_no_grad_set.update(no_grad_vars)

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    no_grad_dict[0].update(list(map(_append_grad_suffix_, block_no_grad_set)))
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    grad_to_var = dict()
    grad_info_map = dict()
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    _append_backward_ops_(
        block,
        op_path,
        block,
        no_grad_dict,
        grad_to_var,
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        input_grad_names_set=input_grad_names_set,
        op_path_dict=op_path_dict)
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    # Because calc_gradient may be called multiple times,
    # we need rename the internal gradient variables so that they have
    # different names.
    _rename_grad_(block, fwd_op_num, grad_to_var, target_grad_map)

    _append_backward_vars_(block, fwd_op_num, grad_to_var, grad_info_map)
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    prog._sync_with_cpp()
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    grad_vars = []
    for input_var in inputs:
        if input_var.name not in grad_info_map:
            grad_vars.append(None)
        else:
            grad_info = grad_info_map[input_var.name]
            grad_block = grad_info[1]
            grad_var = grad_block.var(grad_info[0])
            grad_vars.append(grad_var)

    if len(grad_vars) == 1:
        return grad_vars[0]
    else:
        return grad_vars
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@framework.static_only
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def gradients(targets, inputs, target_gradients=None, no_grad_set=None):
    """
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    :api_attr: Static Graph
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    Backpropagate the gradients of targets to inputs.

    Args:
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        targets (Tensor|list[Tensor]): The target Tensors.
        inputs (Tensor|list[Tensor]): The input Tensors.
        target_gradients (Tensor|list[Tensor], optional): The gradient Tensor
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            of targets which has the same shape with targets, If None, ones will
            be created for them.
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        no_grad_set (set[Tensor|str], optional): Set of Tensors or Tensor.names in the :ref:`api_guide_Block_en` 0 whose gradients
            should be ignored. All Tensors with ``stop_gradient=True`` from all blocks will
            be automatically added into this set. If this parameter is not None, the Tensors or Tensor.names
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            in this set will be added to the default set. Default: None.
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    Return:
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        (list[Tensor]): A list of gradients for inputs
        If an input does not affect targets, the corresponding gradient Tensor
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        will be None.

    Examples:
        .. code-block:: python

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            import paddle
            import paddle.nn.functional as F

            paddle.enable_static()
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            x = paddle.static.data(name='x', shape=[None, 2, 8, 8], dtype='float32')
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            x.stop_gradient=False
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            y = paddle.static.nn.conv2d(x, 4, 1, bias_attr=False)
            y = F.relu(y)
            z = paddle.static.gradients([y], x)
            print(z) # [var x@GRAD : fluid.VarType.LOD_TENSOR.shape(-1L, 2L, 8L, 8L).astype(VarType.FP32)]
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    """
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    check_type(targets, 'targets', (framework.Variable, list),
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               'paddle.static.gradients')
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    check_type(inputs, 'inputs', (framework.Variable, list),
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               'paddle.static.gradients')
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    check_type(target_gradients, 'target_gradients', (
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        framework.Variable, list, type(None)), 'paddle.static.gradients')
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    outs = calc_gradient(targets, inputs, target_gradients, no_grad_set)
    return _as_list(outs)