loss.py 155.7 KB
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# -*- coding: utf-8 -*
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#   Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved.
#
# 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
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# 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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import paddle
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from ...fluid.data_feeder import check_variable_and_dtype
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# TODO: define loss functions of neural network
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import numpy as np
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import paddle
import paddle.fluid as fluid
from ...fluid.layers.nn import _elementwise_op_in_dygraph
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from ...tensor.manipulation import reshape
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from ...fluid.layer_helper import LayerHelper
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from ...fluid.framework import _varbase_creator
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from ...static import Variable
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from paddle.utils import deprecated
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from paddle import _C_ops, _legacy_C_ops
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from paddle import in_dynamic_mode
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from paddle.framework import core, _non_static_mode
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from ...fluid.framework import _in_legacy_dygraph, in_dygraph_mode, _non_static_mode, _current_expected_place
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__all__ = []

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def dice_loss(input, label, epsilon=0.00001, name=None):
    r"""

    Dice loss for comparing the similarity between the input predictions and the label.
    This implementation is for binary classification, where the input is sigmoid
    predictions of each pixel, usually used for segmentation task. The dice loss can
    be defined as the following equation:

    .. math::

        dice\_loss &= 1 - \frac{2 * intersection\_area}{total\_area} \\
                  &= \frac{(total\_area - intersection\_area) - intersection\_area}{total\_area} \\
                  &= \frac{(union\_area - intersection\_area)}{total\_area}


    Parameters:
        input (Tensor): Tensor, rank>=2, shape is :math:`[N_1, N_2, ..., N_k, D]`, where :math:`N_1` is
                          the batch_size, :math:`D` is the number of categories. It is usually the output
                          predictions of sigmoid activation. The data type can be float32 or float64.
        label (Tensor): Tensor, the groud truth with the same rank as input, shape is :math:`[N_1, N_2, ..., N_k, 1]`.
                          where :math:`N_1` is the batch_size. The data type can be int32 or int64.
        epsilon (float): The epsilon will be added to the numerator and denominator.
                         If both input and label are empty, it makes sure dice is 1.
                         Default: 0.00001
        name(str, optional): The default value is None.
                             Normally there is no need for user to set this property.
                             For more information, please refer to :ref:`api_guide_Name`

    Returns:
        Tensor, which shape is [1], data type is the same as `input` .

    Example:
        .. code-block:: python

            import paddle
            import paddle.nn.functional as F

            x = paddle.randn((3,224,224,2))
            label = paddle.randint(high=2, shape=(3,224,224,1))
            predictions = F.softmax(x)
            loss = F.dice_loss(input=predictions, label=label)
    """
    assert input.dtype in (paddle.float32, paddle.float64)
    assert label.dtype in (paddle.int32, paddle.int64)
    assert len(input.shape) >= 2, \
        "The rank of input should be greater than or equal to 2."
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    assert len(input.shape) == len(
        label.shape), ("The rank of input and label should be equal, "
                       "but received input: %d, label: %d." %
                       (len(input.shape), len(label.shape)))
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    assert label.shape[-1] == 1, ("The last dimension of label should be 1, "
                                  "but received %d." % label.shape[-1])
    assert input.shape[:-1] == label.shape[:-1], (
        "All dimensions should be equal except the last one.")
    assert input.numel() > 0 and label.numel() > 0, \
        "Any dimension of input and label cannot be equal to 0."

    label = paddle.squeeze(label, [-1])
    label = paddle.nn.functional.one_hot(label, input.shape[-1])
    reduce_dim = list(range(1, len(input.shape)))
    inse = paddle.sum(input * label, axis=reduce_dim)
    dice_denominator = paddle.sum(input, axis=reduce_dim) + paddle.sum(
        label, axis=reduce_dim)
    dice_score = 1 - inse * 2 / (dice_denominator + epsilon)
    return paddle.mean(dice_score)


def log_loss(input, label, epsilon=1e-4, name=None):
    r"""

    **Negative Log Loss Layer**

    This layer accepts input predictions and target label and returns the
    negative log loss.

    .. math::

        Out = -label * \log{(input + \epsilon)}
              - (1 - label) * \log{(1 - input + \epsilon)}

    Args:
        input (Tensor|list):  A 2-D tensor with shape [N x 1], where N is the
                                batch size. This input is a probability computed
                                by the previous operator. Data type float32.
        label (Tensor|list):  The ground truth which is a 2-D tensor with
                                shape [N x 1], where N is the batch size.
                                Data type float32.
        epsilon (float, optional): A small number for numerical stability. Default 1e-4.
        name(str|None): For detailed information, please refer to
            :ref:`api_guide_Name` . Usually name is no need to set and None by default.

    Returns:
        Tensor, which shape is [N x 1], data type is float32.

    Examples:
        .. code-block:: python

          import paddle
          import paddle.nn.functional as F

          label = paddle.randn((10,1))
          prob = paddle.randn((10,1))
          cost = F.log_loss(input=prob, label=label)
    """
    if in_dygraph_mode():
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        return _C_ops.log_loss(input, label, epsilon)
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    helper = LayerHelper('log_loss', **locals())
    check_variable_and_dtype(input, 'input', ['float32'], 'log_loss')
    check_variable_and_dtype(label, 'label', ['float32'], 'log_loss')

    loss = helper.create_variable_for_type_inference(dtype=input.dtype)

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    helper.append_op(type='log_loss',
                     inputs={
                         'Predicted': [input],
                         'Labels': [label]
                     },
                     outputs={'Loss': [loss]},
                     attrs={'epsilon': epsilon})
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    return loss


def fluid_softmax_with_cross_entropy(logits,
                                     label,
                                     soft_label=False,
                                     ignore_index=-100,
                                     numeric_stable_mode=True,
                                     return_softmax=False,
                                     axis=-1):
    r"""

    This operator implements the cross entropy loss function with softmax. This function 
    combines the calculation of the softmax operation and the cross entropy loss function 
    to provide a more numerically stable gradient.

    Because this operator performs a softmax on logits internally, it expects
    unscaled logits. This operator should not be used with the output of
    softmax operator since that would produce incorrect results.

    When the attribute :attr:`soft_label` is set :attr:`False`, this operators 
    expects mutually exclusive hard labels, each sample in a batch is in exactly 
    one class with a probability of 1.0. Each sample in the batch will have a 
    single label.

    The equation is as follows:

    1) Hard label (one-hot label, so every sample has exactly one class)

    .. math::
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        \\loss_j=-\text{logits}_{label_j} +\log\left(\sum_{i=0}^{K}\exp(\text{logits}_i)\right), j = 1,..., K
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    2) Soft label (each sample can have a distribution over all classes)

    .. math::
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        \\loss_j= -\sum_{i=0}^{K}\text{label}_i\left(\text{logits}_i - \log\left(\sum_{i=0}^{K}\exp(\text{logits}_i)\right)\right), j = 1,...,K
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    3) If :attr:`numeric_stable_mode` is :attr:`True`, softmax is calculated first by:

    .. math::
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        \\max_j&=\max_{i=0}^{K}{\text{logits}_i} \\
                log\_max\_sum_j &= \log\sum_{i=0}^{K}\exp(logits_i - max_j)\\
                softmax_j &= \exp(logits_j - max_j - {log\_max\_sum}_j)
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    and then cross entropy loss is calculated by softmax and label.

    Args:
        logits (Tensor): A multi-dimension ``Tensor`` , and the data type is float32 or float64. The input tensor of unscaled log probabilities.
        label (Tensor): The ground truth  ``Tensor`` , data type is the same
            as the ``logits`` . If :attr:`soft_label` is set to :attr:`True`, 
            Label is a ``Tensor``  in the same shape with :attr:`logits`. 
            If :attr:`soft_label` is set to :attr:`True`, Label is a ``Tensor`` 
            in the same shape with :attr:`logits` expect shape in dimension :attr:`axis` as 1.
        soft_label (bool, optional): A flag to indicate whether to interpretant the given
            labels as soft labels. Default False.
        ignore_index (int, optional): Specifies a target value that is ignored and does
                                      not contribute to the input gradient. Only valid
                                      if :attr:`soft_label` is set to :attr:`False`. 
                                      Default: kIgnoreIndex(-100).
        numeric_stable_mode (bool, optional): A flag to indicate whether to use a more
                                              numerically stable algorithm. Only valid
                                              when :attr:`soft_label` is :attr:`False` 
                                              and GPU is used. When :attr:`soft_label` 
                                              is :attr:`True` or CPU is used, the 
                                              algorithm is always numerically stable.
                                              Note that the speed may be slower when use
                                              stable algorithm. Default: True.
        return_softmax (bool, optional): A flag indicating whether to return the softmax
                                         along with the cross entropy loss. Default: False.
        axis (int, optional): The index of dimension to perform softmax calculations. It 
                              should be in range :math:`[-1, rank - 1]`, while :math:`rank`
                              is the rank of input :attr:`logits`. Default: -1.

    Returns:
        ``Tensor`` or Tuple of two ``Tensor`` : Return the cross entropy loss if \
                                                    `return_softmax` is False, otherwise the tuple \
                                                    (loss, softmax), softmax is in the same shape \
                                                    with input logits and cross entropy loss is in \
                                                    the same shape with input logits except shape \
                                                    in dimension :attr:`axis` as 1.

    Examples:
        .. code-block:: python

            import paddle
            import numpy as np

            data = np.random.rand(128).astype("float32")
            label = np.random.rand(1).astype("int64")
            data = paddle.to_tensor(data)
            label = paddle.to_tensor(label)
            linear = paddle.nn.Linear(128, 100)
            x = linear(data)
            out = paddle.nn.functional.softmax_with_cross_entropy(logits=x, label=label)
            print(out)
    """
    if _non_static_mode():
        if core.is_compiled_with_npu():
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            softmax, backprop, loss = _legacy_C_ops.softmax_with_cross_entropy(
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                logits, label, 'soft_label', soft_label, 'ignore_index',
                ignore_index, 'numeric_stable_mode', numeric_stable_mode,
                'axis', axis)
        else:
            if in_dygraph_mode():
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                softmax, loss = _C_ops.cross_entropy_with_softmax(
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                    logits, label, soft_label, True, numeric_stable_mode,
                    ignore_index, axis)
            if _in_legacy_dygraph():
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                softmax, loss = _legacy_C_ops.softmax_with_cross_entropy(
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                    logits, label, 'soft_label', soft_label, 'ignore_index',
                    ignore_index, 'numeric_stable_mode', numeric_stable_mode,
                    'axis', axis)
        if not return_softmax:
            return loss
        else:
            return loss, softmax

    attrs = {
        'soft_label': soft_label,
        'ignore_index': ignore_index,
        'numeric_stable_mode': numeric_stable_mode,
        'axis': axis
    }
    helper = LayerHelper('softmax_with_cross_entropy', **locals())
    softmax = helper.create_variable_for_type_inference(dtype=logits.dtype)
    loss = helper.create_variable_for_type_inference(dtype=logits.dtype)

    outputs = {'Softmax': softmax, 'Loss': loss}
    if core.is_compiled_with_npu() or core.is_compiled_with_mlu():
        backprop = helper.create_variable_for_type_inference(dtype=logits.dtype)
        outputs['Backprop'] = backprop
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    helper.append_op(type='softmax_with_cross_entropy',
                     inputs={
                         'Logits': logits,
                         'Label': label
                     },
                     outputs=outputs,
                     attrs=attrs)
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    if return_softmax:
        return loss, softmax

    return loss


def npair_loss(anchor, positive, labels, l2_reg=0.002):
    """ 
  
    Npair loss requires paired data. Npair loss has two parts: the first part is L2
    regularizer on the embedding vector; the second part is cross entropy loss which
    takes the similarity matrix of anchor and positive as logits.
  
    For more information, please refer to:
    `Improved Deep Metric Learning with Multi class N pair Loss Objective <http://www.nec-labs.com/uploads/images/Department-Images/MediaAnalytics/papers/nips16_npairmetriclearning.pdf>`_
  
    Args:
      anchor(Tensor): embedding vector for the anchor image. shape=[batch_size, embedding_dims], 
                        the data type is float32 or float64.
      positive(Tensor): embedding vector for the positive image. shape=[batch_size, embedding_dims], 
                        the data type is float32 or float64.
      labels(Tensor): 1-D tensor. shape=[batch_size], the data type is float32 or float64 or int64.
      l2_reg(float32): L2 regularization term on embedding vector, default: 0.002.

  
    Returns:
      A Tensor representing the npair loss, the data type is the same as anchor, the shape is [1].
  
    Examples:

      .. code-block:: python
  
          import paddle
          
          DATATYPE = "float32"
  
          anchor = paddle.rand(shape=(18, 6), dtype=DATATYPE)
          positive = paddle.rand(shape=(18, 6), dtype=DATATYPE)
          labels = paddle.rand(shape=(18,), dtype=DATATYPE)
          
          npair_loss = paddle.nn.functional.npair_loss(anchor, positive, labels, l2_reg = 0.002)
          print(npair_loss)
  
    """
    check_variable_and_dtype(anchor, 'anchor', ['float32', 'float64'],
                             'npair_loss')
    check_variable_and_dtype(positive, 'positive', ['float32', 'float64'],
                             'positive')
    check_variable_and_dtype(labels, 'labels', ['float32', 'float64', 'int64'],
                             'labels')
    Beta = 0.25
    batch_size = labels.shape[0]

    labels = paddle.reshape(labels, shape=[batch_size, 1])
    labels = paddle.tile(labels, repeat_times=[1, batch_size])

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    labels = paddle.equal(labels, paddle.transpose(labels,
                                                   perm=[1,
                                                         0])).astype('float32')
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    labels = labels / paddle.sum(labels, axis=1, keepdim=True)

    l2loss = paddle.mean(paddle.sum(paddle.square(anchor), 1)) \
             + paddle.mean(paddle.sum(paddle.square(positive), 1))
    l2loss = l2loss * Beta * l2_reg

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    similarity_matrix = paddle.matmul(anchor,
                                      positive,
                                      transpose_x=False,
                                      transpose_y=True)
    softmax_ce = fluid_softmax_with_cross_entropy(logits=similarity_matrix,
                                                  label=labels,
                                                  soft_label=True)
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    cross_entropy = paddle.sum(labels * softmax_ce, 0)
    celoss = paddle.mean(cross_entropy)

    return l2loss + celoss


def square_error_cost(input, label):
    r"""

    This op accepts input predictions and target label and returns the
    squared error cost.

    For predictions label, and target label, the equation is:

    .. math::

        Out = (input - label)^2

    Parameters:
        input (Tensor): Input tensor, the data type should be float32.
        label (Tensor): Label tensor, the data type should be float32.

    Returns:
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        Tensor, The tensor storing the element-wise squared error
        difference between input and label.
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    Examples:

        .. code-block:: python

            import paddle
            input = paddle.to_tensor([1.1, 1.9])
            label = paddle.to_tensor([1.0, 2.0])
            output = paddle.nn.functional.square_error_cost(input, label)
            print(output)
            # [0.01, 0.01]

    """
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    if in_dygraph_mode():
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        minus_out = _C_ops.subtract(input, label)
        square_out = _C_ops.square(minus_out)
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        return square_out
    elif _in_legacy_dygraph():
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        minus_out = _legacy_C_ops.elementwise_sub(input, label)
        square_out = _legacy_C_ops.square(minus_out)
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        return square_out

    check_variable_and_dtype(input, "input", ['float32', 'float64'],
                             'square_error_cost')
    check_variable_and_dtype(label, "label", ['float32', 'float64'],
                             'square_error_cost')
    helper = LayerHelper('square_error_cost', **locals())
    minus_out = helper.create_variable_for_type_inference(dtype=input.dtype)
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    helper.append_op(type='elementwise_sub',
                     inputs={
                         'X': [input],
                         'Y': [label]
                     },
                     outputs={'Out': [minus_out]})
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    square_out = helper.create_variable_for_type_inference(dtype=input.dtype)
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    helper.append_op(type='square',
                     inputs={'X': [minus_out]},
                     outputs={'Out': [square_out]})
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    return square_out


def edit_distance(input,
                  label,
                  normalized=True,
                  ignored_tokens=None,
                  input_length=None,
                  label_length=None):
    """
    This op computes the edit distances, also called Levenshtein distance, between a batch of
    hypothesis strings and their references. It measures how dissimilar two strings are by counting
    the minimum number of operations to transform one string into another.
    The operations include insertion, deletion, and substitution.

    For example, given hypothesis string A = "kitten" and reference
    B = "sitting", A will be transformed into B
    at least after two substitutions and one insertion:

    "kitten" -> "sitten" -> "sittin" -> "sitting"

    So the edit distance between A and B is 3.

    The input is a Tensor, the input_length and label_length should be supported.

    The `batch_size` of labels should be same as `input`.

    The output include the edit distance value between every pair of input and related label, and the number of sequence.
    If Attr(normalized) is true,
    the edit distance value will be divided by the length of label.

    Parameters:
        input(Tensor): The input tensor, its rank should be equal to 2 and its data type should be int64.
        label(Tensor): The label tensor, its rank should be equal to 2 and its data type should be int64.
        normalized(bool, default True): Indicated whether to normalize the edit distance.
        ignored_tokens(list<int>, default None): Tokens that will be removed before
                                     calculating edit distance.
        input_length(Tensor): The length for each sequence in `input` if it's of Tensor type, it should have shape `(batch_size, )` and its data type should be int64.
        label_length(Tensor): The length for each sequence in `label` if it's of Tensor type, it should have shape `(batch_size, )` and its data type should be int64.
        NOTE: To be avoid unexpected result, the value of every elements in input_length and label_length should be equal to the value of the second dimension of input and label. For example, The input: [[1,2,3,4],[5,6,7,8],[9,10,11,12]], the shape of input is [3,4] and the input_length should be [4,4,4]
        NOTE: This Api is different from fluid.metrics.EditDistance

    Returns:
	Tuple:

        distance(Tensor): edit distance result, its data type is float32, and its shape is (batch_size, 1).
        sequence_num(Tensor): sequence number, its data type is float32, and its shape is (1,).

    Examples:
        .. code-block:: python

            import paddle
            import paddle.nn.functional as F

            input = paddle.to_tensor([[1,2,3],[4,5,6],[4,4,4],[1,1,1]], dtype='int64')
            label = paddle.to_tensor([[1,3,4,1],[4,5,8,1],[7,7,7,1],[1,1,1,1]], dtype='int64')
            input_len = paddle.to_tensor([3,3,3,3], dtype='int64')
            label_len = paddle.to_tensor([4,4,4,4], dtype='int64')

            distance, sequence_num = F.loss.edit_distance(input=input, label=label, input_length=input_len, label_length=label_len, normalized=False)

            # print(distance)
            # [[3.]
            #  [2.]
            #  [4.]
            #  [1.]]
            # if set normalized to True
            # [[0.75]
            #  [0.5 ]
            #  [1.  ]
            #  [0.25]
            #
            # print(sequence_num)
            # [4]

    """
    check_variable_and_dtype(input, 'input', ['int64'], 'edit_distance')
    check_variable_and_dtype(label, 'label', ['int64'], 'edit_distance')
    helper = LayerHelper("edit_distance", **locals())

    # remove some tokens from input and labels
    if ignored_tokens is not None and len(ignored_tokens) > 0:
        erased_input = helper.create_variable_for_type_inference(dtype="int64")
        erased_label = helper.create_variable_for_type_inference(dtype="int64")

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        helper.append_op(type="sequence_erase",
                         inputs={"X": [input]},
                         outputs={"Out": [erased_input]},
                         attrs={"tokens": ignored_tokens})
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        input = erased_input

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        helper.append_op(type="sequence_erase",
                         inputs={"X": [label]},
                         outputs={"Out": [erased_label]},
                         attrs={"tokens": ignored_tokens})
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        label = erased_label

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    if in_dygraph_mode():
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        return _C_ops.edit_distance(input, label, input_length, label_length,
                                    normalized)
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    this_inputs = {"Hyps": [input], "Refs": [label]}
    if input_length is not None and label_length is not None:
        this_inputs['HypsLength'] = [input_length]
        this_inputs['RefsLength'] = [label_length]

    # edit distance op
    edit_distance_out = helper.create_variable_for_type_inference(dtype="int64")
    sequence_num = helper.create_variable_for_type_inference(dtype="int64")
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    helper.append_op(type="edit_distance",
                     inputs=this_inputs,
                     outputs={
                         "Out": [edit_distance_out],
                         "SequenceNum": [sequence_num]
                     },
                     attrs={"normalized": normalized})
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    return edit_distance_out, sequence_num


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def binary_cross_entropy(input,
                         label,
                         weight=None,
                         reduction='mean',
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                         name=None):
    """
    This op measures the binary_cross_entropy loss between input predictions ``input``
    and target labels ``label`` . The binary_cross_entropy loss can be described as:

    If :attr:`weight` is set, the loss is:

    .. math::
        Out = -1 * weight * (label * log(input) + (1 - label) * log(1 - input))

    If :attr:`weight` is None, the loss is:

    .. math::
        Out = -1 * (label * log(input) + (1 - label) * log(1 - input))

    If :attr:`reduction` set to ``'none'``, the interface will return the original loss `Out`.

    If :attr:`reduction` set to ``'mean'``, the reduced mean loss is:

    .. math::
        Out = MEAN(Out)

    If :attr:`reduction` set to ``'sum'``, the reduced sum loss is:

    .. math::
        Out = SUM(Out)

    Note that the input predictions ``input`` always be the output of sigmoid, and the target labels ``label``
    should be numbers between 0 and 1.

    Parameters:
        input (Tensor): The input predications tensor. 2-D tensor with shape: [N, *],
            N is batch_size, `*` means number of additional dimensions. The ``input``
            should always be the output of sigmod.  Available dtype is float32, float64.
        label (Tensor): The target labels tensor. 2-D tensor with the same shape as
            ``input``. The target labels which values should be numbers between 0 and 1.
            Available dtype is float32, float64.
        weight (Tensor, optional): A manual rescaling weight given to the loss of each
            batch element. If given, has to be a Tensor of size nbatch and the data type
            is float32, float64. Default is ``'None'``.
        reduction (str, optional): Indicate how to average the loss by batch_size,
            the candicates are ``'none'`` | ``'mean'`` | ``'sum'``.
            If :attr:`reduction` is ``'none'``, the unreduced loss is returned;
            If :attr:`reduction` is ``'mean'``, the reduced mean loss is returned;
            If :attr:`reduction` is ``'sum'``, the summed loss is returned.
            Default is ``'mean'``.
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.


    Returns:
        output (Tensor): If ``reduction`` is ``'none'``, the shape of output is
            same as ``input`` , else the shape of output is scalar.

    Examples:
        .. code-block:: python

            import paddle

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            input = paddle.to_tensor([0.5, 0.6, 0.7], 'float32')
            label = paddle.to_tensor([1.0, 0.0, 1.0], 'float32')
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            output = paddle.nn.functional.binary_cross_entropy(input, label)
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            print(output)  # [0.65537095]
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    """
    if reduction not in ['sum', 'mean', 'none']:
        raise ValueError(
            "The value of 'reduction' in binary_cross_entropy should be 'sum', "
            "'mean' or 'none', but received %s, which is not allowed." %
            reduction)

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    if in_dygraph_mode():
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        out = _C_ops.bce_loss(input, label)
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        if weight is not None:
630
            out = _C_ops.multiply(out, weight, 'axis', -1)
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        if reduction == 'sum':
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            return _C_ops.sum(out, [], None, False)
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        elif reduction == 'mean':
636
            return _C_ops.mean_all(out)
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        else:
            return out
    else:
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        if _in_legacy_dygraph():
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            out = _legacy_C_ops.bce_loss(input, label)
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            if weight is not None:
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                out = _legacy_C_ops.elementwise_mul(out, weight, 'axis', -1)
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            if reduction == 'sum':
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                return _legacy_C_ops.reduce_sum(out, 'dim', [0], 'keep_dim',
                                                False, "reduce_all", True)
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            elif reduction == 'mean':
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                return _legacy_C_ops.mean(out)
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            else:
                return out
        else:
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            check_variable_and_dtype(input, 'input', ['float32', 'float64'],
                                     'binary_cross_entropy')
            check_variable_and_dtype(label, 'label', ['float32', 'float64'],
                                     'binary_cross_entropy')
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            sub_name = name if weight is None and reduction == 'none' else None
            helper = LayerHelper("binary_cross_entropy", name=sub_name)
            out = helper.create_variable_for_type_inference(dtype=input.dtype)
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            helper.append_op(type='bce_loss',
                             inputs={
                                 'X': [input],
                                 'Label': [label],
                             },
                             outputs={'Out': [out]})
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            if weight is not None:
                if isinstance(weight, paddle.static.Variable):
                    weight_name = name if reduction == 'none' else None
                    out = paddle.multiply(out, weight, name=weight_name)
                else:
                    raise ValueError(
                        "The weight is not a Tensor, please convert to Tensor.")

            if reduction == 'sum':
                return paddle.sum(out, name=name)
            elif reduction == 'mean':
                return paddle.mean(out, name=name)
            else:
                return out
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def binary_cross_entropy_with_logits(logit,
                                     label,
                                     weight=None,
                                     reduction='mean',
                                     pos_weight=None,
                                     name=None):
689
    r"""
690 691 692 693 694 695 696 697 698 699 700 701 702
    This operator combines the sigmoid layer and the :ref:`api_nn_loss_BCELoss` layer.
    Also, we can see it as the combine of ``sigmoid_cross_entropy_with_logits``
    layer and some reduce operations.

    This measures the element-wise probability error in classification tasks
    in which each class is independent.
    This can be thought of as predicting labels for a data-point, where labels
    are not mutually exclusive. For example, a news article can be about
    politics, technology or sports at the same time or none of these.

    First this operator calculate loss function as follows:

    .. math::
703
           Out = -Labels * \log(\sigma(Logit)) - (1 - Labels) * \log(1 - \sigma(Logit))
704

705
    We know that :math:`\sigma(Logit) = \frac{1}{1 + e^{-Logit}}`. By substituting this we get:
706 707

    .. math::
708
           Out = Logit - Logit * Labels + \log(1 + e^{-Logit})
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    For stability and to prevent overflow of :math:`e^{-Logit}` when Logit < 0,
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    we reformulate the loss as follows:

    .. math::
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           Out = \max(Logit, 0) - Logit * Labels + \log(1 + e^{-\|Logit\|})
715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758

    Then, if ``weight`` or ``pos_weight`` is not None, this operator multiply the
    weight tensor on the loss `Out`. The ``weight`` tensor will attach different
    weight on every items in the batch. The ``pos_weight`` will attach different
    weight on the positive label of each class.

    Finally, this operator applies reduce operation on the loss.
    If :attr:`reduction` set to ``'none'``, the operator will return the original loss `Out`.
    If :attr:`reduction` set to ``'mean'``, the reduced mean loss is :math:`Out = MEAN(Out)`.
    If :attr:`reduction` set to ``'sum'``, the reduced sum loss is :math:`Out = SUM(Out)`.

    Note that the target labels ``label`` should be numbers between 0 and 1.

    Args:
        logit (Tensor): The input predications tensor. 2-D tensor with shape: [N, *],
            N is batch_size, `*` means number of additional dimensions. The ``logit``
            is usually the output of Linear layer. Available dtype is float32, float64.
        label (Tensor): The target labels tensor. 2-D tensor with the same shape as
            ``logit``. The target labels which values should be numbers between 0 and 1.
            Available dtype is float32, float64.
        weight (Tensor, optional): A manual rescaling weight given to the loss of each
            batch element. If given, it has to be a 1D Tensor whose size is `[N, ]`,
            The data type is float32, float64. Default is ``'None'``.
        reduction (str, optional): Indicate how to average the loss by batch_size,
            the candicates are ``'none'`` | ``'mean'`` | ``'sum'``.
            If :attr:`reduction` is ``'none'``, the unreduced loss is returned;
            If :attr:`reduction` is ``'mean'``, the reduced mean loss is returned;
            If :attr:`reduction` is ``'sum'``, the summed loss is returned.
            Default is ``'mean'``.
        pos_weight (Tensor, optional): A weight of positive examples. Must be a vector
            with length equal to the number of classes. The data type is float32, float64.
            Default is ``'None'``.
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        output (Tensor): If ``reduction`` is ``'none'``, the shape of output is
            same as ``logit`` , else the shape of output is scalar.

    Examples:

        .. code-block:: python

            import paddle
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            logit = paddle.to_tensor([5.0, 1.0, 3.0])
            label = paddle.to_tensor([1.0, 0.0, 1.0])
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            output = paddle.nn.functional.binary_cross_entropy_with_logits(logit, label)
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            print(output)  # [0.45618808]
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    """
    if reduction not in ['sum', 'mean', 'none']:
        raise ValueError(
            "The value of 'reduction' in binary_cross_entropy_with_logits "
            "should be 'sum', 'mean' or 'none', but received %s, which is not allowed."
            % reduction)

772
    if in_dygraph_mode():
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        one = _C_ops.full([1], float(1.0), core.VarDesc.VarType.FP32,
                          _current_expected_place())
        out = _C_ops.sigmoid_cross_entropy_with_logits(logit, label, False,
                                                       -100)
777
        if pos_weight is not None:
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            log_weight = _C_ops.add(
                _C_ops.multiply(label, _C_ops.subtract(pos_weight, one)), one)
            out = _C_ops.multiply(out, log_weight)
781
        if weight is not None:
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            out = _C_ops.multiply(out, weight)
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        if reduction == "sum":
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            return _C_ops.sum(out, [], None, False)
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        elif reduction == "mean":
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            return _C_ops.mean_all(out)
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        else:
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            return out
    elif _in_legacy_dygraph():
        one = _varbase_creator(dtype=logit.dtype)
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        _legacy_C_ops.fill_constant(one, 'value', float(1.0), 'force_cpu',
                                    False, 'dtype', one.dtype, 'str_value',
                                    '1.0', 'shape', [1])
        out = _legacy_C_ops.sigmoid_cross_entropy_with_logits(logit, label)
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        if pos_weight is not None:
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            log_weight = _legacy_C_ops.elementwise_add(
                _legacy_C_ops.elementwise_mul(
                    label, _legacy_C_ops.elementwise_sub(pos_weight, one)), one)
            out = _legacy_C_ops.elementwise_mul(out, log_weight)
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        if weight is not None:
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            out = _legacy_C_ops.elementwise_mul(out, weight)
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        if reduction == "sum":
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            return _legacy_C_ops.reduce_sum(out, 'reduce_all', True)
806
        elif reduction == "mean":
807
            return _legacy_C_ops.mean(out)
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        else:
            return out

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    check_variable_and_dtype(logit, 'logit', ['float32', 'float64'],
                             'binary_cross_entropy_with_logits')
    check_variable_and_dtype(label, 'label', ['float32', 'float64'],
                             'binary_cross_entropy_with_logits')
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    sigmoid_name = None
    if reduction == 'none' and pos_weight is None and weight is None:
        sigmoid_name = name

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    out = paddle.fluid.layers.sigmoid_cross_entropy_with_logits(
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        logit, label, name=sigmoid_name)

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    one = paddle.full(shape=[1], fill_value=1.0, dtype=logit.dtype)
823
    if pos_weight is not None:
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        check_variable_and_dtype(pos_weight, 'pos_weight',
                                 ['float32', 'float64'],
                                 'binary_cross_entropy_with_logits')
827
        log_weight = paddle.add(
828
            paddle.multiply(label, paddle.subtract(pos_weight, one)), one)
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        pos_weight_name = name if reduction == 'none' and weight is None else None
        out = paddle.multiply(out, log_weight, name=pos_weight_name)

    if weight is not None:
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        check_variable_and_dtype(weight, 'weight', ['float32', 'float64'],
                                 'binary_cross_entropy_with_logits')
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        weight_name = name if reduction == 'none' else None
        out = paddle.multiply(out, weight, name=weight_name)

    if reduction == "sum":
        return paddle.sum(out, name=name)
    elif reduction == "mean":
        return paddle.mean(out, name=name)
    return out


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def hsigmoid_loss(input,
                  label,
                  num_classes,
                  weight,
                  bias=None,
                  path_table=None,
                  path_code=None,
                  is_sparse=False,
                  name=None):
    """
    The hierarchical sigmoid organizes the classes into a complete binary tree to reduce the computational complexity
    and speed up the model training, especially the training of language model.
    Each leaf node of the complete binary tree represents a class(word) and each non-leaf node acts as a binary classifier.
    For each class(word), there's a unique path from root to itself, hsigmoid calculate the cost for each non-leaf node on
    the path, and sum them to get a total cost.
    Comparing to softmax, the OP can reduce the computational complexity from :math:`O(N)` to :math:`O(logN)`, where :math:`N`
    represents the number of classes or the size of word dict.

    The OP supports default tree and custom tree. For the default tree, you can refer to `Hierarchical Probabilistic Neural
    Network Language Model <http://www.iro.umontreal.ca/~lisa/pointeurs/hierarchical-nnlm-aistats05.pdf>`_. For the custom
    tree, you need to set :attr:`is_custom` to True, and do the following steps (take the language model as an example):

    1. Using a custom word dict to build a binary tree, each leaf node should be an word in the word dict.
    2. Creating a dict map word_id -> path that from the word to the root node, we call it path_table.
    3. Creating a dict map word_id -> code of path that from the word to the root node, we call it path_code.
       Code means the label of each binary classifier, 1 indicate true, 0 indicate false.
    4. Now, each word should has its path and code along the path, you can pass a batch of path and code related
       to the same batch of inputs.

    Parameters:
        input (Tensor): A tensor with the shape [N, D], where N is the size of mini-batch,
            and D is the feature size. Its data type supports float32 or float64.
        label (Tensor): A tensor contains the labels of training data. Its shape is [N, 1]
            and data type is int64.
        num_classes (int): The number of classes or the size of word dict, must be greater than 2.
            If the default tree is used (path_code and path_table is None are None), `num_classes`
            should not be None. If the custom tree is used (path_code and path_table is None are not None),
            `num_classes` should be the number of non-leaf nodes, which indicates the num of
            classes using by the binary classifier.
        weight (Tensor): A tensor with shape (num_classes - 1, D), with the same data type as `input`.
        bias (Tensor, optional): A tensor with shape (num_classes - 1, 1), with the same data type as `input`.
            If `bias` is None, no bias will be add. Default is None.
        path_table (Tensor, optional): A tensor that stores each batch of samples' path from leaf to root
            node, its shape is [N, L] and data type is int64, where L is the length of path. For each sample i,
            path_table[i] is a np.array like structure and each element in this array is the indexes in parent
            nodes' weight matrix. If `path_table` and `path_code` are None, the default tree will be used.
            Default is None.
        path_code (Tensor, optional): A tensor that stores each batch of samples' code of path from leaf
            to root node, its shape is [N, L] and data type is int64, which is the same as :attr:`path_table`.
            Each code of path is consisted with the code of nodes from leaf to root node. If `path_table` and
            `path_code` are None, the default tree will be used. Default is None.
        is_sparse (bool, optional): Whether use sparse updating instead of dense updating. If `is_sparse` is True,
            the gradient of `weight` and `input` will be sparse. Default is False.
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        A tensor with the cost of hierarchical sigmoid, its shape is [N, 1] and data type is the same as `input`.

    Examples:
        .. code-block:: python

            import paddle
            import paddle.nn.functional as F

            paddle.set_device('cpu')

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            input = paddle.uniform([4, 3])
            # [[0.45424712  -0.77296764  0.82943869] # random
            #  [0.85062802  0.63303483  0.35312140] # random
            #  [0.57170701  0.16627562  0.21588242] # random
            #  [0.27610803  -0.99303514  -0.17114788]] # random
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            label = paddle.to_tensor([0, 1, 4, 5])
            num_classes = 5
            weight=paddle.uniform([num_classes-1, 3])
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            # [[-0.64477652  0.24821866  -0.17456549] # random
            #  [-0.04635394  0.07473493  -0.25081766] # random
            #  [ 0.05986035  -0.12185556  0.45153677] # random
            #  [-0.66236806  0.91271877  -0.88088769]] # random
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            out=F.hsigmoid_loss(input, label, num_classes, weight)
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            # [[1.96709502]
            #  [2.40019274]
            #  [2.11009121]
            #  [1.92374969]]
930
    """
931
    if in_dygraph_mode():
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        out, _, _ = _C_ops.hierarchical_sigmoid(input, weight, label,
                                                path_table, path_code, bias,
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                                                num_classes, is_sparse, 0, [],
                                                [], [], is_sparse)
        return out
    elif _in_legacy_dygraph():
        out, _, _ = _legacy_C_ops.hierarchical_sigmoid(
            input, weight, label, path_table, path_code, bias, 'num_classes',
            num_classes, 'is_sparse', is_sparse, 'remote_prefetch', is_sparse)
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        return out

    check_variable_and_dtype(input, 'input', ['float32', 'float64'],
                             'hsigmoid_loss')
    check_variable_and_dtype(label, 'label', ['int64'], 'hsigmoid_loss')
    check_variable_and_dtype(weight, 'weight', ['float32', 'float64'],
                             'hsigmoid_loss')
    if bias is not None:
        check_variable_and_dtype(bias, 'bias', ['float32', 'float64'],
                                 'hsigmoid_loss')
    if path_table is not None:
        check_variable_and_dtype(path_table, 'path_table', ['int64'],
                                 'hsigmoid_loss')
    if path_code is not None:
        check_variable_and_dtype(path_code, 'path_code', ['int64'],
                                 'hsigmoid_loss')

    attrs = {
        "num_classes": num_classes,
        "is_sparse": is_sparse,
        "remote_prefetch": is_sparse
    }

    inputs = {
        "X": input,
        "W": weight,
        "Bias": bias,
        "PathTable": path_table,
        "PathCode": path_code,
        "Label": label
    }

    helper = LayerHelper('hsigmoid_loss', **locals())
    out = helper.create_variable_for_type_inference(input.dtype)
    pre_out = helper.create_variable_for_type_inference(input.dtype)
    outputs = {"Out": out, "PreOut": pre_out, "W_Out": weight}

978 979 980 981
    helper.append_op(type="hierarchical_sigmoid",
                     inputs=inputs,
                     outputs=outputs,
                     attrs=attrs)
982 983 984
    return out


985
def smooth_l1_loss(input, label, reduction='mean', delta=1.0, name=None):
986
    r"""
987
    Calculate smooth_l1_loss. Creates a criterion that uses a squared
988 989 990 991 992 993
    term if the absolute element-wise error falls below 1 and an L1 term otherwise.
    In some cases it can prevent exploding gradients and it is more robust and less
    sensitivity to outliers. Also known as the Huber loss:

    .. math::

994
         loss(x,y) = \frac{1}{n}\sum_{i}z_i
995 996 997 998 999 1000


    where z_i is given by:

    .. math::

1001 1002
        \mathop{z_i} = \left\{\begin{array}{rcl}
        0.5(x_i - y_i)^2 & & {if |x_i - y_i| < delta} \\
1003
        delta * |x_i - y_i| - 0.5 * delta^2 & & {otherwise}
1004
        \end{array} \right.
1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017

    Parameters:
        input (Tensor): Input tensor, the data type is float32 or float64. Shape is
            (N, C), where C is number of classes, and if shape is more than 2D, this
            is (N, C, D1, D2,..., Dk), k >= 1.
        label (Tensor): Label tensor, the data type is float32 or float64. The shape of label
            is the same as the shape of input.
        reduction (str, optional): Indicate how to average the loss by batch_size,
            the candicates are ``'none'`` | ``'mean'`` | ``'sum'``.
            If :attr:`reduction` is ``'mean'``, the reduced mean loss is returned;
            If :attr:`reduction` is ``'sum'``, the reduced sum loss is returned.
            If :attr:`reduction` is ``'none'``, the unreduced loss is returned.
            Default is ``'mean'``.
1018
        delta (float, optional): Specifies the hyperparameter delta to be used.
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            The value determines how large the errors need to be to use L1. Errors
            smaller than delta are minimized with L2. Parameter is ignored for
            negative/zero values. Default = 1.0
        name (str, optional): Name for the operation (optional, default is
            None). For more information, please refer to :ref:`api_guide_Name`.

    Returns:
1026
        Tensor, The tensor variable storing the smooth_l1_loss of input and label.
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    Examples:
        .. code-block:: python

            import paddle
            import numpy as np

            input_data = np.random.rand(3,3).astype("float32")
            label_data = np.random.rand(3,3).astype("float32")
            input = paddle.to_tensor(input_data)
            label = paddle.to_tensor(label_data)
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            output = paddle.nn.functional.smooth_l1_loss(input, label)
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            print(output)
1040
    """
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    check_variable_and_dtype(input, 'input', ['float32', 'float64'],
                             'smooth_l1_loss')
    check_variable_and_dtype(label, 'label', ['float32', 'float64'],
                             'smooth_l1_loss')
1045

1046
    if in_dygraph_mode():
1047
        out, residual = _C_ops.huber_loss(input, label, delta)
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    else:
        helper = LayerHelper('huber_loss', **locals())
        residual = helper.create_variable_for_type_inference(
            dtype=helper.input_dtype())
        out = helper.create_variable_for_type_inference(
            dtype=helper.input_dtype())
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        helper.append_op(type='huber_loss',
                         inputs={
                             'X': input,
                             'Y': label
                         },
                         outputs={
                             'Out': out,
                             'Residual': residual
                         },
                         attrs={'delta': delta})
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    if reduction not in ['sum', 'mean', 'none']:
        raise ValueError(
            "The value of 'reduction' in smooth_l1_loss should be 'sum', 'mean' or"
            " 'none', but received %s, which is not allowed." % reduction)
    if reduction == 'none':
        return out
    elif reduction == 'mean':
1072
        return paddle.mean(out)
1073
    elif reduction == 'sum':
1074
        return paddle.sum(out)
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1077 1078
def margin_ranking_loss(input,
                        other,
1079
                        label,
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                        margin=0.0,
                        reduction='mean',
                        name=None):
1083
    r"""
1084

1085
    Calcluate the margin rank loss between the input, other and label, use the math function as follows.
1086

1087
    .. math::
1088
        margin\_rank\_loss = max(0, -label * (input - other) + margin)
1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104

    If :attr:`reduction` set to ``'mean'``, the reduced mean loss is:

    .. math::
        Out = MEAN(margin\_rank\_loss)

    If :attr:`reduction` set to ``'sum'``, the reduced sum loss is:

    .. math::
        Out = SUM(margin\_rank\_loss)

    If :attr:`reduction` set to ``'none'``, just return the origin ``margin_rank_loss``.

    Parameters:
        input(Tensor): the first input tensor, it's data type should be float32, float64.
        other(Tensor): the second input tensor, it's data type should be float32, float64.
1105
        label(Tensor): the label value corresponding to input, it's data type should be float32, float64.
1106 1107 1108 1109
        margin (float, optional): The margin value to add, default value is 0;
        reduction (str, optional): Indicate the reduction to apply to the loss, the candicates are ``'none'``, ``'mean'``, ``'sum'``.If :attr:`reduction` is ``'none'``, the unreduced loss is returned; If :attr:`reduction` is ``'mean'``, the reduced mean loss is returned. If :attr:`reduction` is ``'sum'``, the reduced sum loss is returned. Default is ``'mean'``.
        name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.

1110 1111
    Returns: 
        Tensor, if :attr:`reduction` is ``'mean'`` or ``'sum'``, the out shape is :math:`[1]`, otherwise the shape is the same as `input` .The same dtype as input tensor.
1112 1113 1114 1115 1116

    Examples:

        .. code-block:: python

1117 1118
            import paddle

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            input = paddle.to_tensor([[1, 2], [3, 4]], dtype='float32')
            other = paddle.to_tensor([[2, 1], [2, 4]], dtype='float32')
            label = paddle.to_tensor([[1, -1], [-1, -1]], dtype='float32')
1122
            loss = paddle.nn.functional.margin_ranking_loss(input, other, label)
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            print(loss) # [0.75]
1124
    """
1125 1126 1127 1128
    if reduction not in ['sum', 'mean', 'none']:
        raise ValueError(
            "The value of 'reduction' in MarginRankingLoss should be 'sum', 'mean' or 'none', but "
            "received %s, which is not allowed." % reduction)
1129
    if in_dygraph_mode():
1130 1131
        out = _C_ops.subtract(other, input)
        out = _C_ops.multiply(out, label)
1132 1133
        if margin != 0.0:
            margin = fluid.dygraph.base.to_variable([margin], dtype=out.dtype)
1134 1135
            out = _C_ops.add(out, margin)
        out = _C_ops.relu(out)
1136
        if reduction == 'sum':
1137
            return _C_ops.sum(out, [], None, False)
1138
        elif reduction == 'mean':
1139
            return _C_ops.mean_all(out)
1140 1141
        return out
    elif _in_legacy_dygraph():
1142 1143
        out = _legacy_C_ops.elementwise_sub(other, input)
        out = _legacy_C_ops.elementwise_mul(out, label)
1144 1145
        if margin != 0.0:
            margin = fluid.dygraph.base.to_variable([margin], dtype=out.dtype)
1146 1147
            out = _legacy_C_ops.elementwise_add(out, margin)
        out = _legacy_C_ops.relu(out)
1148
        if reduction == 'sum':
1149
            return _legacy_C_ops.reduce_sum(out, 'reduce_all', True)
1150
        elif reduction == 'mean':
1151
            return _legacy_C_ops.mean(out)
1152 1153 1154
        return out

    helper = LayerHelper("margin_ranking_loss", **locals())
1155 1156 1157 1158 1159 1160
    check_variable_and_dtype(input, 'input', ['float32', 'float64'],
                             'margin_rank_loss')
    check_variable_and_dtype(other, 'other', ['float32', 'float64'],
                             'margin_rank_loss')
    check_variable_and_dtype(label, 'label', ['float32', 'float64'],
                             'margin_rank_loss')
1161

1162
    out = paddle.subtract(other, input)
1163
    out = paddle.multiply(out, label)
1164 1165 1166

    if margin != 0.0:
        margin_var = out.block.create_var(dtype=out.dtype)
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        margin_var = paddle.full(shape=[1], fill_value=margin, dtype=out.dtype)
1168 1169 1170 1171 1172
        out = paddle.add(out, margin_var)

    result_out = helper.create_variable_for_type_inference(input.dtype)

    if reduction == 'none':
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        helper.append_op(type="relu",
                         inputs={"X": out},
                         outputs={"Out": result_out})
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        return result_out
    elif reduction == 'sum':
        out = paddle.nn.functional.relu(out)
        attrs = {"dim": [0], "keep_dim": False, "reduce_all": True}
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        helper.append_op(type="reduce_sum",
                         inputs={"X": out},
                         outputs={"Out": result_out},
                         attrs=attrs)
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        return result_out
    elif reduction == 'mean':
        out = paddle.nn.functional.relu(out)
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        helper.append_op(type="mean",
                         inputs={"X": out},
                         outputs={"Out": result_out},
                         attrs={})
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        return result_out


1194
def l1_loss(input, label, reduction='mean', name=None):
1195
    r"""
1196
    This operator computes the L1 Loss of Tensor ``input`` and ``label`` as follows.
1197

1198
    If `reduction` set to ``'none'``, the loss is:
1199 1200

    .. math::
1201
        Out = \lvert input - label \rvert
1202

1203
    If `reduction` set to ``'mean'``, the loss is:
1204 1205

    .. math::
1206
        Out = MEAN(\lvert input - label \rvert)
1207

1208
    If `reduction` set to ``'sum'``, the loss is:
1209 1210

    .. math::
1211
        Out = SUM(\lvert input - label \rvert)
1212

1213

1214
    Parameters:
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        input (Tensor): The input tensor. The shapes is [N, `*`], where N is batch size and `*` means any number of additional dimensions. It's data type should be float32, float64, int32, int64.
        label (Tensor): label. The shapes is [N, `*`], same shape as ``input`` . It's data type should be float32, float64, int32, int64.
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        reduction (str, optional): Indicate the reduction to apply to the loss,
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            the candicates are ``'none'`` | ``'mean'`` | ``'sum'``.
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            If `reduction` is ``'none'``, the unreduced loss is returned;
            If `reduction` is ``'mean'``, the reduced mean loss is returned.
            If `reduction` is ``'sum'``, the reduced sum loss is returned.
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            Default is ``'mean'``.
        name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.
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    Returns:
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        Tensor, the L1 Loss of Tensor ``input`` and ``label``.
            If `reduction` is ``'none'``, the shape of output loss is [N, *], the same as ``input`` .
            If `reduction` is ``'mean'`` or ``'sum'``, the shape of output loss is [1].
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    Examples:
        .. code-block:: python
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1233
            import paddle
1234

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            input = paddle.to_tensor([[1.5, 0.8], [0.2, 1.3]])
            label = paddle.to_tensor([[1.7, 1], [0.4, 0.5]])
1237

1238
            l1_loss = paddle.nn.functional.l1_loss(input, label)
1239
            print(l1_loss.numpy())
1240 1241
            # [0.35]

1242
            l1_loss = paddle.nn.functional.l1_loss(input, label, reduction='none')
1243
            print(l1_loss.numpy())
1244 1245 1246
            # [[0.20000005 0.19999999]
            # [0.2        0.79999995]]

1247
            l1_loss = paddle.nn.functional.l1_loss(input, label, reduction='sum')
1248
            print(l1_loss.numpy())
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            # [1.4]
    """
    if reduction not in ['sum', 'mean', 'none']:
        raise ValueError(
            "The value of 'reduction' in L1Loss should be 'sum', 'mean' or 'none', but "
            "received %s, which is not allowed." % reduction)

1256
    if in_dygraph_mode():
1257 1258
        unreduced = _C_ops.abs(_C_ops.subtract(input, label))

1259
        if reduction == 'mean':
1260
            return _C_ops.mean_all(unreduced)
1261
        elif reduction == 'sum':
1262
            return _C_ops.sum(unreduced, [], None, False)
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        else:
            return unreduced
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    elif _in_legacy_dygraph():
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        unreduced = _elementwise_op_in_dygraph(input,
                                               label,
                                               axis=-1,
                                               act='abs',
                                               op_name='elementwise_sub')
1271
        if reduction == 'mean':
1272
            return _legacy_C_ops.mean(unreduced)
1273
        elif reduction == 'sum':
1274 1275
            return _legacy_C_ops.reduce_sum(unreduced, 'dim', [0], 'keep_dim',
                                            False, 'reduce_all', True)
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        else:
            return unreduced

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    check_variable_and_dtype(input, 'input',
                             ['float32', 'float64', 'int32', 'int64'],
                             'l1_loss')
    check_variable_and_dtype(label, 'label',
                             ['float32', 'float64', 'int32', 'int64'],
                             'l1_loss')
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    if reduction == 'sum':
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        unreduced = paddle.fluid.layers.elementwise_sub(input, label, act='abs')
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        return paddle.sum(unreduced, name=name)
    elif reduction == 'mean':
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        unreduced = paddle.fluid.layers.elementwise_sub(input, label, act='abs')
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        return paddle.mean(unreduced, name=name)
    else:
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        return paddle.fluid.layers.elementwise_sub(input,
                                                   label,
                                                   act='abs',
                                                   name=name)
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def nll_loss(input,
             label,
             weight=None,
             ignore_index=-100,
             reduction='mean',
             name=None):
    """
    This api returns negative log likelihood.
    See more detail in :ref:`api_nn_loss_NLLLoss` .

    Parameters:
         input (Tensor): Input tensor, the shape is :math:`[N, C]`, `C` is the number of classes.
             But in K-dimension situation, the shape is :math:`[N, C, d_1, d_2, ..., d_K]`.
             The data type is float32, float64.
         label (Tensor): Label tensor, the shape is :math:`[N,]` or :math:`[N, d_1, d_2, ..., d_K]`.
             The data type is int64.
         weight (Tensor, optional): Weight tensor, a manual rescaling weight given
             to each class. If given, it has to be a 1D Tensor whose size is `[C, ]`. Otherwise,
             it treated as if having all ones. the data type is
             float32, float64, Default is ``'None'``.
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         ignore_index (int, optional): Specifies a target value that is ignored
             and does not contribute to the input gradient. Default is -100.
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         reduction (str, optional): Indicate how to average the loss,
             the candicates are ``'none'`` | ``'mean'`` | ``'sum'``.
             If `reduction` is ``'mean'``, the reduced mean loss is returned;
             if `reduction` is ``'sum'``, the reduced sum loss is returned;
             if `reduction` is ``'none'``, no reduction will be apllied.
             Default is ``'mean'``.
         name (str, optional): Name for the operation (optional, default is None).
             For more information, please refer to :ref:`api_guide_Name`.

    Returns:
         `Tensor`, the value of negative log likelihood loss.

    Examples:
        .. code-block:: python
1335

1336 1337 1338 1339
                import paddle
                from paddle.nn.functional import nll_loss
                log_softmax = paddle.nn.LogSoftmax(axis=1)

1340 1341 1342 1343 1344
                input = paddle.to_tensor([[0.88103855, 0.9908683 , 0.6226845 ],
                          [0.53331435, 0.07999352, 0.8549948 ],
                          [0.25879037, 0.39530203, 0.698465  ],
                          [0.73427284, 0.63575995, 0.18827209],
                          [0.05689114, 0.0862954 , 0.6325046 ]], "float32")
1345
                log_out = log_softmax(input)
1346
                label = paddle.to_tensor([0, 2, 1, 1, 0], "int64")
1347
                result = nll_loss(log_out, label)
1348
                print(result) # Tensor(shape=[1], dtype=float32, place=CPUPlace, stop_gradient=True, [1.07202101])
1349 1350 1351 1352 1353 1354 1355 1356 1357
    """
    if reduction not in ['sum', 'mean', 'none']:
        raise ValueError(
            "The value of 'reduction' in nll_loss should be 'sum', 'mean' or "
            "'none', but received %s, which is not allowed." % reduction)

    input_shape = list(input.shape)
    input_dims = len(input_shape)
    if input_dims < 2:
1358 1359
        raise ValueError(
            'Expected 2 or more dimensions (got {})'.format(input_dims))
1360 1361
    n = input_shape[0]
    c = input_shape[1]
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    if in_dygraph_mode():
        if input_dims != 2 and input_dims != 4:
1364 1365
            input = _C_ops.reshape(input, [n, c, 1, -1])
            label = _C_ops.reshape(label, [n, 1, -1])
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            out_shape = [n] + input_shape[2:]
1367 1368
        out, total_weight = _C_ops.nll_loss(input, label, weight, ignore_index,
                                            reduction)
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        if input_dims != 2 and input_dims != 4 and reduction == 'none':
1370
            out = _C_ops.reshape(out, out_shape)
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        return out
1372
    elif _in_legacy_dygraph():
1373
        if input_dims != 2 and input_dims != 4:
1374 1375 1376
            input, _ = _legacy_C_ops.reshape2(input, None, 'shape',
                                              [n, c, 1, -1])
            label, _ = _legacy_C_ops.reshape2(label, None, 'shape', [n, 1, -1])
1377
            out_shape = [n] + input_shape[2:]
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1379 1380 1381
        out, total_weight = _legacy_C_ops.nll_loss(input, label, weight,
                                                   'ignore_index', ignore_index,
                                                   'reduction', reduction)
1382
        if input_dims != 2 and input_dims != 4 and reduction == 'none':
1383
            out, _ = _legacy_C_ops.reshape2(out, None, 'shape', out_shape)
1384 1385 1386 1387 1388 1389 1390 1391 1392
        return out

    helper = LayerHelper('nll_loss', **locals())

    if input_dims != 2 and input_dims != 4:
        input = reshape(input, shape=[n, c, 1, -1])
        label = reshape(label, shape=[n, 1, -1])
        out_shape = [n] + input_shape[2:]

1393 1394
    check_variable_and_dtype(input, 'input', ['float32', 'float64'], 'nll_loss')
    check_variable_and_dtype(label, 'label', ['int64'], 'nll_loss')
1395 1396 1397 1398 1399 1400 1401 1402 1403 1404
    inputs = {'X': input, 'Label': label}
    attrs = {'reduction': reduction, 'ignore_index': ignore_index}
    if weight is not None:
        if isinstance(weight, Variable):
            inputs['Weight'] = weight

    out = helper.create_variable_for_type_inference(dtype=input.dtype)
    total_weight = helper.create_variable_for_type_inference(dtype=input.dtype)
    outputs = {'Out': out, 'Total_weight': total_weight}

1405 1406 1407 1408
    helper.append_op(type='nll_loss',
                     inputs=inputs,
                     outputs=outputs,
                     attrs=attrs)
1409 1410 1411 1412
    if input_dims != 2 and input_dims != 4 and reduction == 'none':
        out = reshape(out, shape=out_shape)

    return out
1413 1414


1415
def kl_div(input, label, reduction='mean', name=None):
1416
    r"""
1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427
    This operator calculates the Kullback-Leibler divergence loss
    between Input(X) and Input(Target). Notes that Input(X) is the
    log-probability and Input(Target) is the probability.

    KL divergence loss is calculated as follows:

    $$l(x, y) = y * (\log(y) - x)$$

    While :math:`x` is input and :math:`y` is label.

    While :attr:`reduction` is :attr:`none`, output loss is in
1428
    the same shape as input, loss in each point is calculated
1429
    separately and no reduction is applied.
1430

1431 1432
    While :attr:`reduction` is :attr:`mean`, output loss is in
    shape of [1] and loss value is the mean value of all losses.
1433

1434 1435
    While :attr:`reduction` is :attr:`sum`, output loss is in
    shape of [1] and loss value is the sum value of all losses.
1436 1437

    While :attr:`reduction` is :attr:`batchmean`, output loss is
1438 1439 1440 1441
    in shape of [1] and loss value is the sum value of all losses
    divided by batch size.

    Args:
1442
        input (Tensor): The input tensor. The shapes is [N, *], where N is batch size and `*` means
1443 1444 1445 1446 1447 1448 1449 1450 1451
             any number of additional dimensions. It's data type should be float32, float64.
        label (Tensor): label. The shapes is [N, *], same shape as ``input`` . It's data type should be float32, float64.
        reduction (Tensor): Indicate how to average the loss,
             the candicates are ``'none'`` | ``'batchmean'`` | ``'mean'`` | ``'sum'``.
             If `reduction` is ``'mean'``, the reduced mean loss is returned;
             If `reduction` is ``'batchmean'``, the sum loss divided by batch size is returned;
             if `reduction` is ``'sum'``, the reduced sum loss is returned;
             if `reduction` is ``'none'``, no reduction will be apllied.
             Default is ``'mean'``.
1452
        name(str, optional): Name for the operation (optional, default is None). For more information,
1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463
            please refer to :ref:`api_guide_Name`.

    Returns:
        Tensor: The KL divergence loss. The data type is same as input tensor

    Examples:
        .. code-block:: python

            import paddle
            import numpy as np
            import paddle.nn.functional as F
1464

1465 1466 1467 1468
            shape = (5, 20)
            input = np.random.uniform(-10, 10, shape).astype('float32')
            target = np.random.uniform(-10, 10, shape).astype('float32')

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            # 'batchmean' reduction, loss shape will be [1]
1470 1471
            pred_loss = F.kl_div(paddle.to_tensor(input),
                                 paddle.to_tensor(target), reduction='batchmean')
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            # shape=[1]
1473

1474
            # 'mean' reduction, loss shape will be [1]
1475 1476
            pred_loss = F.kl_div(paddle.to_tensor(input),
                                 paddle.to_tensor(target), reduction='mean')
1477 1478 1479
            # shape=[1]

            # 'sum' reduction, loss shape will be [1]
1480 1481
            pred_loss = F.kl_div(paddle.to_tensor(input),
                                 paddle.to_tensor(target), reduction='sum')
1482 1483 1484
            # shape=[1]

            # 'none' reduction, loss shape is same with input shape
1485 1486
            pred_loss = F.kl_div(paddle.to_tensor(input),
                                 paddle.to_tensor(target), reduction='none')
1487 1488 1489
            # shape=[5, 20]

    """
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    # ugly type promotion
    if fluid.data_feeder.convert_dtype(
            input.dtype) == 'float32' and fluid.data_feeder.convert_dtype(
                label.dtype) == 'float64':
1494
        input = paddle.cast(input, 'float64')
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    elif fluid.data_feeder.convert_dtype(
            input.dtype) == 'float64' and fluid.data_feeder.convert_dtype(
                label.dtype) == 'float32':
1498
        label = paddle.cast(label, 'float64')
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1500
    if in_dygraph_mode():
1501
        out = _C_ops.kldiv_loss(input, label, 'none')
1502 1503 1504 1505 1506 1507 1508 1509 1510 1511
        if reduction == 'mean':
            out = paddle.mean(out)
        elif reduction == 'sum':
            out = paddle.sum(out)
        elif reduction == 'batchmean':
            if len(input.shape) > 0:
                batch_size = input.shape[0]
                out = paddle.sum(out) / batch_size
        return out
    elif _in_legacy_dygraph():
1512
        out = _legacy_C_ops.kldiv_loss(input, label, 'reduction', 'none')
1513 1514 1515 1516 1517 1518 1519 1520
        if reduction == 'mean':
            out = paddle.mean(out)
        elif reduction == 'sum':
            out = paddle.sum(out)
        elif reduction == 'batchmean':
            if len(input.shape) > 0:
                batch_size = input.shape[0]
                out = paddle.sum(out) / batch_size
1521 1522 1523 1524
        return out

    helper = LayerHelper('kl_div', **locals())

1525 1526
    check_variable_and_dtype(input, 'input', ['float32', 'float64'], 'kl_div')
    check_variable_and_dtype(label, 'label', ['float32', 'float64'], 'kl_div')
1527 1528 1529
    fluid.data_feeder.check_type(reduction, 'reduction', str, 'kl_div')

    loss = helper.create_variable_for_type_inference(dtype=input.dtype)
1530 1531 1532 1533 1534 1535 1536
    helper.append_op(type='kldiv_loss',
                     inputs={
                         'X': input,
                         'Target': label
                     },
                     outputs={'Loss': loss},
                     attrs={'reduction': 'none'})
1537 1538 1539 1540 1541 1542 1543 1544

    if reduction == 'mean':
        loss = paddle.mean(loss)
    elif reduction == 'sum':
        loss = paddle.sum(loss)
    elif reduction == 'batchmean':
        batch_size = paddle.shape(input)[0]
        loss = paddle.sum(loss) / batch_size
1545 1546 1547
    return loss


1548
def mse_loss(input, label, reduction='mean', name=None):
1549
    r"""
1550
    Accept input predications and label and returns the mean square error.
1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579

    If :attr:`reduction` is set to ``'none'``, loss is calculated as:

    .. math::
        Out = (input - label)^2

    If :attr:`reduction` is set to ``'mean'``, loss is calculated as:

    .. math::
        Out = \operatorname{mean}((input - label)^2)

    If :attr:`reduction` is set to ``'sum'``, loss is calculated as:

    .. math::
        Out = \operatorname{sum}((input - label)^2)

    Parameters:
        input (Tensor): Input tensor, the data type should be float32 or float64.
        label (Tensor): Label tensor, the data type should be float32 or float64.
        reduction (string, optional): The reduction method for the output,
            could be 'none' | 'mean' | 'sum'.
            If :attr:`reduction` is ``'mean'``, the reduced mean loss is returned.
            If :attr:`reduction` is ``'sum'``, the reduced sum loss is returned.
            If :attr:`reduction` is ``'none'``, the unreduced loss is returned.
            Default is ``'mean'``.
        name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.


    Returns:
1580
        Tensor, The tensor tensor storing the mean square error difference of input and label.
1581

1582 1583 1584
    Examples:

        .. code-block:: python
1585

1586 1587
            import paddle
            mse_loss = paddle.nn.loss.MSELoss()
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            input = paddle.to_tensor(1.5)
            label = paddle.to_tensor(1.7)
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            output = mse_loss(input, label)
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            print(output)
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            # [0.04000002]

    """

    if reduction not in ['sum', 'mean', 'none']:
        raise ValueError(
            "'reduction' in 'mse_loss' should be 'sum', 'mean' or 'none', "
            "but received {}.".format(reduction))

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    if not in_dynamic_mode():
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        check_variable_and_dtype(input, 'input', ['float32', 'float64'],
                                 'mse_loss')
        check_variable_and_dtype(label, 'label', ['float32', 'float64'],
                                 'mse_loss')
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    if reduction == 'none':
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        return paddle.square(paddle.subtract(input, label), name=name)
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    elif reduction == 'mean':
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        return paddle.mean(paddle.square(paddle.subtract(input, label)),
                           name=name)
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    else:
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        return paddle.sum(paddle.square(paddle.subtract(input, label)),
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                          name=name)
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def ctc_loss(log_probs,
             labels,
             input_lengths,
             label_lengths,
             blank=0,
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             reduction='mean',
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             norm_by_times=False):
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    """

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    An operator integrating the open source Warp-CTC library (https://github.com/baidu-research/warp-ctc)
    to compute Connectionist Temporal Classification (CTC) loss.
    It can be aliased as softmax with CTC, since a native softmax activation
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    is interated to the Warp-CTC library to normalize values for each row of the input tensor.

    Parameters:
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        log_probs (Tensor): The unscaled probability sequence with padding, which is a 3-D Tensor. The tensor shape is [max_logit_length, batch_size, num_classes + 1], where max_logit_length is the longest length of input logit sequence. The data type should be float32 or float64.
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        labels (Tensor): The ground truth sequence with padding, which must be a 3-D Tensor. The tensor shape is [batch_size, max_label_length], where max_label_length is the longest length of label sequence. The data type must be int32.
        input_lengths (Tensor): The length for each input sequence, it should have shape [batch_size] and dtype int64.
        label_lengths (Tensor): The length for each label sequence, it should have shape [batch_size] and dtype int64.
        blank (int, optional): The blank label index of Connectionist Temporal Classification (CTC) loss, which is in the half-opened interval [0, num_classes + 1). The data type must be int32. Default is 0.
        reduction (string, optional): Indicate how to average the loss, the candicates are ``'none'`` | ``'mean'`` | ``'sum'``. If :attr:`reduction` is ``'mean'``, the output loss will be divided by the label_lengths, and then return the mean of quotient; If :attr:`reduction` is ``'sum'``, return the sum of loss; If :attr:`reduction` is ``'none'``, no reduction will be applied. Default is ``'mean'``.
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        norm_by_times (bool, default False) – Whether to normalize the gradients by the number of time-step, which is also the sequence’s length. There is no need to normalize the gradients if reduction mode is 'mean'.
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    Returns:
        Tensor, The Connectionist Temporal Classification (CTC) loss between ``log_probs`` and  ``labels``. If attr:`reduction` is ``'none'``, the shape of loss is [batch_size], otherwise, the shape of loss is [1]. Data type is the same as ``log_probs``.
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    Examples:

        .. code-block:: python

            # declarative mode
            import paddle.nn.functional as F
            import numpy as np
            import paddle

            # length of the longest logit sequence
            max_seq_length = 4
            #length of the longest label sequence
            max_label_length = 3
            # number of logit sequences
            batch_size = 2
            # class num
            class_num = 3

            np.random.seed(1)
            log_probs = np.array([[[4.17021990e-01, 7.20324516e-01, 1.14374816e-04],
                                    [3.02332580e-01, 1.46755889e-01, 9.23385918e-02]],

                                    [[1.86260208e-01, 3.45560730e-01, 3.96767467e-01],
                                    [5.38816750e-01, 4.19194520e-01, 6.85219526e-01]],

                                    [[2.04452246e-01, 8.78117442e-01, 2.73875929e-02],
                                    [6.70467496e-01, 4.17304814e-01, 5.58689833e-01]],

                                    [[1.40386939e-01, 1.98101491e-01, 8.00744593e-01],
                                    [9.68261600e-01, 3.13424170e-01, 6.92322612e-01]],

                                    [[8.76389146e-01, 8.94606650e-01, 8.50442126e-02],
                                    [3.90547849e-02, 1.69830427e-01, 8.78142476e-01]]]).astype("float32")
            labels = np.array([[1, 2, 2],
                            [1, 2, 2]]).astype("int32")
            input_lengths = np.array([5, 5]).astype("int64")
            label_lengths = np.array([3, 3]).astype("int64")

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            log_probs = paddle.to_tensor(log_probs)
            labels = paddle.to_tensor(labels)
            input_lengths = paddle.to_tensor(input_lengths)
            label_lengths = paddle.to_tensor(label_lengths)
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            loss = F.ctc_loss(log_probs, labels,
                input_lengths,
                label_lengths,
                blank=0,
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                reduction='none')
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            print(loss)  #[3.9179852 2.9076521]
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            loss = F.ctc_loss(log_probs, labels,
                input_lengths,
                label_lengths,
                blank=0,
                reduction='mean')
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            print(loss)  #[1.1376063]
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    """

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    loss_out = fluid.layers.warpctc(log_probs, labels, blank, norm_by_times,
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                                    input_lengths, label_lengths)
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    loss_out = paddle.squeeze(loss_out, [-1])
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    assert reduction in ['mean', 'sum', 'none']
    if reduction == 'mean':
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        loss_out = paddle.mean(loss_out / label_lengths)
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    elif reduction == 'sum':
        loss_out = paddle.sum(loss_out)
    return loss_out


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def margin_cross_entropy(logits,
                         label,
                         margin1=1.0,
                         margin2=0.5,
                         margin3=0.0,
                         scale=64.0,
                         group=None,
                         return_softmax=False,
                         reduction='mean'):
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    r"""
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    .. math::

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        L=-\frac{1}{N}\sum^N_{i=1}\log\frac{e^{s(cos(m_{1}\theta_{y_i}+m_{2})-m_{3})}}{e^{s(cos(m_{1}\theta_{y_i}+m_{2})-m_{3})}+\sum^n_{j=1,j\neq y_i} e^{scos\theta_{y_i}}}
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    where the :math:`\theta_{y_i}` is the angle between the feature :math:`x` and
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    the representation of class :math:`i`. The details of ArcFace loss
    could be referred to https://arxiv.org/abs/1801.07698.

    .. hint::
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        The API supports single GPU and multi GPU, and don't supports CPU.

        For data parallel mode, set ``group=False``.

        For model parallel mode, set ``group=None`` or the group instance return by paddle.distributed.new_group.
        And logits.shape[-1] can be different at each rank.
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    Args:
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        logits (Tensor): shape[N, local_num_classes], the output of the normalized X multiply the normalized W.
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                The logits is shard_logits when using model parallel.
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        label (Tensor): shape[N] or shape[N, 1], the groud truth label.
        margin1 (float, optional): m1 of margin loss, default value is `1.0`.
        margin2 (float, optional): m2 of margin loss, default value is `0.5`.
        margin3 (float, optional): m3 of margin loss, default value is `0.0`.
        scale (float, optional): s of margin loss, default value is `64.0`.
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        group (Group, optional): The group instance return by paddle.distributed.new_group 
            or ``None`` for global default group or ``False`` for data parallel (do not communication cross ranks).
            Default is ``None``.
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        return_softmax (bool, optional): Whether return softmax probability. Default value is `False`.
        reduction (str, optional): The candicates are ``'none'`` | ``'mean'`` | ``'sum'``.
                    If :attr:`reduction` is ``'mean'``, return the average of loss;
                    If :attr:`reduction` is ``'sum'``, return the sum of loss;
                    If :attr:`reduction` is ``'none'``, no reduction will be applied.
                    Default value is `'mean'`.

    Returns:
        ``Tensor`` or Tuple of two ``Tensor`` : Return the cross entropy loss if \
            `return_softmax` is False, otherwise the tuple \
            (loss, softmax), softmax is shard_softmax when \
            using model parallel, otherwise softmax is in \
            the same shape with input logits. If ``reduction == None``, \
            the shape of loss is ``[N, 1]``, otherwise the shape is ``[1]``.

    Examples:

    .. code-block:: python
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        :name: code-example1
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        # required: gpu
        # Single GPU
        import paddle
        m1 = 1.0
        m2 = 0.5
        m3 = 0.0
        s = 64.0
        batch_size = 2
        feature_length = 4
        num_classes = 4

        label = paddle.randint(low=0, high=num_classes, shape=[batch_size], dtype='int64')

        X = paddle.randn(
            shape=[batch_size, feature_length],
            dtype='float64')
        X_l2 = paddle.sqrt(paddle.sum(paddle.square(X), axis=1, keepdim=True))
        X = paddle.divide(X, X_l2)

        W = paddle.randn(
            shape=[feature_length, num_classes],
            dtype='float64')
        W_l2 = paddle.sqrt(paddle.sum(paddle.square(W), axis=0, keepdim=True))
        W = paddle.divide(W, W_l2)

        logits = paddle.matmul(X, W)
        loss, softmax = paddle.nn.functional.margin_cross_entropy(
            logits, label, margin1=m1, margin2=m2, margin3=m3, scale=s, return_softmax=True, reduction=None)

        print(logits)
        print(label)
        print(loss)
        print(softmax)
        
        #Tensor(shape=[2, 4], dtype=float64, place=CUDAPlace(0), stop_gradient=True,
        #       [[ 0.85204151, -0.55557678,  0.04994566,  0.71986042],
        #        [-0.20198586, -0.35270476, -0.55182702,  0.09749021]])
        #Tensor(shape=[2], dtype=int64, place=CUDAPlace(0), stop_gradient=True,
        #       [2, 3])
        #Tensor(shape=[2, 1], dtype=float64, place=CUDAPlace(0), stop_gradient=True,
        #       [[82.37059586],
        #        [12.13448420]])
        #Tensor(shape=[2, 4], dtype=float64, place=CUDAPlace(0), stop_gradient=True,
        #       [[0.99978819, 0.00000000, 0.00000000, 0.00021181],
        #        [0.99992995, 0.00006468, 0.00000000, 0.00000537]])

    .. code-block:: python
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        :name: code-example2
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        # required: distributed
        # Multi GPU, test_margin_cross_entropy.py
        import paddle
        import paddle.distributed as dist
        strategy = dist.fleet.DistributedStrategy()
        dist.fleet.init(is_collective=True, strategy=strategy)
        rank_id = dist.get_rank()
        m1 = 1.0
        m2 = 0.5
        m3 = 0.0
        s = 64.0
        batch_size = 2
        feature_length = 4
        num_class_per_card = [4, 8]
        num_classes = paddle.sum(paddle.to_tensor(num_class_per_card))

        label = paddle.randint(low=0, high=num_classes.item(), shape=[batch_size], dtype='int64')
        label_list = []
        dist.all_gather(label_list, label)
        label = paddle.concat(label_list, axis=0)

        X = paddle.randn(
            shape=[batch_size, feature_length],
            dtype='float64')
        X_list = []
        dist.all_gather(X_list, X)
        X = paddle.concat(X_list, axis=0)
        X_l2 = paddle.sqrt(paddle.sum(paddle.square(X), axis=1, keepdim=True))
        X = paddle.divide(X, X_l2)

        W = paddle.randn(
            shape=[feature_length, num_class_per_card[rank_id]],
            dtype='float64')
        W_l2 = paddle.sqrt(paddle.sum(paddle.square(W), axis=0, keepdim=True))
        W = paddle.divide(W, W_l2)

        logits = paddle.matmul(X, W)
        loss, softmax = paddle.nn.functional.margin_cross_entropy(
            logits, label, margin1=m1, margin2=m2, margin3=m3, scale=s, return_softmax=True, reduction=None)

        print(logits)
        print(label)
        print(loss)
        print(softmax)

        # python -m paddle.distributed.launch --gpus=0,1 test_margin_cross_entropy.py 
        ## for rank0 input
        #Tensor(shape=[4, 4], dtype=float64, place=CUDAPlace(0), stop_gradient=True,
        #       [[ 0.32888934,  0.02408748, -0.02763289,  0.18173063],
        #        [-0.52893978, -0.10623845, -0.21596515, -0.06432517],
        #        [-0.00536345, -0.03924667,  0.66735314, -0.28640926],
        #        [-0.09907366, -0.48534973, -0.10365338, -0.39472322]])
        #Tensor(shape=[4], dtype=int64, place=CUDAPlace(0), stop_gradient=True,
        #       [11, 1 , 10, 11])

        ## for rank1 input
        #Tensor(shape=[4, 8], dtype=float64, place=CUDAPlace(1), stop_gradient=True,
        #       [[ 0.68654754,  0.28137170,  0.69694954, -0.60923933, -0.57077653,  0.54576703, -0.38709028,  0.56028204],
        #        [-0.80360371, -0.03042448, -0.45107338,  0.49559349,  0.69998950, -0.45411693,  0.61927630, -0.82808600],
        #        [ 0.11457570, -0.34785879, -0.68819499, -0.26189226, -0.48241491, -0.67685711,  0.06510185,  0.49660849],
        #        [ 0.31604851,  0.52087884,  0.53124749, -0.86176582, -0.43426329,  0.34786144, -0.10850784,  0.51566383]])
        #Tensor(shape=[4], dtype=int64, place=CUDAPlace(1), stop_gradient=True,
        #       [11, 1 , 10, 11])

        ## for rank0 output
        #Tensor(shape=[4, 1], dtype=float64, place=CUDAPlace(0), stop_gradient=True,
        #       [[38.96608230],
        #        [81.28152394],
        #        [69.67229865],
        #        [31.74197251]])
        #Tensor(shape=[4, 4], dtype=float64, place=CUDAPlace(0), stop_gradient=True,
        #       [[0.00000000, 0.00000000, 0.00000000, 0.00000000],
        #        [0.00000000, 0.00000000, 0.00000000, 0.00000000],
        #        [0.00000000, 0.00000000, 0.99998205, 0.00000000],
        #        [0.00000000, 0.00000000, 0.00000000, 0.00000000]])
        ## for rank1 output
        #Tensor(shape=[4, 1], dtype=float64, place=CUDAPlace(1), stop_gradient=True,
        #       [[38.96608230],
        #        [81.28152394],
        #        [69.67229865],
        #        [31.74197251]])
        #Tensor(shape=[4, 8], dtype=float64, place=CUDAPlace(1), stop_gradient=True,
        #       [[0.33943993, 0.00000000, 0.66051859, 0.00000000, 0.00000000, 0.00004148, 0.00000000, 0.00000000],
        #        [0.00000000, 0.00000000, 0.00000000, 0.00000207, 0.99432097, 0.00000000, 0.00567696, 0.00000000],
        #        [0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00001795],
        #        [0.00000069, 0.33993085, 0.66006319, 0.00000000, 0.00000000, 0.00000528, 0.00000000, 0.00000000]])
    """

    assert reduction in ['mean', 'sum', 'none', None]
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    if not (group == False or group is None or hasattr(group, 'is_member')):
        raise ValueError(
            'Expected group is False, None or instance of paddle.distributed.collective.Group \
             (got group: {})'.format(group))
        return

    if hasattr(group, 'is_member') and not group.is_member():
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        return

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    ring_id = 0
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    rank = 0
    nranks = 1
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    if group != False:
        ring_id = 0 if group is None else group.id
        if core.is_compiled_with_dist():
            parallel_env = paddle.distributed.ParallelEnv()
            global_rank = parallel_env.rank
            rank = global_rank if group is None else group.get_group_rank(
                global_rank)
            nranks = parallel_env.world_size if group is None else group.nranks
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    input_dims = len(list(logits.shape))
    label_dims = len(list(label.shape))
    if input_dims - 1 != label_dims and input_dims != label_dims:
        raise ValueError(
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            'Expected input_dims - 1 = label_dims or input_dims == label_dims\
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             (got nput_dims{}, label_dims{})'.format(input_dims, label_dims))
    if input_dims - 1 == label_dims:
        label = paddle.unsqueeze(label, axis=-1)

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    if in_dygraph_mode():
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        softmax, loss = _C_ops.margin_cross_entropy(logits, label,
                                                    return_softmax, ring_id,
                                                    rank, nranks, margin1,
                                                    margin2, margin3, scale)
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        if reduction == 'mean':
            loss = paddle.mean(loss)
        elif reduction == 'sum':
            loss = paddle.sum(loss)
        if not return_softmax:
            return loss
        else:
            return loss, softmax
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    elif _in_legacy_dygraph():
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        softmax, loss = _legacy_C_ops.margin_cross_entropy(
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            logits, label, 'ring_id', ring_id, 'rank', rank, 'nranks', nranks,
            'margin1', margin1, 'margin2', margin2, 'margin3', margin3, 'scale',
            scale, 'return_softmax', return_softmax)
        if reduction == 'mean':
            loss = paddle.mean(loss)
        elif reduction == 'sum':
            loss = paddle.sum(loss)
        if not return_softmax:
            return loss
        else:
            return loss, softmax

    op_type = 'margin_cross_entropy'
    helper = LayerHelper(op_type, **locals())
    softmax = helper.create_variable_for_type_inference(dtype=logits.dtype)
    loss = helper.create_variable_for_type_inference(dtype=logits.dtype)

    check_variable_and_dtype(logits, 'logits',
                             ['float16', 'float32', 'float64'],
                             'margin_cross_entropy')
    check_variable_and_dtype(label, 'label', ['int32', 'int64'],
                             'margin_cross_entropy')

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    helper.append_op(type=op_type,
                     inputs={
                         'Logits': logits,
                         'Label': label
                     },
                     outputs={
                         'Softmax': softmax,
                         'Loss': loss
                     },
                     attrs={
                         'return_softmax': return_softmax,
                         'ring_id': ring_id,
                         'rank': rank,
                         'nranks': nranks,
                         'margin1': margin1,
                         'margin2': margin2,
                         'margin3': margin3,
                         'scale': scale,
                     })
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    if reduction == 'mean':
        loss = paddle.mean(loss)
    elif reduction == 'sum':
        loss = paddle.sum(loss)

    if not return_softmax:
        return loss
    else:
        return loss, softmax


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@deprecated(
    since="2.0.0",
    update_to="paddle.nn.functional.cross_entropy",
    level=1,
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    reason=
    ('Please notice that behavior of "paddle.nn.functional.softmax_with_cross_entropy" '
     'and "paddle.nn.functional.cross_entropy" is different.'))
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def softmax_with_cross_entropy(logits,
                               label,
                               soft_label=False,
                               ignore_index=-100,
                               numeric_stable_mode=True,
                               return_softmax=False,
                               axis=-1):
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    r"""
    This operator implements the cross entropy loss function with softmax. This function 
    combines the calculation of the softmax operation and the cross entropy loss function 
    to provide a more numerically stable gradient.

    Because this operator performs a softmax on logits internally, it expects
    unscaled logits. This operator should not be used with the output of
    softmax operator since that would produce incorrect results.

    When the attribute :attr:`soft_label` is set :attr:`False`, this operators 
    expects mutually exclusive hard labels, each sample in a batch is in exactly 
    one class with a probability of 1.0. Each sample in the batch will have a 
    single label.

    The equation is as follows:

    1) Hard label (one-hot label, so every sample has exactly one class)

    .. math::
        \\loss_j=-\text{logits}_{label_j} +\log\left(\sum_{i=0}^{K}\exp(\text{logits}_i)\right), j = 1,..., K

    2) Soft label (each sample can have a distribution over all classes)

    .. math::
        \\loss_j= -\sum_{i=0}^{K}\text{label}_i\left(\text{logits}_i - \log\left(\sum_{i=0}^{K}\exp(\text{logits}_i)\right)\right), j = 1,...,K

    3) If :attr:`numeric_stable_mode` is :attr:`True`, softmax is calculated first by:

    .. math::
        \\max_j&=\max_{i=0}^{K}{\text{logits}_i} \\
                log\_max\_sum_j &= \log\sum_{i=0}^{K}\exp(logits_i - max_j)\\
                softmax_j &= \exp(logits_j - max_j - {log\_max\_sum}_j)

    and then cross entropy loss is calculated by softmax and label.

    Args:
        logits (Tensor): A multi-dimension ``Tensor`` , and the data type is float32 or float64. The input tensor of unscaled log probabilities.
        label (Tensor): The ground truth  ``Tensor`` , data type is the same
            as the ``logits`` . If :attr:`soft_label` is set to :attr:`True`, 
            Label is a ``Tensor``  in the same shape with :attr:`logits`. 
            If :attr:`soft_label` is set to :attr:`True`, Label is a ``Tensor`` 
            in the same shape with :attr:`logits` expect shape in dimension :attr:`axis` as 1.
        soft_label (bool, optional): A flag to indicate whether to interpretant the given
            labels as soft labels. Default False.
        ignore_index (int, optional): Specifies a target value that is ignored and does
                                      not contribute to the input gradient. Only valid
                                      if :attr:`soft_label` is set to :attr:`False`. 
                                      Default: kIgnoreIndex(-100).
        numeric_stable_mode (bool, optional): A flag to indicate whether to use a more
                                              numerically stable algorithm. Only valid
                                              when :attr:`soft_label` is :attr:`False` 
                                              and GPU is used. When :attr:`soft_label` 
                                              is :attr:`True` or CPU is used, the 
                                              algorithm is always numerically stable.
                                              Note that the speed may be slower when use
                                              stable algorithm. Default: True.
        return_softmax (bool, optional): A flag indicating whether to return the softmax
                                         along with the cross entropy loss. Default: False.
        axis (int, optional): The index of dimension to perform softmax calculations. It 
                              should be in range :math:`[-1, rank - 1]`, while :math:`rank`
                              is the rank of input :attr:`logits`. Default: -1.

    Returns:
        ``Tensor`` or Tuple of two ``Tensor`` : Return the cross entropy loss if \
                                                    `return_softmax` is False, otherwise the tuple \
                                                    (loss, softmax), softmax is in the same shape \
                                                    with input logits and cross entropy loss is in \
                                                    the same shape with input logits except shape \
                                                    in dimension :attr:`axis` as 1.

    Examples:
        .. code-block:: python

            import paddle
            import numpy as np

            data = np.random.rand(128).astype("float32")
            label = np.random.rand(1).astype("int64")
            data = paddle.to_tensor(data)
            label = paddle.to_tensor(label)
            linear = paddle.nn.Linear(128, 100)
            x = linear(data)
            out = paddle.nn.functional.softmax_with_cross_entropy(logits=x, label=label)
            print(out)
    """
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    return fluid_softmax_with_cross_entropy(logits, label, soft_label,
                                            ignore_index, numeric_stable_mode,
                                            return_softmax, axis)


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def cross_entropy(input,
                  label,
                  weight=None,
                  ignore_index=-100,
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                  reduction='mean',
                  soft_label=False,
                  axis=-1,
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                  use_softmax=True,
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                  name=None):
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    r"""
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    By default, this operator implements the cross entropy loss function with softmax. This function 
    combines the calculation of the softmax operation and the cross entropy loss function 
    to provide a more numerically stable computing. 
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    This operator will calculate the cross entropy loss function without softmax when use_softmax=False.
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    By default, this operator will calculate the mean of the result, and you can also affect 
    the default behavior by using the reduction parameter. Please refer to the part of 
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    parameters for details.
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    This operator can be used to calculate the softmax cross entropy loss with soft and hard labels.
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    Where, the hard labels mean the actual label value, 0, 1, 2, etc.  And the soft labels 
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    mean the probability of the actual label, 0.6, 0.8, 0.2, etc.
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    The calculation of this operator includes the following two steps.
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    - **1.softmax cross entropy**
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        1. Hard label (each sample can only be assigned into one category)
2141

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        1.1. when use_softmax=True
2143

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            .. math::
              \\loss_j=-\text{logits}_{label_j}+\log\left(\sum_{i=0}^{C}\exp(\text{logits}_i)\right) , j = 1,...,N
2146

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            where, N is the number of samples and C is the number of categories.

        1.2. when use_softmax=False

            .. math::
              \\loss_j=-\log\left({P}_{label_j}\right) , j = 1,...,N

            where, N is the number of samples and C is the number of categories, P is input(the output of softmax).


        2. Soft label (each sample is assigned to multiple categories with a certain probability, and the probability sum is 1).

        2.1. when use_softmax=True

            .. math::
              \\loss_j=-\sum_{i=0}^{C}\text{label}_i\left(\text{logits}_i-\log\left(\sum_{i=0}^{C}\exp(\text{logits}_i)\right)\right) , j = 1,...,N

            where, N is the number of samples and C is the number of categories.

        2.2. when use_softmax=False

            .. math::
              \\loss_j=-\sum_{j=0}^{C}\left({label}_j*\log\left({P}_{label_j}\right)\right) , j = 1,...,N

            where, N is the number of samples and C is the number of categories, P is input(the output of softmax).




    - **2. Weight and reduction processing**

        1. Weight

            If the ``weight`` parameter is ``None`` , go to the next step directly.

            If the ``weight`` parameter is not ``None`` , the cross entropy of each sample is weighted by weight
            according to soft_label = False or True as follows.

            1.1. Hard labels (soft_label = False)

            .. math::
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                \\loss_j=loss_j*weight[label_j] 
2189

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            1.2. Soft labels (soft_label = True)

             .. math::
                \\loss_j=loss_j*\sum_{i}\left(weight[label_i]*logits_i\right)

        2. reduction

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            2.1 if the ``reduction`` parameter is ``none`` 
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                Return the previous result directly

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            2.2 if the ``reduction`` parameter is ``sum`` 
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                Return the sum of the previous results

            .. math::
               \\loss=\sum_{j}loss_j

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            2.3 if the ``reduction`` parameter is ``mean`` , it will be processed according to 
            the ``weight`` parameter as follows. 
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            2.3.1. If the  ``weight``  parameter is ``None`` 
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                   Return the average value of the previous results

2216
            .. math::
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                \\loss=\sum_{j}loss_j/N

                  where, N is the number of samples and C is the number of categories.

            2.3.2. If the 'weight' parameter is not 'None', the weighted average value of the previous result will be returned

            1. Hard labels (soft_label = False)

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            .. math::
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                \\loss=\sum_{j}loss_j/\sum_{j}weight[label_j] 
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            2. Soft labels (soft_label = True)

2230
            .. math::
2231
                \\loss=\sum_{j}loss_j/\sum_{j}\left(\sum_{i}weight[label_i]\right)
2232 2233


2234
    Parameters:
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        - **input** (Tensor)

            Input tensor, the data type is float32, float64. Shape is
2239
        :math:`[N_1, N_2, ..., N_k, C]`, where C is number of classes ,  ``k >= 1`` . 
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            Note: 
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                1. when use_softmax=True, it expects unscaled logits. This operator should not be used with the 
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                output of softmax operator, which will produce incorrect results.

                2. when use_softmax=False, it expects the output of softmax operator.
2247

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        - **label** (Tensor)

            1. If soft_label=False, the shape is
            :math:`[N_1, N_2, ..., N_k]` or :math:`[N_1, N_2, ..., N_k, 1]`, k >= 1.
            the data type is int32, int64, float32, float64, where each value is [0, C-1].

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            2. If soft_label=True, the shape and data type should be same with ``input`` , 
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            and the sum of the labels for each sample should be 1.

        - **weight** (Tensor, optional)

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            a manual rescaling weight given to each class. 
            If given, has to be a Tensor of size C and the data type is float32, float64. 
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            Default is ``'None'`` .

        - **ignore_index** (int64, optional)

            Specifies a target value that is ignored
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            and does not contribute to the loss. A negative value means that no label 
            value needs to be ignored. Only valid when soft_label = False.  
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            Default is ``-100`` .

        - **reduction** (str, optional)

            Indicate how to average the loss by batch_size,
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            the candicates are ``'none'`` | ``'mean'`` | ``'sum'``.
            If :attr:`reduction` is ``'mean'``, the reduced mean loss is returned;
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            If :attr:`size_average` is ``'sum'``, the reduced sum loss is returned.
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            If :attr:`reduction` is ``'none'``, the unreduced loss is returned.
            Default is ``'mean'``.
2278

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        - **soft_label** (bool, optional)

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            Indicate whether label is soft. 
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            Default is ``False``.

        - **axis** (int, optional)

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            The index of dimension to perform softmax calculations. 
            It should be in range :math:`[-1, rank - 1]`, where :math:`rank` is the 
            number of dimensions of input :attr:`input`. 
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            Default is ``-1`` .

        - **use_softmax** (bool, optional)

            Indicate whether compute softmax before cross_entropy.
            Default is ``True``.

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        - **name** (str, optional)
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            The name of the operator. Default is ``None`` .
            For more information, please refer to :ref:`api_guide_Name` .
2300 2301 2302

    Returns:

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        Tensor. Return the softmax cross_entropy loss of ``input`` and ``label``.
        The data type is the same as input.
2305

2306
        If :attr:`reduction` is ``'mean'`` or ``'sum'`` , the dimension of return value is ``1``.
2307

2308
        If :attr:`reduction` is ``'none'``:
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        1. If soft_label = False, the dimension of return value is the same with ``label`` . 
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        2. if soft_label = True, the dimension of return value is :math:`[N_1, N_2, ..., N_k, 1]` . 
2313 2314


2315
    Examples:
2316 2317

        .. code-block:: python
2318 2319

            # hard labels
2320 2321 2322 2323 2324
            import paddle
            paddle.seed(99999)
            N=100
            C=200
            reduction='mean'
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            input =  paddle.rand([N, C], dtype='float64')  
2326
            label =  paddle.randint(0, C, shape=[N], dtype='int64')
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            weight = paddle.rand([C], dtype='float64') 
            
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            cross_entropy_loss = paddle.nn.loss.CrossEntropyLoss(
                weight=weight, reduction=reduction)
            dy_ret = cross_entropy_loss(
                                       input,
                                       label)
            print(dy_ret.numpy()) #[5.41993642]

        .. code-block:: python
2337 2338

            # soft labels
2339 2340 2341 2342 2343 2344 2345 2346 2347 2348 2349 2350 2351
            import paddle
            paddle.seed(99999)
            axis = -1
            ignore_index = -100
            N = 4
            C = 3
            shape = [N, C]
            reduction='mean'
            weight = None
            logits = paddle.uniform(shape, dtype='float64', min=0.1, max=1.0)
            labels = paddle.uniform(shape, dtype='float64', min=0.1, max=1.0)
            labels /= paddle.sum(labels, axis=axis, keepdim=True)
            paddle_loss_mean = paddle.nn.functional.cross_entropy(
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                                                                  logits,  
                                                                  labels, 
                                                                  soft_label=True, 
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                                                                  axis=axis,
                                                                  weight=weight,
                                                                  reduction=reduction)
            print(paddle_loss_mean.numpy()) #[1.12908343]
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    """

    if reduction not in ['sum', 'mean', 'none']:
        raise ValueError(
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            "The value of 'reduction' in softmax_cross_entropy"
            "should be 'sum', 'mean' or 'none', but received %s, which is not allowed."
            % reduction)
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    if ignore_index > 0 and soft_label == True:
        raise ValueError(
            "When soft_label == True, the value of 'ignore_index' in softmax_cross_entropy"
            "should be '-100', but received %s, which is not allowed." %
            ignore_index)

2373
    input_dims = len(list(input.shape))
2374 2375 2376
    if input_dims == 0:
        raise ValueError('The dimention of input should be larger than zero!')

2377 2378
    label_dims = len(list(label.shape))
    if input_dims - 1 != label_dims and input_dims != label_dims:
2379
        raise ValueError(
2380 2381 2382 2383
            'Expected nput_dims - 1 = label_dims or input_dims == label_dims\
             (got nput_dims{}, label_dims{})'.format(input_dims, label_dims))
    if input_dims - 1 == label_dims:
        label = paddle.unsqueeze(label, axis=axis)
2384

2385
    if in_dygraph_mode():
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        if soft_label == False:
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            valid_label = paddle.cast(label != ignore_index,
                                      dtype=label.dtype) * label
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            label_min = paddle.min(valid_label)
            label_max = paddle.max(valid_label)
            if label_min < 0:
2392 2393
                raise ValueError("Target {} is out of lower bound.".format(
                    label_min.item()))
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            if label_max >= input.shape[axis]:
2395 2396
                raise ValueError("Target {} is out of upper bound.".format(
                    label_max.item()))
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        if core.is_compiled_with_npu() or core.is_compiled_with_mlu():
2398
            if soft_label == False:
2399
                _, _, out = _legacy_C_ops.softmax_with_cross_entropy(
2400 2401 2402 2403
                    input, valid_label, 'soft_label', soft_label,
                    'ignore_index', ignore_index, 'numeric_stable_mode', True,
                    'axis', axis, 'use_softmax', use_softmax)
            else:
2404
                _, _, out = _legacy_C_ops.softmax_with_cross_entropy(
2405 2406 2407
                    input, label, 'soft_label', soft_label, 'ignore_index',
                    ignore_index, 'numeric_stable_mode', True, 'axis', axis,
                    'use_softmax', use_softmax)
2408
        else:
2409 2410 2411
            _, out = _C_ops.cross_entropy_with_softmax(input, label, soft_label,
                                                       use_softmax, True,
                                                       ignore_index, axis)
2412 2413 2414 2415 2416 2417 2418 2419 2420 2421 2422 2423 2424 2425 2426 2427 2428 2429

        if weight is not None:

            # trans weight from class to sample, shape:N or [N,H,W] for 1d and 2d cases.
            if soft_label == True:
                # chajchaj:
                # weight's shape is C, where C is class num.
                # for 1d case: label's shape is [N,C], weight_gather's shape is N.
                # for 2d case: label's shape is [N,H,W,C], weight_gather's shape is [N,H,W].
                weight_gather = paddle.matmul(x=paddle.cast(
                    label, weight.dtype),
                                              y=weight,
                                              transpose_x=False,
                                              transpose_y=True)
                out_shape = list(out.shape)
                weight_gather_reshape = reshape(weight_gather, shape=out_shape)
                out = paddle.cast(out, weight_gather_reshape.dtype)

2430
                out = _C_ops.multiply(out, weight_gather_reshape)
2431 2432 2433 2434 2435 2436 2437 2438 2439 2440 2441 2442 2443 2444 2445 2446 2447 2448 2449
            else:
                if input.shape[axis] != weight.shape[-1]:
                    raise ValueError(
                        "input's class_dimension({}) must equal to "
                        "weight's class_dimension({}) "
                        "when weight is provided" \
                            .format(input.shape[axis], weight.shape[-1]))

                ignore_weight_mask = paddle.cast((label != ignore_index),
                                                 out.dtype)
                if ignore_weight_mask.ndim > 1 and ignore_weight_mask.shape[
                        axis] == 1:
                    # TODO: Temporarily use squeeze instead of squeeze_
                    ignore_weight_mask = paddle.squeeze(ignore_weight_mask,
                                                        axis)
                if axis != -1 and axis != valid_label.ndim - 1:
                    temp_perm = list(range(axis % valid_label.ndim)) \
                                + list(range((axis % valid_label.ndim + 1), valid_label.ndim)) \
                                + [axis % valid_label.ndim]
2450
                    weight_gather = _C_ops.gather_nd(
2451 2452
                        weight, valid_label.transpose(temp_perm))
                else:
2453 2454 2455
                    weight_gather = _C_ops.gather_nd(weight, valid_label)
                weight_gather = _C_ops.multiply(weight_gather,
                                                ignore_weight_mask)
2456 2457 2458 2459
                input_shape = list(label.shape)
                weight_gather_reshape = reshape(weight_gather,
                                                shape=input_shape)
                out = paddle.cast(out, weight_gather_reshape.dtype)
2460
                out = _C_ops.multiply(out, weight_gather_reshape)
2461 2462 2463 2464 2465

        if reduction == "sum":
            #   because of fluid_softmax_with_cross_entropy op's inner logic,
            #   in the out tensor of this op, the loss of sample with class_index==ignore_index is 0
            #   so, reduce_sum all directly is ok
2466
            return _C_ops.sum(out, [], None, False)
2467 2468 2469 2470 2471 2472 2473 2474
        elif reduction == "mean":
            # 1. if weight==none,
            #     numerator: reduce_sum all loss directly is ok causeof fluid_softmax_with_cross_entropy's inner logic
            #     denominator: count sample num with class_index!=ignore_index
            # 2. else
            #     numerator: loss's weighted sum
            #     denominator: cal the sum of weight where the sample's class_index!=ignore_index
            if ignore_index >= 0:
2475
                out_sum = _C_ops.sum(out, [], None, False)
2476 2477 2478 2479 2480 2481
                # for each label[i],set 1 or 0, according to ignore_index
                # mask[i]=0, if label[i]==ignore_index
                # mask[i]=1, otherwise
                mask = (label != ignore_index)
                if weight is None:
                    mask = paddle.cast(mask, dtype=out_sum.dtype)
2482
                    count = _C_ops.sum(mask, [], None, False)
2483 2484 2485
                    ret = out_sum / (count + (count == 0.0))
                else:
                    mask = paddle.cast(mask, weight_gather_reshape.dtype)
2486 2487 2488
                    weight_ignored = _C_ops.multiply(mask,
                                                     weight_gather_reshape)
                    weight_sum = _C_ops.sum(weight_ignored, [], None, False)
2489 2490 2491
                    ret = out_sum / (weight_sum + (weight_sum == 0.0))
                return ret
            elif weight is not None:
2492 2493 2494
                out_sum = _C_ops.sum(out, [], None, False)
                total_weight = _C_ops.sum(weight_gather_reshape, [], None,
                                          False)
2495 2496
                return out_sum / (total_weight + (total_weight == 0.0))
            else:
2497
                return _C_ops.mean_all(out)
2498 2499 2500 2501 2502 2503 2504 2505 2506 2507 2508 2509 2510 2511 2512 2513 2514 2515 2516 2517

        else:
            if input_dims - 1 == label_dims:
                out = paddle.squeeze(out, axis=axis)
            return out

    elif _in_legacy_dygraph():
        if soft_label == False:
            valid_label = paddle.cast(label != ignore_index,
                                      dtype=label.dtype) * label
            label_min = paddle.min(valid_label)
            label_max = paddle.max(valid_label)
            if label_min < 0:
                raise ValueError("Target {} is out of lower bound.".format(
                    label_min.item()))
            if label_max >= input.shape[axis]:
                raise ValueError("Target {} is out of upper bound.".format(
                    label_max.item()))
        if core.is_compiled_with_npu() or core.is_compiled_with_mlu():
            if soft_label == False:
2518
                _, _, out = _legacy_C_ops.softmax_with_cross_entropy(
2519 2520 2521 2522
                    input, valid_label, 'soft_label', soft_label,
                    'ignore_index', ignore_index, 'numeric_stable_mode', True,
                    'axis', axis, 'use_softmax', use_softmax)
            else:
2523
                _, _, out = _legacy_C_ops.softmax_with_cross_entropy(
2524 2525 2526
                    input, label, 'soft_label', soft_label, 'ignore_index',
                    ignore_index, 'numeric_stable_mode', True, 'axis', axis,
                    'use_softmax', use_softmax)
2527
        else:
2528
            _, out = _legacy_C_ops.softmax_with_cross_entropy(
2529 2530 2531
                input, label, 'soft_label', soft_label, 'ignore_index',
                ignore_index, 'numeric_stable_mode', True, 'axis', axis,
                'use_softmax', use_softmax)
2532

2533
        if weight is not None:
2534

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            # trans weight from class to sample, shape:N or [N,H,W] for 1d and 2d cases.
2536 2537
            if soft_label == True:
                # chajchaj:
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                # weight's shape is C, where C is class num.
2539 2540
                # for 1d case: label's shape is [N,C], weight_gather's shape is N.
                # for 2d case: label's shape is [N,H,W,C], weight_gather's shape is [N,H,W].
2541 2542 2543 2544 2545
                weight_gather = paddle.matmul(x=paddle.cast(
                    label, weight.dtype),
                                              y=weight,
                                              transpose_x=False,
                                              transpose_y=True)
2546 2547 2548 2549
                out_shape = list(out.shape)
                weight_gather_reshape = reshape(weight_gather, shape=out_shape)
                out = paddle.cast(out, weight_gather_reshape.dtype)

2550
                out = _legacy_C_ops.elementwise_mul(out, weight_gather_reshape)
2551 2552

            else:
2553 2554 2555 2556 2557 2558 2559
                if input.shape[axis] != weight.shape[-1]:
                    raise ValueError(
                        "input's class_dimension({}) must equal to "
                        "weight's class_dimension({}) "
                        "when weight is provided" \
                            .format(input.shape[axis], weight.shape[-1]))

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                ignore_weight_mask = paddle.cast((label != ignore_index),
                                                 out.dtype)
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                if ignore_weight_mask.ndim > 1 and ignore_weight_mask.shape[
2563
                        axis] == 1:
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                    # TODO: Temporarily use squeeze instead of squeeze_
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                    ignore_weight_mask = paddle.squeeze(ignore_weight_mask,
                                                        axis)
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                if axis != -1 and axis != valid_label.ndim - 1:
2568
                    temp_perm = list(range(axis % valid_label.ndim)) \
2569
                                + list(range((axis % valid_label.ndim + 1), valid_label.ndim)) \
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                                + [axis % valid_label.ndim]
2571
                    weight_gather = _legacy_C_ops.gather_nd(
2572 2573
                        weight, valid_label.transpose(temp_perm))
                else:
2574 2575 2576
                    weight_gather = _legacy_C_ops.gather_nd(weight, valid_label)
                weight_gather = _legacy_C_ops.elementwise_mul(
                    weight_gather, ignore_weight_mask)
2577
                input_shape = list(label.shape)
2578 2579
                weight_gather_reshape = reshape(weight_gather,
                                                shape=input_shape)
2580
                out = paddle.cast(out, weight_gather_reshape.dtype)
2581
                out = _legacy_C_ops.elementwise_mul(out, weight_gather_reshape)
2582

2583
        if reduction == "sum":
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            #   because of fluid_softmax_with_cross_entropy op's inner logic,
2585 2586
            #   in the out tensor of this op, the loss of sample with class_index==ignore_index is 0
            #   so, reduce_sum all directly is ok
2587
            return _legacy_C_ops.reduce_sum(out, 'reduce_all', True)
2588
        elif reduction == "mean":
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            # 1. if weight==none,
            #     numerator: reduce_sum all loss directly is ok causeof fluid_softmax_with_cross_entropy's inner logic
            #     denominator: count sample num with class_index!=ignore_index
            # 2. else
            #     numerator: loss's weighted sum
            #     denominator: cal the sum of weight where the sample's class_index!=ignore_index
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            if ignore_index >= 0:
2596
                out_sum = _legacy_C_ops.reduce_sum(out, 'reduce_all', True)
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                # for each label[i],set 1 or 0, according to ignore_index
                # mask[i]=0, if label[i]==ignore_index
                # mask[i]=1, otherwise
2600
                mask = (label != ignore_index)
2601
                if weight is None:
2602
                    mask = paddle.cast(mask, dtype=out_sum.dtype)
2603
                    count = _legacy_C_ops.reduce_sum(mask, 'reduce_all', True)
2604
                    ret = out_sum / (count + (count == 0.0))
2605 2606
                else:
                    mask = paddle.cast(mask, weight_gather_reshape.dtype)
2607
                    weight_ignored = _legacy_C_ops.elementwise_mul(
2608
                        mask, weight_gather_reshape)
2609 2610
                    weight_sum = _legacy_C_ops.reduce_sum(
                        weight_ignored, 'reduce_all', True)
2611
                    ret = out_sum / (weight_sum + (weight_sum == 0.0))
2612 2613
                return ret
            elif weight is not None:
2614 2615 2616
                out_sum = _legacy_C_ops.reduce_sum(out, 'reduce_all', True)
                total_weight = _legacy_C_ops.reduce_sum(weight_gather_reshape,
                                                        'reduce_all', True)
2617
                return out_sum / (total_weight + (total_weight == 0.0))
2618
            else:
2619
                return _legacy_C_ops.mean(out)
2620
        else:
2621 2622
            if input_dims - 1 == label_dims:
                out = paddle.squeeze(out, axis=axis)
2623
            return out
2624

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    check_variable_and_dtype(input, 'input', ['float16', 'float32', 'float64'],
2626 2627
                             'softmax_cross_entropy')
    check_variable_and_dtype(
2628 2629
        label, 'label',
        ['uint8', 'int8', 'int16', 'int32', 'int64', 'float32', 'float64'],
2630
        'softmax_cross_entropy')
2631 2632 2633 2634 2635
    attrs = {
        'soft_label': soft_label,
        'ignore_index': ignore_index,
        'numeric_stable_mode': True,
        'axis': axis,
2636
        'use_softmax': use_softmax
2637 2638 2639 2640
    }
    helper = LayerHelper('softmax_with_cross_entropy', **locals())
    softmax = helper.create_variable_for_type_inference(dtype=input.dtype)
    out = helper.create_variable_for_type_inference(dtype=input.dtype)
2641 2642 2643 2644 2645

    outputs = {'Softmax': softmax, 'Loss': out}
    if core.is_compiled_with_npu() or core.is_compiled_with_mlu():
        backprop = helper.create_variable_for_type_inference(dtype=input.dtype)
        outputs['Backprop'] = backprop
2646 2647 2648 2649 2650 2651 2652
    helper.append_op(type='softmax_with_cross_entropy',
                     inputs={
                         'Logits': input,
                         'Label': label
                     },
                     outputs=outputs,
                     attrs=attrs)
2653

2654
    if weight is not None:
2655 2656
        check_variable_and_dtype(weight, 'weight', ['float32', 'float64'],
                                 'softmax_cross_entropy')
2657
        weight_name = name if reduction == 'none' else None
2658 2659
        if soft_label == True:
            # chajchaj:
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            # trans weight from class to sample, shape:N or [N,H,W] for 1d and 2d cases.
2661 2662 2663
            # weight's shape is C, where C is class num.
            # for 1d case: label's shape is [N,C], weight_gather's shape is N.
            # for 2d case: label's shape is [N,H,W,C], weight_gather's shape is [N,H,W].
2664 2665 2666 2667
            weight_gather = paddle.matmul(x=paddle.cast(label, weight.dtype),
                                          y=weight,
                                          transpose_x=False,
                                          transpose_y=True)
2668 2669 2670 2671 2672

            out_shape = list(out.shape)
            weight_gather_reshape = reshape(weight_gather, shape=out_shape)
            out = paddle.cast(out, weight_gather_reshape.dtype)
        else:
2673 2674
            if input.shape[axis] != weight.shape[-1]:
                raise ValueError("input's class_dimension({}) must equal to "
2675 2676
                                 "weight's class_dimension({}) "
                                 "when weight is provided" \
2677
                                 .format(input.shape[axis], weight.shape[-1]))
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            valid_label = paddle.multiply(
2680
                paddle.cast(label != ignore_index, dtype=label.dtype), label)
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            ignore_weight_mask = paddle.cast((label != ignore_index),
                                             input.dtype)
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            if ignore_weight_mask.ndim > 1 and ignore_weight_mask.shape[
2684 2685
                    axis] == 1:
                ignore_weight_mask = paddle.squeeze(ignore_weight_mask, axis)
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            if axis != -1 and axis != valid_label.ndim - 1:
2687
                temp_perm = list(range(axis % valid_label.ndim)) \
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                            + list(range((axis % valid_label.ndim + 1), valid_label.ndim)) \
2689 2690 2691 2692 2693
                            + [axis % valid_label.ndim]
                weight_gather = paddle.gather_nd(
                    weight, paddle.transpose(valid_label, temp_perm))
            else:
                weight_gather = paddle.gather_nd(weight, valid_label)
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            weight_gather = paddle.multiply(weight_gather, ignore_weight_mask)

2696 2697
            input_shape = list(label.shape)
            weight_gather_reshape = reshape(weight_gather, shape=input_shape)
2698
        out = paddle.multiply(out, weight_gather_reshape, name=weight_name)
2699

2700 2701 2702
    if reduction == "sum":
        return paddle.sum(out, name=name)
    elif reduction == "mean":
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        if ignore_index >= 0:
2704
            out_sum = paddle.sum(out, name=name)
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            # for each label[i],set 1 or 0, according to ignore_index
            # mask[i]=0, if label[i]==ignore_index
            # mask[i]=1, otherwise
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            mask = (label != ignore_index)
            if (weight is None):
                mask = paddle.cast(mask, dtype=out_sum.dtype)
                count = paddle.sum(mask, name=name)
2712
                ret = out_sum / (count + (count == 0.0))
2713 2714 2715 2716
            else:
                mask = paddle.cast(mask, weight_gather_reshape.dtype)
                weight_ignored = paddle.multiply(mask, weight_gather_reshape)
                weight_sum = paddle.sum(weight_ignored, name=name)
2717
                ret = out_sum / (weight_sum + (weight_sum == 0.0))
2718 2719
            return ret
        elif weight is not None:
2720 2721
            out_sum = paddle.sum(out, name=name)
            total_weight = paddle.sum(weight_gather_reshape)
2722
            return out_sum / (total_weight + (total_weight == 0.0))
2723 2724
        else:
            return paddle.mean(out, name=name)
2725

2726
    else:
2727 2728 2729
        if input_dims - 1 == label_dims:
            out = paddle.squeeze(out, axis=axis)

2730
        return out
2731 2732 2733 2734 2735 2736 2737 2738 2739


def sigmoid_focal_loss(logit,
                       label,
                       normalizer=None,
                       alpha=0.25,
                       gamma=2.0,
                       reduction='sum',
                       name=None):
2740
    r"""
2741 2742 2743 2744 2745 2746
    `Focal Loss <https://arxiv.org/abs/1708.02002>`_ is proposed to address the
    foreground-background class imbalance for classification tasks. It down-weights
    easily-classified examples and thus focuses training on hard examples. For example,
    it is used in one-stage object detection where the foreground-background class
    imbalance is extremely high.

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    This operator measures focal loss function as follows: 
2748 2749

    .. math::
2750
           Out = -Labels * alpha * {(1 - \sigma(Logit))}^{gamma}\log(\sigma(Logit)) - (1 - Labels) * (1 - alpha) * {\sigma(Logit)}^{gamma}\log(1 - \sigma(Logit))
2751

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    We know that :math:`\sigma(Logit) = \frac{1}{1 + \exp(-Logit)}`. 
2753 2754 2755 2756 2757

    Then, if :attr:`normalizer` is not None, this operator divides the
    normalizer tensor on the loss `Out`:

    .. math::
2758
           Out = \frac{Out}{normalizer}
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    Finally, this operator applies reduce operation on the loss.
    If :attr:`reduction` set to ``'none'``, the operator will return the original loss `Out`.
    If :attr:`reduction` set to ``'mean'``, the reduced mean loss is :math:`Out = MEAN(Out)`.
    If :attr:`reduction` set to ``'sum'``, the reduced sum loss is :math:`Out = SUM(Out)`.

    Note that the target ``label`` is 0 for the negative class and is 1 for the positive class.

    Args:
        logit (Tensor): The input logit tensor. The shape is [N, *], where N is batch_size,
            `*` means any number of additional dimensions. The ``logit`` is usually the
            output of a convolution layer. Available dtype is float32, float64.
        label (Tensor): The target label tensor with the same shape as
            ``logit``. The target label whose value should be numbers between 0 and 1.
            Available dtype is float32, float64.
        normalizer (Tensor, optional): The number normalizes the focal loss. It has to be
            a 1-D Tensor whose shape is `[1, ]`. The data type is float32, float64.
2776
            For object detection task, it is the number of positive samples.
2777 2778
            If set to None, the focal loss will not be normalized. Default is None.
        alpha(int|float, optional): Hyper-parameter to balance the positive and negative example,
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            it should be between 0 and 1.  Default value is set to 0.25. 
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        gamma(int|float, optional): Hyper-parameter to modulate the easy and hard examples.
            Default value is set to 2.0.
        reduction (str, optional): Indicate how to average the loss by batch_size,
            the candicates are ``'none'`` | ``'mean'`` | ``'sum'``.
            If :attr:`reduction` is ``'none'``, the unreduced loss is returned;
            If :attr:`reduction` is ``'mean'``, the reduced mean loss is returned;
            If :attr:`reduction` is ``'sum'``, the summed loss is returned.
            Default is ``'sum'``.
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        Tensor, if :attr:`reduction` is ``'mean'`` or ``'sum'``, the out shape is :math:`[1]`, otherwise the shape is the same as ``logit``. The same dtype as ``logit`` tensor.

    Examples:

        .. code-block:: python

            import paddle

            logit = paddle.to_tensor([[0.97, 0.91, 0.03], [0.55, 0.43, 0.71]], dtype='float32')
            label = paddle.to_tensor([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0]], dtype='float32')
            one = paddle.to_tensor([1.], dtype='float32')
            fg_label = paddle.greater_equal(label, one)
2804
            fg_num = paddle.sum(paddle.cast(fg_label, dtype='float32'))
2805
            output = paddle.nn.functional.sigmoid_focal_loss(logit, label, normalizer=fg_num)
2806
            print(output)  # [0.65782464]
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    """
    if reduction not in ['sum', 'mean', 'none']:
        raise ValueError(
            "The value of 'reduction' in sigmoid_focal_loss "
            "should be 'sum', 'mean' or 'none', but received %s, which is not allowed."
            % reduction)

    if normalizer is not None:
2816 2817
        check_variable_and_dtype(normalizer, 'normalizer',
                                 ['float32', 'float64'], 'sigmoid_focal_loss')
2818 2819 2820 2821
        normalizer_shape = list(normalizer.shape)
        normalizer_dims = len(normalizer_shape)
        if normalizer_dims > 1:
            raise ValueError(
2822 2823
                "Expected one dimension of normalizer in sigmoid_focal_loss but got {}."
                .format(normalizer_dims))
2824

2825 2826
    if in_dygraph_mode():
        place = _current_expected_place()
2827
        one = _C_ops.full(logit.shape, float(1.0), logit.dtype, place)
2828

2829 2830
        loss = _C_ops.sigmoid_cross_entropy_with_logits(logit, label, False,
                                                        -100)
2831

2832
        pred = _C_ops.sigmoid(logit)
2833

2834 2835 2836 2837
        p_t = _C_ops.add(
            _C_ops.multiply(pred, label),
            _C_ops.multiply(_C_ops.subtract(one, pred),
                            _C_ops.subtract(one, label)))
2838 2839

        alpha = fluid.dygraph.base.to_variable([alpha], dtype=loss.dtype)
2840 2841 2842 2843 2844
        alpha_t = _C_ops.add(
            _C_ops.multiply(alpha, label),
            _C_ops.multiply(_C_ops.subtract(one, alpha),
                            _C_ops.subtract(one, label)))
        loss = _C_ops.multiply(alpha_t, loss)
2845 2846

        gamma = fluid.dygraph.base.to_variable([gamma], dtype=loss.dtype)
2847 2848
        gamma_t = _C_ops.pow(_C_ops.subtract(one, p_t), gamma)
        loss = _C_ops.multiply(gamma_t, loss)
2849 2850

        if normalizer is not None:
2851
            loss = _C_ops.divide(loss, normalizer)
2852 2853

        if reduction == "sum":
2854
            return _C_ops.sum(loss, [], None, False)
2855
        elif reduction == "mean":
2856
            return _C_ops.mean_all(loss)
2857 2858 2859 2860 2861

        return loss

    elif _in_legacy_dygraph():
        one = _varbase_creator(dtype=logit.dtype)
2862 2863 2864 2865
        _legacy_C_ops.fill_constant(one, 'value', float(1.0), 'force_cpu',
                                    False, 'dtype', one.dtype, 'str_value',
                                    '1.0', 'shape', logit.shape)
        loss = _legacy_C_ops.sigmoid_cross_entropy_with_logits(logit, label)
2866

2867
        pred = _legacy_C_ops.sigmoid(logit)
2868

2869 2870 2871 2872 2873
        p_t = _legacy_C_ops.elementwise_add(
            _legacy_C_ops.elementwise_mul(pred, label),
            _legacy_C_ops.elementwise_mul(
                _legacy_C_ops.elementwise_sub(one, pred),
                _legacy_C_ops.elementwise_sub(one, label)))
2874 2875

        alpha = fluid.dygraph.base.to_variable([alpha], dtype=loss.dtype)
2876 2877 2878 2879 2880 2881
        alpha_t = _legacy_C_ops.elementwise_add(
            _legacy_C_ops.elementwise_mul(alpha, label),
            _legacy_C_ops.elementwise_mul(
                _legacy_C_ops.elementwise_sub(one, alpha),
                _legacy_C_ops.elementwise_sub(one, label)))
        loss = _legacy_C_ops.elementwise_mul(alpha_t, loss)
2882 2883

        gamma = fluid.dygraph.base.to_variable([gamma], dtype=loss.dtype)
2884 2885 2886
        gamma_t = _legacy_C_ops.elementwise_pow(
            _legacy_C_ops.elementwise_sub(one, p_t), gamma)
        loss = _legacy_C_ops.elementwise_mul(gamma_t, loss)
2887 2888

        if normalizer is not None:
2889
            loss = _legacy_C_ops.elementwise_div(loss, normalizer)
2890 2891

        if reduction == "sum":
2892
            return _legacy_C_ops.reduce_sum(loss, 'reduce_all', True)
2893
        elif reduction == "mean":
2894
            return _legacy_C_ops.mean(loss)
2895 2896 2897

        return loss

2898 2899 2900 2901
    check_variable_and_dtype(logit, 'logit', ['float32', 'float64'],
                             'sigmoid_focal_loss')
    check_variable_and_dtype(label, 'label', ['float32', 'float64'],
                             'sigmoid_focal_loss')
2902 2903 2904 2905 2906 2907 2908

    bce_name = None
    if reduction == 'none' and normalizer is None:
        bce_name = name
    loss = paddle.nn.functional.binary_cross_entropy_with_logits(
        logit, label, reduction='none', name=bce_name)

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    pred = paddle.nn.functional.sigmoid(logit)
2910 2911 2912 2913 2914 2915 2916 2917 2918 2919 2920 2921 2922 2923 2924 2925 2926 2927
    p_t = pred * label + (1 - pred) * (1 - label)

    alpha_t = alpha * label + (1 - alpha) * (1 - label)
    loss = paddle.multiply(alpha_t, loss)

    gamma_t = paddle.pow((1 - p_t), gamma)
    loss = paddle.multiply(gamma_t, loss)

    if normalizer is not None:
        normalizer_name = name if reduction == 'none' else None
        loss = paddle.divide(loss, normalizer, name=normalizer_name)

    if reduction == 'mean':
        loss = paddle.mean(loss, name=name)
    elif reduction == 'sum':
        loss = paddle.sum(loss, name=name)

    return loss
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def multi_label_soft_margin_loss(input,
                                 label,
                                 weight=None,
                                 reduction="mean",
                                 name=None):
    r"""

        Parameters:
            input (Tensor): Input tensor, the data type is float32 or float64. Shape is (N, C), where C is number of classes, and if shape is more than 2D, this is (N, C, D1, D2,..., Dk), k >= 1.
            label (Tensor): Label tensor, the data type is float32 or float64. The shape of label is the same as the shape of input.
            weight (Tensor,optional): a manual rescaling weight given to each class.
                    If given, has to be a Tensor of size C and the data type is float32, float64.
                    Default is ``'None'`` .
            reduction (str, optional): Indicate how to average the loss by batch_size,
                    the candicates are ``'none'`` | ``'mean'`` | ``'sum'``.
                    If :attr:`reduction` is ``'none'``, the unreduced loss is returned;
                    If :attr:`reduction` is ``'mean'``, the reduced mean loss is returned;
                    If :attr:`reduction` is ``'sum'``, the summed loss is returned.
                    Default: ``'mean'``
            name (str, optional): Name for the operation (optional, default is None).
                    For more information, please refer to :ref:`api_guide_Name`.

	Shape:
            input: N-D Tensor, the shape is [N, \*], N is batch size and `\*` means number of classes, available dtype is float32, float64. The sum operationoperates over all the elements.
            label: N-D Tensor, same shape as the input.
            weight:N-D Tensor, the shape is [N,1]
            output: scalar. If :attr:`reduction` is ``'none'``, then same shape as the input.

	Returns:
            Tensor, The tensor variable storing the multi_label_soft_margin_loss of input and label.

	Examples:
            .. code-block:: python

                import paddle
                import paddle.nn.functional as F
                input = paddle.to_tensor([[1, -2, 3], [0, -1, 2], [1, 0, 1]], dtype=paddle.float32)
                # label elements in {1., -1.}
                label = paddle.to_tensor([[-1, 1, -1], [1, 1, 1], [1, -1, 1]], dtype=paddle.float32)
                loss = F.multi_label_soft_margin_loss(input, label, reduction='none')
                print(loss)
                # Tensor([3.49625897, 0.71111226, 0.43989015])
                loss = F.multi_label_soft_margin_loss(input, label, reduction='mean')
                print(loss)
                # Tensor([1.54908717])
    """
    if reduction not in ['sum', 'mean', 'none']:
        raise ValueError(
            "'reduction' in 'multi_label_soft_margin_loss' should be 'sum', 'mean' or 'none', "
            "but received {}.".format(reduction))

    if not (input.shape == label.shape):
        raise ValueError("The input and label should have same dimension,"
                         "but received {}!={}".format(input.shape, label.shape))

    if not _non_static_mode():
        check_variable_and_dtype(input, 'input', ['float32', 'float64'],
                                 'multilabel_soft_margin_loss')
        check_variable_and_dtype(label, 'label', ['float32', 'float64'],
                                 'multilabel_soft_margin_loss')

    loss = -(label * paddle.nn.functional.log_sigmoid(input) +
             (1 - label) * paddle.nn.functional.log_sigmoid(-input))

    if weight is not None:
        if not _non_static_mode():
            check_variable_and_dtype(weight, 'weight', ['float32', 'float64'],
                                     'multilabel_soft_margin_loss')
        loss = loss * weight

    loss = loss.mean(axis=-1)  # only return N loss values

    if reduction == "none":
        return loss
    elif reduction == "mean":
        return paddle.mean(loss)
    elif reduction == "sum":
        return paddle.sum(loss)


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def hinge_embedding_loss(input, label, margin=1.0, reduction='mean', name=None):
    r"""
    This operator calculates hinge_embedding_loss. Measures the loss given an input tensor :math:`x` and a labels tensor :math:`y`(containing 1 or -1).
    This is usually used for measuring whether two inputs are similar or dissimilar, e.g. using the L1 pairwise distance as :math:`x`,
    and is typically used for learning nonlinear embeddings or semi-supervised learning.

    The loss function for :math:`n`-th sample in the mini-batch is

    .. math::
        l_n = \begin{cases}
            x_n, & \text{if}\; y_n = 1,\\
            \max \{0, \Delta - x_n\}, & \text{if}\; y_n = -1,
        \end{cases}

    and the total loss functions is

    .. math::
        \ell(x, y) = \begin{cases}
            \operatorname{mean}(L), & \text{if reduction} = \text{'mean';}\\
            \operatorname{sum}(L),  & \text{if reduction} = \text{'sum'.}
        \end{cases}

    where :math:`L = \{l_1,\dots,l_N\}^\top`.

    Parameters:
        input (Tensor): Input tensor, the data type is float32 or float64.
            the shape is [N, \*], N is batch size and `\*` means any number of additional dimensions, available dtype is float32, float64.
        label (Tensor): Label tensor containing 1 or -1, the data type is float32 or float64.
            The shape of label is the same as the shape of input.
        margin (float, optional): Specifies the hyperparameter margin to be used.
            The value determines how large the input need to be to calculate in
            hinge_embedding_loss. When label is -1, Input smaller than margin are minimized with hinge_embedding_loss.
            Default = 1.0
        reduction (str, optional): Indicate how to average the loss by batch_size.
            the candicates are ``'none'`` | ``'mean'`` | ``'sum'``.
            If :attr:`reduction` is ``'none'``, the unreduced loss is returned;
            If :attr:`reduction` is ``'mean'``, the reduced mean loss is returned;
            If :attr:`reduction` is ``'sum'``, the summed loss is returned.
            Default: ``'mean'``
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Shape:

        input: N-D Tensor, the shape is [N, \*], N is batch size and `\*` means any number of additional dimensions, available dtype is float32, float64. The sum operationoperates over all the elements.

        label: N-D Tensor, same shape as the input. tensor elements should containing 1 or -1, the data type is float32 or float64.

        output: scalar. If :attr:`reduction` is ``'none'``, then same shape as the input.

    Returns:
        Tensor. The tensor variable storing the hinge_embedding_loss of input and label.

    Examples:
        .. code-block:: python

            import paddle
            import paddle.nn.functional as F

            input = paddle.to_tensor([[1, -2, 3], [0, -1, 2], [1, 0, 1]], dtype=paddle.float32)
            # label elements in {1., -1.}
            label = paddle.to_tensor([[-1, 1, -1], [1, 1, 1], [1, -1, 1]], dtype=paddle.float32)

            loss = F.hinge_embedding_loss(input, label, margin=1.0, reduction='none')
            print(loss)
            # Tensor([[0., -2., 0.],
            #         [0., -1., 2.],
            #         [1., 1., 1.]])

            loss = F.hinge_embedding_loss(input, label, margin=1.0, reduction='mean')
            print(loss)
            # Tensor([0.22222222])
    """

    if reduction not in ['sum', 'mean', 'none']:
        raise ValueError(
            "'reduction' in 'hinge_embedding_loss' should be 'sum', 'mean' or 'none', "
            "but received {}.".format(reduction))

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        check_variable_and_dtype(input, 'input', ['float32', 'float64'],
                                 'hinge_embedding_loss')
        check_variable_and_dtype(label, 'label', ['float32', 'float64'],
                                 'hinge_embedding_loss')

    zero_ = paddle.zeros([1], dtype=input.dtype)
    loss = paddle.where(label == 1., input, zero_) + \
           paddle.where(label == -1., paddle.nn.functional.relu(margin - input), zero_)

    if reduction == 'mean':
        return paddle.mean(loss, name=name)
    elif reduction == 'sum':
        return paddle.sum(loss, name=name)
    elif reduction == 'none':
        return loss
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def cosine_embedding_loss(input1,
                          input2,
                          label,
                          margin=0,
                          reduction='mean',
                          name=None):
    r"""
    This operator computes the cosine embedding loss of Tensor ``input1``, ``input2`` and ``label`` as follows.

    If label = 1, then the loss value can be calculated as follow:

    .. math::
        Out = 1 - cos(input1, input2)

    If label = -1, then the loss value can be calculated as follow:

    .. math::
        Out = max(0, cos(input1, input2)) - margin

    The operator cos can be described as follow:
     .. math::
        cos(x1, x2) = \frac{x1 \cdot{} x2}{\Vert x1 \Vert_2 * \Vert x2 \Vert_2}

     Parameters:
        input1 (Tensor): tensor with shape: [N, M] or [M], 'N' means batch size, 'M' means the length of input array.
                         Available dtypes are float32, float64.
        input2 (Tensor): tensor with shape: [N, M] or [M], 'N' means batch size, 'M' means the length of input array.
                         Available dtypes are float32, float64.
        label (Tensor): tensor with shape: [N] or [1]. The target labels values should be -1 or 1.
                         Available dtypes are int32, int64, float32, float64.
        margin (float, optional): Should be a number from :math:`-1` to :math:`1`,
                         :math:`0` to :math:`0.5` is suggested. If :attr:`margin` is missing, the
                         default value is :math:`0`.
        reduction (string, optional): Specifies the reduction to apply to the output:
                         ``'none'`` | ``'mean'`` | ``'sum'``. ``'none'``: no reduction will be applied,
                         ``'mean'``: the sum of the output will be divided by the number of elements in the output
                         ``'sum'``: the output will be summed.
        name (str, optional): Name for the operation (optional, default is None).
                         For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        Tensor, the cosine embedding Loss of Tensor ``input1`` ``input2`` and ``label``.
            If `reduction` is ``'none'``, the shape of output loss is [N], the same as ``input`` .
            If `reduction` is ``'mean'`` or ``'sum'``, the shape of output loss is [1].

    Examples:
        .. code-block:: python

            import paddle

            input1 = paddle.to_tensor([[1.6, 1.2, -0.5], [3.2, 2.6, -5.8]], 'float32')
            input2 = paddle.to_tensor([[0.5, 0.5, -1.8], [2.3, -1.4, 1.1]], 'float32')
            label = paddle.to_tensor([1, -1], 'int64')

            output = paddle.nn.functional.cosine_embedding_loss(input1, input2, label, margin=0.5, reduction='mean')
            print(output)  # [0.21155193]

            output = paddle.nn.functional.cosine_embedding_loss(input1, input2, label, margin=0.5, reduction='sum')
            print(output)  # [0.42310387]

            output = paddle.nn.functional.cosine_embedding_loss(input1, input2, label, margin=0.5, reduction='none')
            print(output)  # [0.42310387, 0.        ]

    """
    if len(label.shape) != 1:
        raise ValueError(
            "1D target tensor expected, multi-target not supported")

    if input1.shape != input2.shape:
        raise ValueError(
            "the shape of input tensor 1 should be equal to input tensor 2, but found inputs with "
            "different sizes")

    if len(input1.shape) > 2:
        raise ValueError(
            "1D target tensor expects 1D or 2D input tensors, but found inputs with different sizes"
        )

    if input1.dtype not in [paddle.float32, paddle.float64]:
        raise ValueError(
            "The data type of input Variable must be 'float32' or 'float64'")
    if label.dtype not in [
            paddle.int32, paddle.int64, paddle.float32, paddle.float64
    ]:
        raise ValueError(
            "The data type of label Variable must be 'int32', 'int64', 'float32', 'float64'"
        )

    prod_sum = (input1 * input2).sum(axis=-1)
    mag_square1 = paddle.square(input1).sum(axis=-1) + 10e-12
    mag_square2 = paddle.square(input2).sum(axis=-1) + 10e-12
    denom = paddle.sqrt(mag_square1 * mag_square2)
    cos = prod_sum / denom
    zeros = paddle.zeros_like(cos)
    pos = 1 - cos
    neg = paddle.clip(cos - margin, min=0)
    out_pos = paddle.where(label == 1, pos, zeros)
    out_neg = paddle.where(label == -1, neg, zeros)
    out = out_pos + out_neg

    if reduction == 'none':
        return out
    if reduction == 'mean':
        return paddle.mean(out, name=name)
    elif reduction == 'sum':
        return paddle.sum(out, name=name)
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def triplet_margin_with_distance_loss(input,
                                      positive,
                                      negative,
                                      distance_function=None,
                                      margin=1.0,
                                      swap=False,
                                      reduction='mean',
                                      name=None):
    r"""
    Measures the triplet loss given an input
    tensors :math:`x1`, :math:`x2`, :math:`x3` and a margin with a value greater than :math:`0`.
    This is used for measuring a relative similarity between samples. A triplet
    is composed by `input`, `positive` and `negative` (i.e., `input`, `positive examples` and `negative
    examples` respectively). The shapes of all input tensors should be
    :math:`(N, D)`.

    The loss function for each sample in the mini-batch is:

    .. math::
        L(input, pos, neg) = \max \{d(input_i, pos_i) - d(input_i, neg_i) + {\rm margin}, 0\}


    where the default distance function

    .. math::
        d(x_i, y_i) = \left\lVert {\bf x}_i - {\bf y}_i \right\rVert_p

    or user can defined their own distance functions. `margin` is a nonnegative margin representing the minimum difference 
    between the positive and negative distances that is required for the loss to be 0. If `swap` is true, it will compare distance of (input, negative) with
    distance of (negative, positive) and change it to the smaller one. For more details see http://www.bmva.org/bmvc/2016/papers/paper119/paper119.pdf.

    Parameters:

        input (Tensor):Input tensor, the data type is float32 or float64.
            the shape is [N, \*], N is batch size and `\*` means any number of additional dimensions, available dtype is float32, float64.

        positive (Tensor):Positive tensor, the data type is float32 or float64.
            The shape of label is the same as the shape of input.

        negative (Tensor):Negative tensor, the data type is float32 or float64.
            The shape of label is the same as the shape of input.

        distance_function (callable, optional): Quantifies the distance between two tensors. if not specified, 2 norm functions will be used.
	
	    margin (float, optional):Default: :math:`1`.A nonnegative margin representing the minimum difference
            between the positive and negative distances required for the loss to be 0.
	
        swap (bool, optional):The distance swap changes the negative distance to the swap distance (distance between positive samples
                and negative samples) if swap distance smaller than negative distance. Default: ``False``.

        reduction (str, optional):Indicate how to average the loss by batch_size.
            the candicates are ``'none'`` | ``'mean'`` | ``'sum'``.
            If :attr:`reduction` is ``'none'``, the unreduced loss is returned;
            If :attr:`reduction` is ``'mean'``, the reduced mean loss is returned;
            If :attr:`reduction` is ``'sum'``, the summed loss is returned.
            Default: ``'mean'``
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.
	    
    Returns:
        Output: Tensor. The tensor variable storing the triplet_margin_with_distance_loss of input and positive and negative.

    Examples:
        .. code-block:: python

            import paddle
            import paddle.nn.functional as F

            input = paddle.to_tensor([[1, 5, 3], [0, 3, 2], [1, 4, 1]], dtype=paddle.float32)
            positive= paddle.to_tensor([[5, 1, 2], [3, 2, 1], [3, -1, 1]], dtype=paddle.float32)
            negative = paddle.to_tensor([[2, 1, -3], [1, 1, -1], [4, -2, 1]], dtype=paddle.float32)
            loss = F.triplet_margin_with_distance_loss(input, positive, negative, margin=1.0, reduction='none')
            print(loss)
            # Tensor([0.        , 0.57496738, 0.        ])


            loss = F.triplet_margin_with_distance_loss(input, positive, negative, margin=1.0, reduction='mean')
            print(loss)
            # Tensor([0.19165580])

    """
    if reduction not in ['sum', 'mean', 'none']:
        raise ValueError("'reduction' in 'triplet_margin_with_distance_loss' "
                         "should be 'sum', 'mean' or 'none', "
                         "but received {}.".format(reduction))
    if margin < 0:
        raise ValueError(
            "The margin between positive samples and negative samples should be greater than 0."
        )
    if not _non_static_mode():
        check_variable_and_dtype(input, 'input', ['float32', 'float64'],
                                 'triplet_margin_with_distance_loss')
        check_variable_and_dtype(positive, 'positive', ['float32', 'float64'],
                                 'triplet_margin_with_distance_loss')
        check_variable_and_dtype(negative, 'negative', ['float32', 'float64'],
                                 'triplet_margin_with_distance_loss')

    if not (input.shape == positive.shape == negative.shape):
        raise ValueError("input's shape must equal to "
                         "positive's shape and  "
                         "negative's shape")

    distance_function = distance_function if distance_function is not None \
        else paddle.nn.PairwiseDistance(2)

    positive_dist = distance_function(input, positive)
    negative_dist = distance_function(input, negative)

    if swap:
        swap_dist = distance_function(positive, negative)
        negative_dist = paddle.minimum(negative_dist, swap_dist)

    if not paddle.all(positive_dist > 0) or not paddle.all(negative_dist > 0):
        raise ValueError(
            "The positive distance or negative distance should be greater than 0, "
            "The distance functions should be checked.")

    loss = paddle.clip(positive_dist - negative_dist + margin, min=0.0)

    if reduction == 'mean':
        return paddle.mean(loss, name=name)
    elif reduction == 'sum':
        return paddle.sum(loss, name=name)
    elif reduction == 'none':
        return loss
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def triplet_margin_loss(input,
                        positive,
                        negative,
                        margin=1.0,
                        p=2,
                        epsilon=1e-6,
                        swap=False,
                        reduction='mean',
                        name=None):
    r"""
        Measures the triplet loss given an input
        tensors :math:`x1`, :math:`x2`, :math:`x3` and a margin with a value greater than :math:`0`.
        This is used for measuring a relative similarity between samples. A triplet
        is composed by `input`, `positive` and `negative` (i.e., `input`, `positive examples` and `negative
        examples` respectively). The shapes of all input tensors should be
        :math:`(N, *)`.

        The loss function for each sample in the mini-batch is:

        .. math::
            L(input, pos, neg) = \max \{d(input_i, pos_i) - d(input_i, neg_i) + {\rm margin}, 0\}


        where

        .. math::
            d(x_i, y_i) = \left\lVert {\bf x}_i - {\bf y}_i \right\rVert_p

    Parameters:
        input (Tensor): Input tensor, the data type is float32 or float64.
            the shape is [N, \*], N is batch size and `\*` means any number of additional dimensions, available dtype is float32, float64.

        positive (Tensor): Positive tensor, the data type is float32 or float64.
            The shape of label is the same as the shape of input.

        negative (Tensor): Negative tensor, the data type is float32 or float64.
            The shape of label is the same as the shape of input.

        margin (float, Optional): Default: :math:`1`.

        p (int, Optional): The norm degree for pairwise distance. Default: :math:`2`.

        epsilon (float, Optional): Add small value to avoid division by zero,
            default value is 1e-6.

        swap (bool,Optional): The distance swap change the negative distance to the distance between
            positive sample and negative sample. For more details, see `Learning shallow convolutional feature descriptors with triplet losses`.
            Default: ``False``.


        reduction (str, Optional):Indicate how to average the loss by batch_size.
            the candicates are ``'none'`` | ``'mean'`` | ``'sum'``.
            If :attr:`reduction` is ``'none'``, the unreduced loss is returned;
            If :attr:`reduction` is ``'mean'``, the reduced mean loss is returned;
            If :attr:`reduction` is ``'sum'``, the summed loss is returned.
            Default: ``'mean'``

        name (str, Optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        Output: Tensor. The tensor variable storing the triplet_margin_loss of input and positive and negative.

    Examples:
        .. code-block:: python

            import paddle
            import paddle.nn.functional as F

            input = paddle.to_tensor([[1, 5, 3], [0, 3, 2], [1, 4, 1]], dtype=paddle.float32)
            positive= paddle.to_tensor([[5, 1, 2], [3, 2, 1], [3, -1, 1]], dtype=paddle.float32)
            negative = paddle.to_tensor([[2, 1, -3], [1, 1, -1], [4, -2, 1]], dtype=paddle.float32)
            loss = F.triplet_margin_loss(input, positive, negative, margin=1.0, reduction='none')
            print(loss)
            # Tensor([0.        , 0.57496738, 0.        ])


            loss = F.triplet_margin_loss(input, positive, negative, margin=1.0, reduction='mean')
            print(loss)
            # Tensor([0.19165580])

    """
    if reduction not in ['sum', 'mean', 'none']:
        raise ValueError(
            "'reduction' in 'triplet_margin_loss' should be 'sum', 'mean' or 'none', "
            "but received {}.".format(reduction))
    if margin < 0:
        raise ValueError(
            "The margin between positive samples and negative samples should be greater than 0."
        )
    if not _non_static_mode():
        check_variable_and_dtype(input, 'input', ['float32', 'float64'],
                                 'triplet_margin_loss')
        check_variable_and_dtype(positive, 'positive', ['float32', 'float64'],
                                 'triplet_margin_loss')
        check_variable_and_dtype(negative, 'negative', ['float32', 'float64'],
                                 'triplet_margin_loss')

    if not (input.shape == positive.shape == negative.shape):
        raise ValueError("input's shape must equal to "
                         "positive's shape and  "
                         "negative's shape")

    distance_function = paddle.nn.PairwiseDistance(p, epsilon=epsilon)
    positive_dist = distance_function(input, positive)
    negative_dist = distance_function(input, negative)

    if swap:
        swap_dist = distance_function(positive, negative)
        negative_dist = paddle.minimum(negative_dist, swap_dist)

    loss = paddle.clip(positive_dist - negative_dist + margin, min=0.0)

    if reduction == 'mean':
        return paddle.mean(loss, name=name)
    elif reduction == 'sum':
        return paddle.sum(loss, name=name)
    elif reduction == 'none':
        return loss
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def soft_margin_loss(input, label, reduction='mean', name=None):
    """
    The API measures the soft margin loss between input predictions ``input``
    and target labels ``label`` . It can be described as:

    .. math::
        Out = log(1 + exp((-label * input)))

    Parameters:

        input (Tensor): The input predications tensor with shape: [N, *],
            N is batch_size, `*` means any number of additional dimensions. The ``input`` ranges from -inf to inf.
             Available dtype is float32, float64.

        label (Tensor): The target labels tensor with the same shape as
            ``input``. The target labels which values should be numbers -1 or 1.
            Available dtype is int32, int64, float32, float64.

        reduction (str, optional): Indicate how to average the loss by batch_size,
            the candidates are ``'none'`` | ``'mean'`` | ``'sum'``.
            If :attr:`reduction` is ``'none'``, the unreduced loss is returned;
            If :attr:`reduction` is ``'mean'``, the reduced mean loss is returned;
            If :attr:`reduction` is ``'sum'``, the summed loss is returned.
            Default is ``'mean'``.

        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:

        Output (Tensor): If ``reduction`` is ``'none'``, the shape of output is
            same as ``input`` , else the shape of output is [1].

    Examples:
        .. code-block:: python

            import paddle
            import numpy as np

            input = paddle.to_tensor([[0.5, 0.6, 0.7],[0.3, 0.5, 0.2]], 'float32')
            label = paddle.to_tensor([[1.0, -1.0, 1.0],[-1.0, 1.0, 1.0]], 'float32')
            output = paddle.nn.functional.soft_margin_loss(input, label)

            input_np = np.random.uniform(0.1, 0.8, size=(5, 5)).astype(np.float64)
            label_np = np.random.randint(0, 2, size=(5, 5)).astype(np.int64)
            label_np[label_np==0]=-1
            input = paddle.to_tensor(input_np)
            label = paddle.to_tensor(label_np)
            output = paddle.nn.functional.soft_margin_loss(input, label, reduction='none')
    """
    if reduction not in ['sum', 'mean', 'none']:
        raise ValueError(
            "The value of 'reduction' in soft_margin_loss should be 'sum', "
            "'mean' or 'none', but received %s, which is not allowed." %
            reduction)

    if not _non_static_mode():
        fluid.data_feeder.check_variable_and_dtype(input, 'input',
                                                   ['float32', 'float64'],
                                                   'soft_margin_loss')
        fluid.data_feeder.check_variable_and_dtype(
            label, 'label', ['int32', 'int64', 'float32', 'float64'],
            'soft_margin_loss')

    if not (input.shape == label.shape):
        raise ValueError("input's shape must equal to "
                         "label's shape")

    label = fluid.layers.cast(label, input.dtype)
    out = paddle.log(1 + paddle.exp(-label * input))

    if reduction == 'sum':
        return paddle.sum(out, name=name)
    elif reduction == 'mean':
        return paddle.mean(out, name=name)
    else:
        return out