MLPY/Lib/site-packages/torch/nn/modules/loss.py

import warnings

from .distance import PairwiseDistance
from .module import Module
from .. import functional as F
from .. import _reduction as _Reduction

from torch import Tensor
from typing import Callable, Optional

__all__ = ['L1Loss', 'NLLLoss', 'NLLLoss2d', 'PoissonNLLLoss', 'GaussianNLLLoss', 'KLDivLoss',
           'MSELoss', 'BCELoss', 'BCEWithLogitsLoss', 'HingeEmbeddingLoss', 'MultiLabelMarginLoss',
           'SmoothL1Loss', 'HuberLoss', 'SoftMarginLoss', 'CrossEntropyLoss', 'MultiLabelSoftMarginLoss',
           'CosineEmbeddingLoss', 'MarginRankingLoss', 'MultiMarginLoss', 'TripletMarginLoss',
           'TripletMarginWithDistanceLoss', 'CTCLoss']

class _Loss(Module):
    reduction: str

    def __init__(self, size_average=None, reduce=None, reduction: str = 'mean') -> None:
        super().__init__()
        if size_average is not None or reduce is not None:
            self.reduction: str = _Reduction.legacy_get_string(size_average, reduce)
        else:
            self.reduction = reduction


class _WeightedLoss(_Loss):
    def __init__(self, weight: Optional[Tensor] = None, size_average=None, reduce=None, reduction: str = 'mean') -> None:
        super().__init__(size_average, reduce, reduction)
        self.register_buffer('weight', weight)
        self.weight: Optional[Tensor]


class L1Loss(_Loss):
    r"""Creates a criterion that measures the mean absolute error (MAE) between each element in

    the input :math:`x` and target :math:`y`.



    The unreduced (i.e. with :attr:`reduction` set to ``'none'``) loss can be described as:



    .. math::

        \ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad

        l_n = \left| x_n - y_n \right|,



    where :math:`N` is the batch size. If :attr:`reduction` is not ``'none'``

    (default ``'mean'``), then:



    .. math::

        \ell(x, y) =

        \begin{cases}

            \operatorname{mean}(L), & \text{if reduction} = \text{`mean';}\\

            \operatorname{sum}(L),  & \text{if reduction} = \text{`sum'.}

        \end{cases}



    :math:`x` and :math:`y` are tensors of arbitrary shapes with a total

    of :math:`n` elements each.



    The sum operation still operates over all the elements, and divides by :math:`n`.



    The division by :math:`n` can be avoided if one sets ``reduction = 'sum'``.



    Supports real-valued and complex-valued inputs.



    Args:

        size_average (bool, optional): Deprecated (see :attr:`reduction`). By default,

            the losses are averaged over each loss element in the batch. Note that for

            some losses, there are multiple elements per sample. If the field :attr:`size_average`

            is set to ``False``, the losses are instead summed for each minibatch. Ignored

            when :attr:`reduce` is ``False``. Default: ``True``

        reduce (bool, optional): Deprecated (see :attr:`reduction`). By default, the

            losses are averaged or summed over observations for each minibatch depending

            on :attr:`size_average`. When :attr:`reduce` is ``False``, returns a loss per

            batch element instead and ignores :attr:`size_average`. Default: ``True``

        reduction (str, 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. Note: :attr:`size_average`

            and :attr:`reduce` are in the process of being deprecated, and in the meantime,

            specifying either of those two args will override :attr:`reduction`. Default: ``'mean'``



    Shape:

        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.

        - Target: :math:`(*)`, same shape as the input.

        - Output: scalar. If :attr:`reduction` is ``'none'``, then

          :math:`(*)`, same shape as the input.



    Examples::



        >>> loss = nn.L1Loss()

        >>> input = torch.randn(3, 5, requires_grad=True)

        >>> target = torch.randn(3, 5)

        >>> output = loss(input, target)

        >>> output.backward()

    """
    __constants__ = ['reduction']

    def __init__(self, size_average=None, reduce=None, reduction: str = 'mean') -> None:
        super().__init__(size_average, reduce, reduction)

    def forward(self, input: Tensor, target: Tensor) -> Tensor:
        return F.l1_loss(input, target, reduction=self.reduction)


class NLLLoss(_WeightedLoss):
    r"""The negative log likelihood loss. It is useful to train a classification

    problem with `C` classes.



    If provided, the optional argument :attr:`weight` should be a 1D Tensor assigning

    weight to each of the classes. This is particularly useful when you have an

    unbalanced training set.



    The `input` given through a forward call is expected to contain

    log-probabilities of each class. `input` has to be a Tensor of size either

    :math:`(minibatch, C)` or :math:`(minibatch, C, d_1, d_2, ..., d_K)`

    with :math:`K \geq 1` for the `K`-dimensional case. The latter is useful for

    higher dimension inputs, such as computing NLL loss per-pixel for 2D images.



    Obtaining log-probabilities in a neural network is easily achieved by

    adding a  `LogSoftmax`  layer in the last layer of your network.

    You may use `CrossEntropyLoss` instead, if you prefer not to add an extra

    layer.



    The `target` that this loss expects should be a class index in the range :math:`[0, C-1]`

    where `C = number of classes`; if `ignore_index` is specified, this loss also accepts

    this class index (this index may not necessarily be in the class range).



    The unreduced (i.e. with :attr:`reduction` set to ``'none'``) loss can be described as:



    .. math::

        \ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad

        l_n = - w_{y_n} x_{n,y_n}, \quad

        w_{c} = \text{weight}[c] \cdot \mathbb{1}\{c \not= \text{ignore\_index}\},



    where :math:`x` is the input, :math:`y` is the target, :math:`w` is the weight, and

    :math:`N` is the batch size. If :attr:`reduction` is not ``'none'``

    (default ``'mean'``), then



    .. math::

        \ell(x, y) = \begin{cases}

            \sum_{n=1}^N \frac{1}{\sum_{n=1}^N w_{y_n}} l_n, &

            \text{if reduction} = \text{`mean';}\\

            \sum_{n=1}^N l_n,  &

            \text{if reduction} = \text{`sum'.}

        \end{cases}



    Args:

        weight (Tensor, optional): a manual rescaling weight given to each

            class. If given, it has to be a Tensor of size `C`. Otherwise, it is

            treated as if having all ones.

        size_average (bool, optional): Deprecated (see :attr:`reduction`). By default,

            the losses are averaged over each loss element in the batch. Note that for

            some losses, there are multiple elements per sample. If the field :attr:`size_average`

            is set to ``False``, the losses are instead summed for each minibatch. Ignored

            when :attr:`reduce` is ``False``. Default: ``None``

        ignore_index (int, optional): Specifies a target value that is ignored

            and does not contribute to the input gradient. When

            :attr:`size_average` is ``True``, the loss is averaged over

            non-ignored targets.

        reduce (bool, optional): Deprecated (see :attr:`reduction`). By default, the

            losses are averaged or summed over observations for each minibatch depending

            on :attr:`size_average`. When :attr:`reduce` is ``False``, returns a loss per

            batch element instead and ignores :attr:`size_average`. Default: ``None``

        reduction (str, optional): Specifies the reduction to apply to the output:

            ``'none'`` | ``'mean'`` | ``'sum'``. ``'none'``: no reduction will

            be applied, ``'mean'``: the weighted mean of the output is taken,

            ``'sum'``: the output will be summed. Note: :attr:`size_average`

            and :attr:`reduce` are in the process of being deprecated, and in

            the meantime, specifying either of those two args will override

            :attr:`reduction`. Default: ``'mean'``



    Shape:

        - Input: :math:`(N, C)` or :math:`(C)`, where `C = number of classes`, or

          :math:`(N, C, d_1, d_2, ..., d_K)` with :math:`K \geq 1`

          in the case of `K`-dimensional loss.

        - Target: :math:`(N)` or :math:`()`, where each value is

          :math:`0 \leq \text{targets}[i] \leq C-1`, or

          :math:`(N, d_1, d_2, ..., d_K)` with :math:`K \geq 1` in the case of

          K-dimensional loss.

        - Output: If :attr:`reduction` is ``'none'``, shape :math:`(N)` or

          :math:`(N, d_1, d_2, ..., d_K)` with :math:`K \geq 1` in the case of K-dimensional loss.

          Otherwise, scalar.



    Examples::



        >>> m = nn.LogSoftmax(dim=1)

        >>> loss = nn.NLLLoss()

        >>> # input is of size N x C = 3 x 5

        >>> input = torch.randn(3, 5, requires_grad=True)

        >>> # each element in target has to have 0 <= value < C

        >>> target = torch.tensor([1, 0, 4])

        >>> output = loss(m(input), target)

        >>> output.backward()

        >>>

        >>>

        >>> # 2D loss example (used, for example, with image inputs)

        >>> N, C = 5, 4

        >>> loss = nn.NLLLoss()

        >>> # input is of size N x C x height x width

        >>> data = torch.randn(N, 16, 10, 10)

        >>> conv = nn.Conv2d(16, C, (3, 3))

        >>> m = nn.LogSoftmax(dim=1)

        >>> # each element in target has to have 0 <= value < C

        >>> target = torch.empty(N, 8, 8, dtype=torch.long).random_(0, C)

        >>> output = loss(m(conv(data)), target)

        >>> output.backward()

    """
    __constants__ = ['ignore_index', 'reduction']
    ignore_index: int

    def __init__(self, weight: Optional[Tensor] = None, size_average=None, ignore_index: int = -100,

                 reduce=None, reduction: str = 'mean') -> None:
        super().__init__(weight, size_average, reduce, reduction)
        self.ignore_index = ignore_index

    def forward(self, input: Tensor, target: Tensor) -> Tensor:
        return F.nll_loss(input, target, weight=self.weight, ignore_index=self.ignore_index, reduction=self.reduction)


class NLLLoss2d(NLLLoss):
    def __init__(self, weight: Optional[Tensor] = None, size_average=None, ignore_index: int = -100,

                 reduce=None, reduction: str = 'mean') -> None:
        warnings.warn("NLLLoss2d has been deprecated. "
                      "Please use NLLLoss instead as a drop-in replacement and see "
                      "https://pytorch.org/docs/master/nn.html#torch.nn.NLLLoss for more details.")
        super().__init__(weight, size_average, ignore_index, reduce, reduction)


class PoissonNLLLoss(_Loss):
    r"""Negative log likelihood loss with Poisson distribution of target.



    The loss can be described as:



    .. math::

        \text{target} \sim \mathrm{Poisson}(\text{input})



        \text{loss}(\text{input}, \text{target}) = \text{input} - \text{target} * \log(\text{input})

                                    + \log(\text{target!})



    The last term can be omitted or approximated with Stirling formula. The

    approximation is used for target values more than 1. For targets less or

    equal to 1 zeros are added to the loss.



    Args:

        log_input (bool, optional): if ``True`` the loss is computed as

            :math:`\exp(\text{input}) - \text{target}*\text{input}`, if ``False`` the loss is

            :math:`\text{input} - \text{target}*\log(\text{input}+\text{eps})`.

        full (bool, optional): whether to compute full loss, i. e. to add the

            Stirling approximation term



            .. math::

                \text{target}*\log(\text{target}) - \text{target} + 0.5 * \log(2\pi\text{target}).

        size_average (bool, optional): Deprecated (see :attr:`reduction`). By default,

            the losses are averaged over each loss element in the batch. Note that for

            some losses, there are multiple elements per sample. If the field :attr:`size_average`

            is set to ``False``, the losses are instead summed for each minibatch. Ignored

            when :attr:`reduce` is ``False``. Default: ``True``

        eps (float, optional): Small value to avoid evaluation of :math:`\log(0)` when

            :attr:`log_input = False`. Default: 1e-8

        reduce (bool, optional): Deprecated (see :attr:`reduction`). By default, the

            losses are averaged or summed over observations for each minibatch depending

            on :attr:`size_average`. When :attr:`reduce` is ``False``, returns a loss per

            batch element instead and ignores :attr:`size_average`. Default: ``True``

        reduction (str, 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. Note: :attr:`size_average`

            and :attr:`reduce` are in the process of being deprecated, and in the meantime,

            specifying either of those two args will override :attr:`reduction`. Default: ``'mean'``



    Examples::



        >>> loss = nn.PoissonNLLLoss()

        >>> log_input = torch.randn(5, 2, requires_grad=True)

        >>> target = torch.randn(5, 2)

        >>> output = loss(log_input, target)

        >>> output.backward()



    Shape:

        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.

        - Target: :math:`(*)`, same shape as the input.

        - Output: scalar by default. If :attr:`reduction` is ``'none'``, then :math:`(*)`,

          the same shape as the input.

    """
    __constants__ = ['log_input', 'full', 'eps', 'reduction']
    log_input: bool
    full: bool
    eps: float

    def __init__(self, log_input: bool = True, full: bool = False, size_average=None,

                 eps: float = 1e-8, reduce=None, reduction: str = 'mean') -> None:
        super().__init__(size_average, reduce, reduction)
        self.log_input = log_input
        self.full = full
        self.eps = eps

    def forward(self, log_input: Tensor, target: Tensor) -> Tensor:
        return F.poisson_nll_loss(log_input, target, log_input=self.log_input, full=self.full,
                                  eps=self.eps, reduction=self.reduction)


class GaussianNLLLoss(_Loss):
    r"""Gaussian negative log likelihood loss.



    The targets are treated as samples from Gaussian distributions with

    expectations and variances predicted by the neural network. For a

    ``target`` tensor modelled as having Gaussian distribution with a tensor

    of expectations ``input`` and a tensor of positive variances ``var`` the loss is:



    .. math::

        \text{loss} = \frac{1}{2}\left(\log\left(\text{max}\left(\text{var},

        \ \text{eps}\right)\right) + \frac{\left(\text{input} - \text{target}\right)^2}

        {\text{max}\left(\text{var}, \ \text{eps}\right)}\right) + \text{const.}



    where :attr:`eps` is used for stability. By default, the constant term of

    the loss function is omitted unless :attr:`full` is ``True``. If ``var`` is not the same

    size as ``input`` (due to a homoscedastic assumption), it must either have a final dimension

    of 1 or have one fewer dimension (with all other sizes being the same) for correct broadcasting.



    Args:

        full (bool, optional): include the constant term in the loss

            calculation. Default: ``False``.

        eps (float, optional): value used to clamp ``var`` (see note below), for

            stability. Default: 1e-6.

        reduction (str, optional): specifies the reduction to apply to the

            output:``'none'`` | ``'mean'`` | ``'sum'``. ``'none'``: no reduction

            will be applied, ``'mean'``: the output is the average of all batch

            member losses, ``'sum'``: the output is the sum of all batch member

            losses. Default: ``'mean'``.



    Shape:

        - Input: :math:`(N, *)` or :math:`(*)` where :math:`*` means any number of additional

          dimensions

        - Target: :math:`(N, *)` or :math:`(*)`, same shape as the input, or same shape as the input

          but with one dimension equal to 1 (to allow for broadcasting)

        - Var: :math:`(N, *)` or :math:`(*)`, same shape as the input, or same shape as the input but

          with one dimension equal to 1, or same shape as the input but with one fewer

          dimension (to allow for broadcasting)

        - Output: scalar if :attr:`reduction` is ``'mean'`` (default) or

          ``'sum'``. If :attr:`reduction` is ``'none'``, then :math:`(N, *)`, same

          shape as the input



    Examples::

        >>> loss = nn.GaussianNLLLoss()

        >>> input = torch.randn(5, 2, requires_grad=True)

        >>> target = torch.randn(5, 2)

        >>> var = torch.ones(5, 2, requires_grad=True)  # heteroscedastic

        >>> output = loss(input, target, var)

        >>> output.backward()



        >>> loss = nn.GaussianNLLLoss()

        >>> input = torch.randn(5, 2, requires_grad=True)

        >>> target = torch.randn(5, 2)

        >>> var = torch.ones(5, 1, requires_grad=True)  # homoscedastic

        >>> output = loss(input, target, var)

        >>> output.backward()



    Note:

        The clamping of ``var`` is ignored with respect to autograd, and so the

        gradients are unaffected by it.



    Reference:

        Nix, D. A. and Weigend, A. S., "Estimating the mean and variance of the

        target probability distribution", Proceedings of 1994 IEEE International

        Conference on Neural Networks (ICNN'94), Orlando, FL, USA, 1994, pp. 55-60

        vol.1, doi: 10.1109/ICNN.1994.374138.

    """
    __constants__ = ['full', 'eps', 'reduction']
    full: bool
    eps: float

    def __init__(self, *, full: bool = False, eps: float = 1e-6, reduction: str = 'mean') -> None:
        super().__init__(None, None, reduction)
        self.full = full
        self.eps = eps

    def forward(self, input: Tensor, target: Tensor, var: Tensor) -> Tensor:
        return F.gaussian_nll_loss(input, target, var, full=self.full, eps=self.eps, reduction=self.reduction)


class KLDivLoss(_Loss):
    r"""The Kullback-Leibler divergence loss.



    For tensors of the same shape :math:`y_{\text{pred}},\ y_{\text{true}}`,

    where :math:`y_{\text{pred}}` is the :attr:`input` and :math:`y_{\text{true}}` is the

    :attr:`target`, we define the **pointwise KL-divergence** as



    .. math::



        L(y_{\text{pred}},\ y_{\text{true}})

            = y_{\text{true}} \cdot \log \frac{y_{\text{true}}}{y_{\text{pred}}}

            = y_{\text{true}} \cdot (\log y_{\text{true}} - \log y_{\text{pred}})



    To avoid underflow issues when computing this quantity, this loss expects the argument

    :attr:`input` in the log-space. The argument :attr:`target` may also be provided in the

    log-space if :attr:`log_target`\ `= True`.



    To summarise, this function is roughly equivalent to computing



    .. code-block:: python



        if not log_target: # default

            loss_pointwise = target * (target.log() - input)

        else:

            loss_pointwise = target.exp() * (target - input)



    and then reducing this result depending on the argument :attr:`reduction` as



    .. code-block:: python



        if reduction == "mean":  # default

            loss = loss_pointwise.mean()

        elif reduction == "batchmean":  # mathematically correct

            loss = loss_pointwise.sum() / input.size(0)

        elif reduction == "sum":

            loss = loss_pointwise.sum()

        else:  # reduction == "none"

            loss = loss_pointwise



    .. note::

        As all the other losses in PyTorch, this function expects the first argument,

        :attr:`input`, to be the output of the model (e.g. the neural network)

        and the second, :attr:`target`, to be the observations in the dataset.

        This differs from the standard mathematical notation :math:`KL(P\ ||\ Q)` where

        :math:`P` denotes the distribution of the observations and :math:`Q` denotes the model.



    .. warning::

        :attr:`reduction`\ `= "mean"` doesn't return the true KL divergence value, please use

        :attr:`reduction`\ `= "batchmean"` which aligns with the mathematical definition.



    Args:

        size_average (bool, optional): Deprecated (see :attr:`reduction`). By default,

            the losses are averaged over each loss element in the batch. Note that for

            some losses, there are multiple elements per sample. If the field :attr:`size_average`

            is set to `False`, the losses are instead summed for each minibatch. Ignored

            when :attr:`reduce` is `False`. Default: `True`

        reduce (bool, optional): Deprecated (see :attr:`reduction`). By default, the

            losses are averaged or summed over observations for each minibatch depending

            on :attr:`size_average`. When :attr:`reduce` is `False`, returns a loss per

            batch element instead and ignores :attr:`size_average`. Default: `True`

        reduction (str, optional): Specifies the reduction to apply to the output. Default: `"mean"`

        log_target (bool, optional): Specifies whether `target` is the log space. Default: `False`



    Shape:

        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.

        - Target: :math:`(*)`, same shape as the input.

        - Output: scalar by default. If :attr:`reduction` is `'none'`, then :math:`(*)`,

          same shape as the input.



    Examples::



        >>> import torch.nn.functional as F

        >>> kl_loss = nn.KLDivLoss(reduction="batchmean")

        >>> # input should be a distribution in the log space

        >>> input = F.log_softmax(torch.randn(3, 5, requires_grad=True), dim=1)

        >>> # Sample a batch of distributions. Usually this would come from the dataset

        >>> target = F.softmax(torch.rand(3, 5), dim=1)

        >>> output = kl_loss(input, target)



        >>> kl_loss = nn.KLDivLoss(reduction="batchmean", log_target=True)

        >>> log_target = F.log_softmax(torch.rand(3, 5), dim=1)

        >>> output = kl_loss(input, log_target)

    """
    __constants__ = ['reduction']

    def __init__(self, size_average=None, reduce=None, reduction: str = 'mean', log_target: bool = False) -> None:
        super().__init__(size_average, reduce, reduction)
        self.log_target = log_target

    def forward(self, input: Tensor, target: Tensor) -> Tensor:
        return F.kl_div(input, target, reduction=self.reduction, log_target=self.log_target)


class MSELoss(_Loss):
    r"""Creates a criterion that measures the mean squared error (squared L2 norm) between

    each element in the input :math:`x` and target :math:`y`.



    The unreduced (i.e. with :attr:`reduction` set to ``'none'``) loss can be described as:



    .. math::

        \ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad

        l_n = \left( x_n - y_n \right)^2,



    where :math:`N` is the batch size. If :attr:`reduction` is not ``'none'``

    (default ``'mean'``), then:



    .. math::

        \ell(x, y) =

        \begin{cases}

            \operatorname{mean}(L), &  \text{if reduction} = \text{`mean';}\\

            \operatorname{sum}(L),  &  \text{if reduction} = \text{`sum'.}

        \end{cases}



    :math:`x` and :math:`y` are tensors of arbitrary shapes with a total

    of :math:`n` elements each.



    The mean operation still operates over all the elements, and divides by :math:`n`.



    The division by :math:`n` can be avoided if one sets ``reduction = 'sum'``.



    Args:

        size_average (bool, optional): Deprecated (see :attr:`reduction`). By default,

            the losses are averaged over each loss element in the batch. Note that for

            some losses, there are multiple elements per sample. If the field :attr:`size_average`

            is set to ``False``, the losses are instead summed for each minibatch. Ignored

            when :attr:`reduce` is ``False``. Default: ``True``

        reduce (bool, optional): Deprecated (see :attr:`reduction`). By default, the

            losses are averaged or summed over observations for each minibatch depending

            on :attr:`size_average`. When :attr:`reduce` is ``False``, returns a loss per

            batch element instead and ignores :attr:`size_average`. Default: ``True``

        reduction (str, 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. Note: :attr:`size_average`

            and :attr:`reduce` are in the process of being deprecated, and in the meantime,

            specifying either of those two args will override :attr:`reduction`. Default: ``'mean'``



    Shape:

        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.

        - Target: :math:`(*)`, same shape as the input.



    Examples::



        >>> loss = nn.MSELoss()

        >>> input = torch.randn(3, 5, requires_grad=True)

        >>> target = torch.randn(3, 5)

        >>> output = loss(input, target)

        >>> output.backward()

    """
    __constants__ = ['reduction']

    def __init__(self, size_average=None, reduce=None, reduction: str = 'mean') -> None:
        super().__init__(size_average, reduce, reduction)

    def forward(self, input: Tensor, target: Tensor) -> Tensor:
        return F.mse_loss(input, target, reduction=self.reduction)


class BCELoss(_WeightedLoss):
    r"""Creates a criterion that measures the Binary Cross Entropy between the target and

    the input probabilities:



    The unreduced (i.e. with :attr:`reduction` set to ``'none'``) loss can be described as:



    .. math::

        \ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad

        l_n = - w_n \left[ y_n \cdot \log x_n + (1 - y_n) \cdot \log (1 - x_n) \right],



    where :math:`N` is the batch size. If :attr:`reduction` is not ``'none'``

    (default ``'mean'``), then



    .. math::

        \ell(x, y) = \begin{cases}

            \operatorname{mean}(L), & \text{if reduction} = \text{`mean';}\\

            \operatorname{sum}(L),  & \text{if reduction} = \text{`sum'.}

        \end{cases}



    This is used for measuring the error of a reconstruction in for example

    an auto-encoder. Note that the targets :math:`y` should be numbers

    between 0 and 1.



    Notice that if :math:`x_n` is either 0 or 1, one of the log terms would be

    mathematically undefined in the above loss equation. PyTorch chooses to set

    :math:`\log (0) = -\infty`, since :math:`\lim_{x\to 0} \log (x) = -\infty`.

    However, an infinite term in the loss equation is not desirable for several reasons.



    For one, if either :math:`y_n = 0` or :math:`(1 - y_n) = 0`, then we would be

    multiplying 0 with infinity. Secondly, if we have an infinite loss value, then

    we would also have an infinite term in our gradient, since

    :math:`\lim_{x\to 0} \frac{d}{dx} \log (x) = \infty`.

    This would make BCELoss's backward method nonlinear with respect to :math:`x_n`,

    and using it for things like linear regression would not be straight-forward.



    Our solution is that BCELoss clamps its log function outputs to be greater than

    or equal to -100. This way, we can always have a finite loss value and a linear

    backward method.





    Args:

        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`.

        size_average (bool, optional): Deprecated (see :attr:`reduction`). By default,

            the losses are averaged over each loss element in the batch. Note that for

            some losses, there are multiple elements per sample. If the field :attr:`size_average`

            is set to ``False``, the losses are instead summed for each minibatch. Ignored

            when :attr:`reduce` is ``False``. Default: ``True``

        reduce (bool, optional): Deprecated (see :attr:`reduction`). By default, the

            losses are averaged or summed over observations for each minibatch depending

            on :attr:`size_average`. When :attr:`reduce` is ``False``, returns a loss per

            batch element instead and ignores :attr:`size_average`. Default: ``True``

        reduction (str, 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. Note: :attr:`size_average`

            and :attr:`reduce` are in the process of being deprecated, and in the meantime,

            specifying either of those two args will override :attr:`reduction`. Default: ``'mean'``



    Shape:

        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.

        - Target: :math:`(*)`, same shape as the input.

        - Output: scalar. If :attr:`reduction` is ``'none'``, then :math:`(*)`, same

          shape as input.



    Examples::



        >>> m = nn.Sigmoid()

        >>> loss = nn.BCELoss()

        >>> input = torch.randn(3, 2, requires_grad=True)

        >>> target = torch.rand(3, 2, requires_grad=False)

        >>> output = loss(m(input), target)

        >>> output.backward()

    """
    __constants__ = ['reduction']

    def __init__(self, weight: Optional[Tensor] = None, size_average=None, reduce=None, reduction: str = 'mean') -> None:
        super().__init__(weight, size_average, reduce, reduction)

    def forward(self, input: Tensor, target: Tensor) -> Tensor:
        return F.binary_cross_entropy(input, target, weight=self.weight, reduction=self.reduction)


class BCEWithLogitsLoss(_Loss):
    r"""This loss combines a `Sigmoid` layer and the `BCELoss` in one single

    class. This version is more numerically stable than using a plain `Sigmoid`

    followed by a `BCELoss` as, by combining the operations into one layer,

    we take advantage of the log-sum-exp trick for numerical stability.



    The unreduced (i.e. with :attr:`reduction` set to ``'none'``) loss can be described as:



    .. math::

        \ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad

        l_n = - w_n \left[ y_n \cdot \log \sigma(x_n)

        + (1 - y_n) \cdot \log (1 - \sigma(x_n)) \right],



    where :math:`N` is the batch size. If :attr:`reduction` is not ``'none'``

    (default ``'mean'``), then



    .. math::

        \ell(x, y) = \begin{cases}

            \operatorname{mean}(L), & \text{if reduction} = \text{`mean';}\\

            \operatorname{sum}(L),  & \text{if reduction} = \text{`sum'.}

        \end{cases}



    This is used for measuring the error of a reconstruction in for example

    an auto-encoder. Note that the targets `t[i]` should be numbers

    between 0 and 1.



    It's possible to trade off recall and precision by adding weights to positive examples.

    In the case of multi-label classification the loss can be described as:



    .. math::

        \ell_c(x, y) = L_c = \{l_{1,c},\dots,l_{N,c}\}^\top, \quad

        l_{n,c} = - w_{n,c} \left[ p_c y_{n,c} \cdot \log \sigma(x_{n,c})

        + (1 - y_{n,c}) \cdot \log (1 - \sigma(x_{n,c})) \right],



    where :math:`c` is the class number (:math:`c > 1` for multi-label binary classification,

    :math:`c = 1` for single-label binary classification),

    :math:`n` is the number of the sample in the batch and

    :math:`p_c` is the weight of the positive answer for the class :math:`c`.



    :math:`p_c > 1` increases the recall, :math:`p_c < 1` increases the precision.



    For example, if a dataset contains 100 positive and 300 negative examples of a single class,

    then ``pos_weight`` for the class should be equal to :math:`\frac{300}{100}=3`.

    The loss would act as if the dataset contains :math:`3\times 100=300` positive examples.



    Examples::



        >>> target = torch.ones([10, 64], dtype=torch.float32)  # 64 classes, batch size = 10

        >>> output = torch.full([10, 64], 1.5)  # A prediction (logit)

        >>> pos_weight = torch.ones([64])  # All weights are equal to 1

        >>> criterion = torch.nn.BCEWithLogitsLoss(pos_weight=pos_weight)

        >>> criterion(output, target)  # -log(sigmoid(1.5))

        tensor(0.20...)



    In the above example, the ``pos_weight`` tensor's elements correspond to the 64 distinct classes

    in a multi-label binary classification scenario. Each element in ``pos_weight`` is designed to adjust the

    loss function based on the imbalance between negative and positive samples for the respective class.

    This approach is useful in datasets with varying levels of class imbalance, ensuring that the loss

    calculation accurately accounts for the distribution in each class.



    Args:

        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`.

        size_average (bool, optional): Deprecated (see :attr:`reduction`). By default,

            the losses are averaged over each loss element in the batch. Note that for

            some losses, there are multiple elements per sample. If the field :attr:`size_average`

            is set to ``False``, the losses are instead summed for each minibatch. Ignored

            when :attr:`reduce` is ``False``. Default: ``True``

        reduce (bool, optional): Deprecated (see :attr:`reduction`). By default, the

            losses are averaged or summed over observations for each minibatch depending

            on :attr:`size_average`. When :attr:`reduce` is ``False``, returns a loss per

            batch element instead and ignores :attr:`size_average`. Default: ``True``

        reduction (str, 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. Note: :attr:`size_average`

            and :attr:`reduce` are in the process of being deprecated, and in the meantime,

            specifying either of those two args will override :attr:`reduction`. Default: ``'mean'``

        pos_weight (Tensor, optional): a weight of positive examples to be broadcasted with target.

            Must be a tensor with equal size along the class dimension to the number of classes.

            Pay close attention to PyTorch's broadcasting semantics in order to achieve the desired

            operations. For a target of size [B, C, H, W] (where B is batch size) pos_weight of

            size [B, C, H, W] will apply different pos_weights to each element of the batch or

            [C, H, W] the same pos_weights across the batch. To apply the same positive weight

            along all spacial dimensions for a 2D multi-class target [C, H, W] use: [C, 1, 1].

            Default: ``None``



    Shape:

        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.

        - Target: :math:`(*)`, same shape as the input.

        - Output: scalar. If :attr:`reduction` is ``'none'``, then :math:`(*)`, same

          shape as input.



     Examples::



        >>> loss = nn.BCEWithLogitsLoss()

        >>> input = torch.randn(3, requires_grad=True)

        >>> target = torch.empty(3).random_(2)

        >>> output = loss(input, target)

        >>> output.backward()

    """
    def __init__(self, weight: Optional[Tensor] = None, size_average=None, reduce=None, reduction: str = 'mean',

                 pos_weight: Optional[Tensor] = None) -> None:
        super().__init__(size_average, reduce, reduction)
        self.register_buffer('weight', weight)
        self.register_buffer('pos_weight', pos_weight)
        self.weight: Optional[Tensor]
        self.pos_weight: Optional[Tensor]

    def forward(self, input: Tensor, target: Tensor) -> Tensor:
        return F.binary_cross_entropy_with_logits(input, target,
                                                  self.weight,
                                                  pos_weight=self.pos_weight,
                                                  reduction=self.reduction)


class HingeEmbeddingLoss(_Loss):
    r"""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, margin - 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`.



    Args:

        margin (float, optional): Has a default value of `1`.

        size_average (bool, optional): Deprecated (see :attr:`reduction`). By default,

            the losses are averaged over each loss element in the batch. Note that for

            some losses, there are multiple elements per sample. If the field :attr:`size_average`

            is set to ``False``, the losses are instead summed for each minibatch. Ignored

            when :attr:`reduce` is ``False``. Default: ``True``

        reduce (bool, optional): Deprecated (see :attr:`reduction`). By default, the

            losses are averaged or summed over observations for each minibatch depending

            on :attr:`size_average`. When :attr:`reduce` is ``False``, returns a loss per

            batch element instead and ignores :attr:`size_average`. Default: ``True``

        reduction (str, 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. Note: :attr:`size_average`

            and :attr:`reduce` are in the process of being deprecated, and in the meantime,

            specifying either of those two args will override :attr:`reduction`. Default: ``'mean'``



    Shape:

        - Input: :math:`(*)` where :math:`*` means, any number of dimensions. The sum operation

          operates over all the elements.

        - Target: :math:`(*)`, same shape as the input

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

    """
    __constants__ = ['margin', 'reduction']
    margin: float

    def __init__(self, margin: float = 1.0, size_average=None, reduce=None, reduction: str = 'mean') -> None:
        super().__init__(size_average, reduce, reduction)
        self.margin = margin

    def forward(self, input: Tensor, target: Tensor) -> Tensor:
        return F.hinge_embedding_loss(input, target, margin=self.margin, reduction=self.reduction)


class MultiLabelMarginLoss(_Loss):
    r"""Creates a criterion that optimizes a multi-class multi-classification

    hinge loss (margin-based loss) between input :math:`x` (a 2D mini-batch `Tensor`)

    and output :math:`y` (which is a 2D `Tensor` of target class indices).

    For each sample in the mini-batch:



    .. math::

        \text{loss}(x, y) = \sum_{ij}\frac{\max(0, 1 - (x[y[j]] - x[i]))}{\text{x.size}(0)}



    where :math:`x \in \left\{0, \; \cdots , \; \text{x.size}(0) - 1\right\}`, \

    :math:`y \in \left\{0, \; \cdots , \; \text{y.size}(0) - 1\right\}`, \

    :math:`0 \leq y[j] \leq \text{x.size}(0)-1`, \

    and :math:`i \neq y[j]` for all :math:`i` and :math:`j`.



    :math:`y` and :math:`x` must have the same size.



    The criterion only considers a contiguous block of non-negative targets that

    starts at the front.



    This allows for different samples to have variable amounts of target classes.



    Args:

        size_average (bool, optional): Deprecated (see :attr:`reduction`). By default,

            the losses are averaged over each loss element in the batch. Note that for

            some losses, there are multiple elements per sample. If the field :attr:`size_average`

            is set to ``False``, the losses are instead summed for each minibatch. Ignored

            when :attr:`reduce` is ``False``. Default: ``True``

        reduce (bool, optional): Deprecated (see :attr:`reduction`). By default, the

            losses are averaged or summed over observations for each minibatch depending

            on :attr:`size_average`. When :attr:`reduce` is ``False``, returns a loss per

            batch element instead and ignores :attr:`size_average`. Default: ``True``

        reduction (str, 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. Note: :attr:`size_average`

            and :attr:`reduce` are in the process of being deprecated, and in the meantime,

            specifying either of those two args will override :attr:`reduction`. Default: ``'mean'``



    Shape:

        - Input: :math:`(C)` or :math:`(N, C)` where `N` is the batch size and `C`

          is the number of classes.

        - Target: :math:`(C)` or :math:`(N, C)`, label targets padded by -1 ensuring same shape as the input.

        - Output: scalar. If :attr:`reduction` is ``'none'``, then :math:`(N)`.



    Examples::



        >>> loss = nn.MultiLabelMarginLoss()

        >>> x = torch.FloatTensor([[0.1, 0.2, 0.4, 0.8]])

        >>> # for target y, only consider labels 3 and 0, not after label -1

        >>> y = torch.LongTensor([[3, 0, -1, 1]])

        >>> # 0.25 * ((1-(0.1-0.2)) + (1-(0.1-0.4)) + (1-(0.8-0.2)) + (1-(0.8-0.4)))

        >>> loss(x, y)

        tensor(0.85...)



    """
    __constants__ = ['reduction']

    def __init__(self, size_average=None, reduce=None, reduction: str = 'mean') -> None:
        super().__init__(size_average, reduce, reduction)

    def forward(self, input: Tensor, target: Tensor) -> Tensor:
        return F.multilabel_margin_loss(input, target, reduction=self.reduction)


class SmoothL1Loss(_Loss):
    r"""Creates a criterion that uses a squared term if the absolute

    element-wise error falls below beta and an L1 term otherwise.

    It is less sensitive to outliers than :class:`torch.nn.MSELoss` and in some cases

    prevents exploding gradients (e.g. see the paper `Fast R-CNN`_ by Ross Girshick).



    For a batch of size :math:`N`, the unreduced loss can be described as:



    .. math::

        \ell(x, y) = L = \{l_1, ..., l_N\}^T



    with



    .. math::

        l_n = \begin{cases}

        0.5 (x_n - y_n)^2 / beta, & \text{if } |x_n - y_n| < beta \\

        |x_n - y_n| - 0.5 * beta, & \text{otherwise }

        \end{cases}



    If `reduction` is not `none`, then:



    .. math::

        \ell(x, y) =

        \begin{cases}

            \operatorname{mean}(L), &  \text{if reduction} = \text{`mean';}\\

            \operatorname{sum}(L),  &  \text{if reduction} = \text{`sum'.}

        \end{cases}



    .. note::

        Smooth L1 loss can be seen as exactly :class:`L1Loss`, but with the :math:`|x - y| < beta`

        portion replaced with a quadratic function such that its slope is 1 at :math:`|x - y| = beta`.

        The quadratic segment smooths the L1 loss near :math:`|x - y| = 0`.



    .. note::

        Smooth L1 loss is closely related to :class:`HuberLoss`, being

        equivalent to :math:`huber(x, y) / beta` (note that Smooth L1's beta hyper-parameter is

        also known as delta for Huber). This leads to the following differences:



        * As beta -> 0, Smooth L1 loss converges to :class:`L1Loss`, while :class:`HuberLoss`

          converges to a constant 0 loss. When beta is 0, Smooth L1 loss is equivalent to L1 loss.

        * As beta -> :math:`+\infty`, Smooth L1 loss converges to a constant 0 loss, while

          :class:`HuberLoss` converges to :class:`MSELoss`.

        * For Smooth L1 loss, as beta varies, the L1 segment of the loss has a constant slope of 1.

          For :class:`HuberLoss`, the slope of the L1 segment is beta.



    .. _`Fast R-CNN`: https://arxiv.org/abs/1504.08083



    Args:

        size_average (bool, optional): Deprecated (see :attr:`reduction`). By default,

            the losses are averaged over each loss element in the batch. Note that for

            some losses, there are multiple elements per sample. If the field :attr:`size_average`

            is set to ``False``, the losses are instead summed for each minibatch. Ignored

            when :attr:`reduce` is ``False``. Default: ``True``

        reduce (bool, optional): Deprecated (see :attr:`reduction`). By default, the

            losses are averaged or summed over observations for each minibatch depending

            on :attr:`size_average`. When :attr:`reduce` is ``False``, returns a loss per

            batch element instead and ignores :attr:`size_average`. Default: ``True``

        reduction (str, 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. Note: :attr:`size_average`

            and :attr:`reduce` are in the process of being deprecated, and in the meantime,

            specifying either of those two args will override :attr:`reduction`. Default: ``'mean'``

        beta (float, optional): Specifies the threshold at which to change between L1 and L2 loss.

            The value must be non-negative. Default: 1.0



    Shape:

        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.

        - Target: :math:`(*)`, same shape as the input.

        - Output: scalar. If :attr:`reduction` is ``'none'``, then :math:`(*)`, same shape as the input.

    """
    __constants__ = ['reduction']

    def __init__(self, size_average=None, reduce=None, reduction: str = 'mean', beta: float = 1.0) -> None:
        super().__init__(size_average, reduce, reduction)
        self.beta = beta

    def forward(self, input: Tensor, target: Tensor) -> Tensor:
        return F.smooth_l1_loss(input, target, reduction=self.reduction, beta=self.beta)


class HuberLoss(_Loss):
    r"""Creates a criterion that uses a squared term if the absolute

    element-wise error falls below delta and a delta-scaled L1 term otherwise.

    This loss combines advantages of both :class:`L1Loss` and :class:`MSELoss`; the

    delta-scaled L1 region makes the loss less sensitive to outliers than :class:`MSELoss`,

    while the L2 region provides smoothness over :class:`L1Loss` near 0. See

    `Huber loss <https://en.wikipedia.org/wiki/Huber_loss>`_ for more information.



    For a batch of size :math:`N`, the unreduced loss can be described as:



    .. math::

        \ell(x, y) = L = \{l_1, ..., l_N\}^T



    with



    .. math::

        l_n = \begin{cases}

        0.5 (x_n - y_n)^2, & \text{if } |x_n - y_n| < delta \\

        delta * (|x_n - y_n| - 0.5 * delta), & \text{otherwise }

        \end{cases}



    If `reduction` is not `none`, then:



    .. math::

        \ell(x, y) =

        \begin{cases}

            \operatorname{mean}(L), &  \text{if reduction} = \text{`mean';}\\

            \operatorname{sum}(L),  &  \text{if reduction} = \text{`sum'.}

        \end{cases}



    .. note::

        When delta is set to 1, this loss is equivalent to :class:`SmoothL1Loss`.

        In general, this loss differs from :class:`SmoothL1Loss` by a factor of delta (AKA beta

        in Smooth L1).

        See :class:`SmoothL1Loss` for additional discussion on the differences in behavior

        between the two losses.



    Args:

        reduction (str, 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. Default: ``'mean'``

        delta (float, optional): Specifies the threshold at which to change between delta-scaled L1 and L2 loss.

            The value must be positive.  Default: 1.0



    Shape:

        - Input: :math:`(*)` where :math:`*` means any number of dimensions.

        - Target: :math:`(*)`, same shape as the input.

        - Output: scalar. If :attr:`reduction` is ``'none'``, then :math:`(*)`, same shape as the input.

    """
    __constants__ = ['reduction', 'delta']

    def __init__(self, reduction: str = 'mean', delta: float = 1.0) -> None:
        super().__init__(reduction=reduction)
        self.delta = delta

    def forward(self, input: Tensor, target: Tensor) -> Tensor:
        return F.huber_loss(input, target, reduction=self.reduction, delta=self.delta)


class SoftMarginLoss(_Loss):
    r"""Creates a criterion that optimizes a two-class classification

    logistic loss between input tensor :math:`x` and target tensor :math:`y`

    (containing 1 or -1).



    .. math::

        \text{loss}(x, y) = \sum_i \frac{\log(1 + \exp(-y[i]*x[i]))}{\text{x.nelement}()}



    Args:

        size_average (bool, optional): Deprecated (see :attr:`reduction`). By default,

            the losses are averaged over each loss element in the batch. Note that for

            some losses, there are multiple elements per sample. If the field :attr:`size_average`

            is set to ``False``, the losses are instead summed for each minibatch. Ignored

            when :attr:`reduce` is ``False``. Default: ``True``

        reduce (bool, optional): Deprecated (see :attr:`reduction`). By default, the

            losses are averaged or summed over observations for each minibatch depending

            on :attr:`size_average`. When :attr:`reduce` is ``False``, returns a loss per

            batch element instead and ignores :attr:`size_average`. Default: ``True``

        reduction (str, 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. Note: :attr:`size_average`

            and :attr:`reduce` are in the process of being deprecated, and in the meantime,

            specifying either of those two args will override :attr:`reduction`. Default: ``'mean'``



    Shape:

        - Input: :math:`(*)`, where :math:`*` means any number of dimensions.

        - Target: :math:`(*)`, same shape as the input.

        - Output: scalar. If :attr:`reduction` is ``'none'``, then :math:`(*)`, same

          shape as input.



    """
    __constants__ = ['reduction']

    def __init__(self, size_average=None, reduce=None, reduction: str = 'mean') -> None:
        super().__init__(size_average, reduce, reduction)

    def forward(self, input: Tensor, target: Tensor) -> Tensor:
        return F.soft_margin_loss(input, target, reduction=self.reduction)


class CrossEntropyLoss(_WeightedLoss):
    r"""This criterion computes the cross entropy loss between input logits

    and target.



    It is useful when training a classification problem with `C` classes.

    If provided, the optional argument :attr:`weight` should be a 1D `Tensor`

    assigning weight to each of the classes.

    This is particularly useful when you have an unbalanced training set.



    The `input` is expected to contain the unnormalized logits for each class (which do `not` need

    to be positive or sum to 1, in general).

    `input` has to be a Tensor of size :math:`(C)` for unbatched input,

    :math:`(minibatch, C)` or :math:`(minibatch, C, d_1, d_2, ..., d_K)` with :math:`K \geq 1` for the

    `K`-dimensional case. The last being useful for higher dimension inputs, such

    as computing cross entropy loss per-pixel for 2D images.



    The `target` that this criterion expects should contain either:



    - Class indices in the range :math:`[0, C)` where :math:`C` is the number of classes; if

      `ignore_index` is specified, this loss also accepts this class index (this index

      may not necessarily be in the class range). The unreduced (i.e. with :attr:`reduction`

      set to ``'none'``) loss for this case can be described as:



      .. math::

          \ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad

          l_n = - w_{y_n} \log \frac{\exp(x_{n,y_n})}{\sum_{c=1}^C \exp(x_{n,c})}

          \cdot \mathbb{1}\{y_n \not= \text{ignore\_index}\}



      where :math:`x` is the input, :math:`y` is the target, :math:`w` is the weight,

      :math:`C` is the number of classes, and :math:`N` spans the minibatch dimension as well as

      :math:`d_1, ..., d_k` for the `K`-dimensional case. If

      :attr:`reduction` is not ``'none'`` (default ``'mean'``), then



      .. math::

          \ell(x, y) = \begin{cases}

              \sum_{n=1}^N \frac{1}{\sum_{n=1}^N w_{y_n} \cdot \mathbb{1}\{y_n \not= \text{ignore\_index}\}} l_n, &

               \text{if reduction} = \text{`mean';}\\

                \sum_{n=1}^N l_n,  &

                \text{if reduction} = \text{`sum'.}

            \end{cases}



      Note that this case is equivalent to applying :class:`~torch.nn.LogSoftmax`

      on an input, followed by :class:`~torch.nn.NLLLoss`.



    - Probabilities for each class; useful when labels beyond a single class per minibatch item

      are required, such as for blended labels, label smoothing, etc. The unreduced (i.e. with

      :attr:`reduction` set to ``'none'``) loss for this case can be described as:



      .. math::

          \ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad

          l_n = - \sum_{c=1}^C w_c \log \frac{\exp(x_{n,c})}{\sum_{i=1}^C \exp(x_{n,i})} y_{n,c}



      where :math:`x` is the input, :math:`y` is the target, :math:`w` is the weight,

      :math:`C` is the number of classes, and :math:`N` spans the minibatch dimension as well as

      :math:`d_1, ..., d_k` for the `K`-dimensional case. If

      :attr:`reduction` is not ``'none'`` (default ``'mean'``), then



      .. math::

          \ell(x, y) = \begin{cases}

              \frac{\sum_{n=1}^N l_n}{N}, &

               \text{if reduction} = \text{`mean';}\\

                \sum_{n=1}^N l_n,  &

                \text{if reduction} = \text{`sum'.}

            \end{cases}



    .. note::

        The performance of this criterion is generally better when `target` contains class

        indices, as this allows for optimized computation. Consider providing `target` as

        class probabilities only when a single class label per minibatch item is too restrictive.



    Args:

        weight (Tensor, optional): a manual rescaling weight given to each class.

            If given, has to be a Tensor of size `C` and floating point dtype

        size_average (bool, optional): Deprecated (see :attr:`reduction`). By default,

            the losses are averaged over each loss element in the batch. Note that for

            some losses, there are multiple elements per sample. If the field :attr:`size_average`

            is set to ``False``, the losses are instead summed for each minibatch. Ignored

            when :attr:`reduce` is ``False``. Default: ``True``

        ignore_index (int, optional): Specifies a target value that is ignored

            and does not contribute to the input gradient. When :attr:`size_average` is

            ``True``, the loss is averaged over non-ignored targets. Note that

            :attr:`ignore_index` is only applicable when the target contains class indices.

        reduce (bool, optional): Deprecated (see :attr:`reduction`). By default, the

            losses are averaged or summed over observations for each minibatch depending

            on :attr:`size_average`. When :attr:`reduce` is ``False``, returns a loss per

            batch element instead and ignores :attr:`size_average`. Default: ``True``

        reduction (str, optional): Specifies the reduction to apply to the output:

            ``'none'`` | ``'mean'`` | ``'sum'``. ``'none'``: no reduction will

            be applied, ``'mean'``: the weighted mean of the output is taken,

            ``'sum'``: the output will be summed. Note: :attr:`size_average`

            and :attr:`reduce` are in the process of being deprecated, and in

            the meantime, specifying either of those two args will override

            :attr:`reduction`. Default: ``'mean'``

        label_smoothing (float, optional): A float in [0.0, 1.0]. Specifies the amount

            of smoothing when computing the loss, where 0.0 means no smoothing. The targets

            become a mixture of the original ground truth and a uniform distribution as described in

            `Rethinking the Inception Architecture for Computer Vision <https://arxiv.org/abs/1512.00567>`__. Default: :math:`0.0`.



    Shape:

        - Input: Shape :math:`(C)`, :math:`(N, C)` or :math:`(N, C, d_1, d_2, ..., d_K)` with :math:`K \geq 1`

          in the case of `K`-dimensional loss.

        - Target: If containing class indices, shape :math:`()`, :math:`(N)` or :math:`(N, d_1, d_2, ..., d_K)` with

          :math:`K \geq 1` in the case of K-dimensional loss where each value should be between :math:`[0, C)`.

          If containing class probabilities, same shape as the input and each value should be between :math:`[0, 1]`.

        - Output: If reduction is 'none', shape :math:`()`, :math:`(N)` or :math:`(N, d_1, d_2, ..., d_K)` with :math:`K \geq 1`

          in the case of K-dimensional loss, depending on the shape of the input. Otherwise, scalar.





        where:



        .. math::

            \begin{aligned}

                C ={} & \text{number of classes} \\

                N ={} & \text{batch size} \\

            \end{aligned}



    Examples::



        >>> # Example of target with class indices

        >>> loss = nn.CrossEntropyLoss()

        >>> input = torch.randn(3, 5, requires_grad=True)

        >>> target = torch.empty(3, dtype=torch.long).random_(5)

        >>> output = loss(input, target)

        >>> output.backward()

        >>>

        >>> # Example of target with class probabilities

        >>> input = torch.randn(3, 5, requires_grad=True)

        >>> target = torch.randn(3, 5).softmax(dim=1)

        >>> output = loss(input, target)

        >>> output.backward()

    """
    __constants__ = ['ignore_index', 'reduction', 'label_smoothing']
    ignore_index: int
    label_smoothing: float

    def __init__(self, weight: Optional[Tensor] = None, size_average=None, ignore_index: int = -100,

                 reduce=None, reduction: str = 'mean', label_smoothing: float = 0.0) -> None:
        super().__init__(weight, size_average, reduce, reduction)
        self.ignore_index = ignore_index
        self.label_smoothing = label_smoothing

    def forward(self, input: Tensor, target: Tensor) -> Tensor:
        return F.cross_entropy(input, target, weight=self.weight,
                               ignore_index=self.ignore_index, reduction=self.reduction,
                               label_smoothing=self.label_smoothing)


class MultiLabelSoftMarginLoss(_WeightedLoss):
    r"""Creates a criterion that optimizes a multi-label one-versus-all

    loss based on max-entropy, between input :math:`x` and target :math:`y` of size

    :math:`(N, C)`.

    For each sample in the minibatch:



    .. math::

        loss(x, y) = - \frac{1}{C} * \sum_i y[i] * \log((1 + \exp(-x[i]))^{-1})

                         + (1-y[i]) * \log\left(\frac{\exp(-x[i])}{(1 + \exp(-x[i]))}\right)



    where :math:`i \in \left\{0, \; \cdots , \; \text{x.nElement}() - 1\right\}`,

    :math:`y[i] \in \left\{0, \; 1\right\}`.



    Args:

        weight (Tensor, optional): a manual rescaling weight given to each

            class. If given, it has to be a Tensor of size `C`. Otherwise, it is

            treated as if having all ones.

        size_average (bool, optional): Deprecated (see :attr:`reduction`). By default,

            the losses are averaged over each loss element in the batch. Note that for

            some losses, there are multiple elements per sample. If the field :attr:`size_average`

            is set to ``False``, the losses are instead summed for each minibatch. Ignored

            when :attr:`reduce` is ``False``. Default: ``True``

        reduce (bool, optional): Deprecated (see :attr:`reduction`). By default, the

            losses are averaged or summed over observations for each minibatch depending

            on :attr:`size_average`. When :attr:`reduce` is ``False``, returns a loss per

            batch element instead and ignores :attr:`size_average`. Default: ``True``

        reduction (str, 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. Note: :attr:`size_average`

            and :attr:`reduce` are in the process of being deprecated, and in the meantime,

            specifying either of those two args will override :attr:`reduction`. Default: ``'mean'``



    Shape:

        - Input: :math:`(N, C)` where `N` is the batch size and `C` is the number of classes.

        - Target: :math:`(N, C)`, label targets must have the same shape as the input.

        - Output: scalar. If :attr:`reduction` is ``'none'``, then :math:`(N)`.

    """
    __constants__ = ['reduction']

    def __init__(self, weight: Optional[Tensor] = None, size_average=None, reduce=None, reduction: str = 'mean') -> None:
        super().__init__(weight, size_average, reduce, reduction)

    def forward(self, input: Tensor, target: Tensor) -> Tensor:
        return F.multilabel_soft_margin_loss(input, target, weight=self.weight, reduction=self.reduction)


class CosineEmbeddingLoss(_Loss):
    r"""Creates a criterion that measures the loss given input tensors

    :math:`x_1`, :math:`x_2` and a `Tensor` label :math:`y` with values 1 or -1.

    Use (:math:`y=1`) to maximize the cosine similarity of two inputs, and (:math:`y=-1`) otherwise.

    This is typically used for learning nonlinear

    embeddings or semi-supervised learning.



    The loss function for each sample is:



    .. math::

        \text{loss}(x, y) =

        \begin{cases}

        1 - \cos(x_1, x_2), & \text{if } y = 1 \\

        \max(0, \cos(x_1, x_2) - \text{margin}), & \text{if } y = -1

        \end{cases}



    Args:

        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`.

        size_average (bool, optional): Deprecated (see :attr:`reduction`). By default,

            the losses are averaged over each loss element in the batch. Note that for

            some losses, there are multiple elements per sample. If the field :attr:`size_average`

            is set to ``False``, the losses are instead summed for each minibatch. Ignored

            when :attr:`reduce` is ``False``. Default: ``True``

        reduce (bool, optional): Deprecated (see :attr:`reduction`). By default, the

            losses are averaged or summed over observations for each minibatch depending

            on :attr:`size_average`. When :attr:`reduce` is ``False``, returns a loss per

            batch element instead and ignores :attr:`size_average`. Default: ``True``

        reduction (str, 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. Note: :attr:`size_average`

            and :attr:`reduce` are in the process of being deprecated, and in the meantime,

            specifying either of those two args will override :attr:`reduction`. Default: ``'mean'``



    Shape:

        - Input1: :math:`(N, D)` or :math:`(D)`, where `N` is the batch size and `D` is the embedding dimension.

        - Input2: :math:`(N, D)` or :math:`(D)`, same shape as Input1.

        - Target: :math:`(N)` or :math:`()`.

        - Output: If :attr:`reduction` is ``'none'``, then :math:`(N)`, otherwise scalar.



    Examples::



        >>> loss = nn.CosineEmbeddingLoss()

        >>> input1 = torch.randn(3, 5, requires_grad=True)

        >>> input2 = torch.randn(3, 5, requires_grad=True)

        >>> target = torch.ones(3)

        >>> output = loss(input1, input2, target)

        >>> output.backward()

    """
    __constants__ = ['margin', 'reduction']
    margin: float

    def __init__(self, margin: float = 0., size_average=None, reduce=None, reduction: str = 'mean') -> None:
        super().__init__(size_average, reduce, reduction)
        self.margin = margin

    def forward(self, input1: Tensor, input2: Tensor, target: Tensor) -> Tensor:
        return F.cosine_embedding_loss(input1, input2, target, margin=self.margin, reduction=self.reduction)


class MarginRankingLoss(_Loss):
    r"""Creates a criterion that measures the loss given

    inputs :math:`x1`, :math:`x2`, two 1D mini-batch or 0D `Tensors`,

    and a label 1D mini-batch or 0D `Tensor` :math:`y` (containing 1 or -1).



    If :math:`y = 1` then it assumed the first input should be ranked higher

    (have a larger value) than the second input, and vice-versa for :math:`y = -1`.



    The loss function for each pair of samples in the mini-batch is:



    .. math::

        \text{loss}(x1, x2, y) = \max(0, -y * (x1 - x2) + \text{margin})



    Args:

        margin (float, optional): Has a default value of :math:`0`.

        size_average (bool, optional): Deprecated (see :attr:`reduction`). By default,

            the losses are averaged over each loss element in the batch. Note that for

            some losses, there are multiple elements per sample. If the field :attr:`size_average`

            is set to ``False``, the losses are instead summed for each minibatch. Ignored

            when :attr:`reduce` is ``False``. Default: ``True``

        reduce (bool, optional): Deprecated (see :attr:`reduction`). By default, the

            losses are averaged or summed over observations for each minibatch depending

            on :attr:`size_average`. When :attr:`reduce` is ``False``, returns a loss per

            batch element instead and ignores :attr:`size_average`. Default: ``True``

        reduction (str, 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. Note: :attr:`size_average`

            and :attr:`reduce` are in the process of being deprecated, and in the meantime,

            specifying either of those two args will override :attr:`reduction`. Default: ``'mean'``



    Shape:

        - Input1: :math:`(N)` or :math:`()` where `N` is the batch size.

        - Input2: :math:`(N)` or :math:`()`, same shape as the Input1.

        - Target: :math:`(N)` or :math:`()`, same shape as the inputs.

        - Output: scalar. If :attr:`reduction` is ``'none'`` and Input size is not :math:`()`, then :math:`(N)`.



    Examples::



        >>> loss = nn.MarginRankingLoss()

        >>> input1 = torch.randn(3, requires_grad=True)

        >>> input2 = torch.randn(3, requires_grad=True)

        >>> target = torch.randn(3).sign()

        >>> output = loss(input1, input2, target)

        >>> output.backward()

    """
    __constants__ = ['margin', 'reduction']
    margin: float

    def __init__(self, margin: float = 0., size_average=None, reduce=None, reduction: str = 'mean') -> None:
        super().__init__(size_average, reduce, reduction)
        self.margin = margin

    def forward(self, input1: Tensor, input2: Tensor, target: Tensor) -> Tensor:
        return F.margin_ranking_loss(input1, input2, target, margin=self.margin, reduction=self.reduction)


class MultiMarginLoss(_WeightedLoss):
    r"""Creates a criterion that optimizes a multi-class classification hinge

    loss (margin-based loss) between input :math:`x` (a 2D mini-batch `Tensor`) and

    output :math:`y` (which is a 1D tensor of target class indices,

    :math:`0 \leq y \leq \text{x.size}(1)-1`):



    For each mini-batch sample, the loss in terms of the 1D input :math:`x` and scalar

    output :math:`y` is:



    .. math::

        \text{loss}(x, y) = \frac{\sum_i \max(0, \text{margin} - x[y] + x[i])^p}{\text{x.size}(0)}



    where :math:`i \in \left\{0, \; \cdots , \; \text{x.size}(0) - 1\right\}`

    and :math:`i \neq y`.



    Optionally, you can give non-equal weighting on the classes by passing

    a 1D :attr:`weight` tensor into the constructor.



    The loss function then becomes:



    .. math::

        \text{loss}(x, y) = \frac{\sum_i w[y] * \max(0, \text{margin} - x[y] + x[i])^p}{\text{x.size}(0)}



    Args:

        p (int, optional): Has a default value of :math:`1`. :math:`1` and :math:`2`

            are the only supported values.

        margin (float, optional): Has a default value of :math:`1`.

        weight (Tensor, optional): a manual rescaling weight given to each

            class. If given, it has to be a Tensor of size `C`. Otherwise, it is

            treated as if having all ones.

        size_average (bool, optional): Deprecated (see :attr:`reduction`). By default,

            the losses are averaged over each loss element in the batch. Note that for

            some losses, there are multiple elements per sample. If the field :attr:`size_average`

            is set to ``False``, the losses are instead summed for each minibatch. Ignored

            when :attr:`reduce` is ``False``. Default: ``True``

        reduce (bool, optional): Deprecated (see :attr:`reduction`). By default, the

            losses are averaged or summed over observations for each minibatch depending

            on :attr:`size_average`. When :attr:`reduce` is ``False``, returns a loss per

            batch element instead and ignores :attr:`size_average`. Default: ``True``

        reduction (str, 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. Note: :attr:`size_average`

            and :attr:`reduce` are in the process of being deprecated, and in the meantime,

            specifying either of those two args will override :attr:`reduction`. Default: ``'mean'``



    Shape:

        - Input: :math:`(N, C)` or :math:`(C)`, where :math:`N` is the batch size and :math:`C` is the number of classes.

        - Target: :math:`(N)` or :math:`()`, where each value is :math:`0 \leq \text{targets}[i] \leq C-1`.

        - Output: scalar. If :attr:`reduction` is ``'none'``, then same shape as the target.



    Examples::



        >>> loss = nn.MultiMarginLoss()

        >>> x = torch.tensor([[0.1, 0.2, 0.4, 0.8]])

        >>> y = torch.tensor([3])

        >>> # 0.25 * ((1-(0.8-0.1)) + (1-(0.8-0.2)) + (1-(0.8-0.4)))

        >>> loss(x, y)

        tensor(0.32...)

    """
    __constants__ = ['p', 'margin', 'reduction']
    margin: float
    p: int

    def __init__(self, p: int = 1, margin: float = 1., weight: Optional[Tensor] = None, size_average=None,

                 reduce=None, reduction: str = 'mean') -> None:
        super().__init__(weight, size_average, reduce, reduction)
        if p != 1 and p != 2:
            raise ValueError("only p == 1 and p == 2 supported")
        if weight is not None and weight.dim() != 1 :
            raise ValueError(
                f"MultiMarginLoss: expected weight to be None or 1D tensor, got {weight.dim()}D instead"
            )
        self.p = p
        self.margin = margin

    def forward(self, input: Tensor, target: Tensor) -> Tensor:
        return F.multi_margin_loss(input, target, p=self.p, margin=self.margin,
                                   weight=self.weight, reduction=self.reduction)


class TripletMarginLoss(_Loss):
    r"""Creates a criterion that 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 `a`, `p` and `n` (i.e., `anchor`, `positive examples` and `negative

    examples` respectively). The shapes of all input tensors should be

    :math:`(N, D)`.



    The distance swap is described in detail in the paper `Learning shallow

    convolutional feature descriptors with triplet losses`_ by

    V. Balntas, E. Riba et al.



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



    .. math::

        L(a, p, n) = \max \{d(a_i, p_i) - d(a_i, n_i) + {\rm margin}, 0\}





    where



    .. math::

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



    The norm is calculated using the specified p value and a small constant :math:`\varepsilon` is

    added for numerical stability.



    See also :class:`~torch.nn.TripletMarginWithDistanceLoss`, which computes the

    triplet margin loss for input tensors using a custom distance function.



    Args:

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

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

        eps (float, optional): Small constant for numerical stability. Default: :math:`1e-6`.

        swap (bool, optional): The distance swap is described in detail in the paper

            `Learning shallow convolutional feature descriptors with triplet losses` by

            V. Balntas, E. Riba et al. Default: ``False``.

        size_average (bool, optional): Deprecated (see :attr:`reduction`). By default,

            the losses are averaged over each loss element in the batch. Note that for

            some losses, there are multiple elements per sample. If the field :attr:`size_average`

            is set to ``False``, the losses are instead summed for each minibatch. Ignored

            when :attr:`reduce` is ``False``. Default: ``True``

        reduce (bool, optional): Deprecated (see :attr:`reduction`). By default, the

            losses are averaged or summed over observations for each minibatch depending

            on :attr:`size_average`. When :attr:`reduce` is ``False``, returns a loss per

            batch element instead and ignores :attr:`size_average`. Default: ``True``

        reduction (str, 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. Note: :attr:`size_average`

            and :attr:`reduce` are in the process of being deprecated, and in the meantime,

            specifying either of those two args will override :attr:`reduction`. Default: ``'mean'``



    Shape:

        - Input: :math:`(N, D)` or :math:`(D)` where :math:`D` is the vector dimension.

        - Output: A Tensor of shape :math:`(N)` if :attr:`reduction` is ``'none'`` and

          input shape is :math:`(N, D)`; a scalar otherwise.



    Examples::



    >>> triplet_loss = nn.TripletMarginLoss(margin=1.0, p=2, eps=1e-7)

    >>> anchor = torch.randn(100, 128, requires_grad=True)

    >>> positive = torch.randn(100, 128, requires_grad=True)

    >>> negative = torch.randn(100, 128, requires_grad=True)

    >>> output = triplet_loss(anchor, positive, negative)

    >>> output.backward()



    .. _Learning shallow convolutional feature descriptors with triplet losses:

        http://www.bmva.org/bmvc/2016/papers/paper119/index.html

    """
    __constants__ = ['margin', 'p', 'eps', 'swap', 'reduction']
    margin: float
    p: float
    eps: float
    swap: bool

    def __init__(self, margin: float = 1.0, p: float = 2., eps: float = 1e-6, swap: bool = False, size_average=None,

                 reduce=None, reduction: str = 'mean'):
        super().__init__(size_average, reduce, reduction)
        self.margin = margin
        self.p = p
        self.eps = eps
        self.swap = swap

    def forward(self, anchor: Tensor, positive: Tensor, negative: Tensor) -> Tensor:
        return F.triplet_margin_loss(anchor, positive, negative, margin=self.margin, p=self.p,
                                     eps=self.eps, swap=self.swap, reduction=self.reduction)


class TripletMarginWithDistanceLoss(_Loss):
    r"""Creates a criterion that measures the triplet loss given input

    tensors :math:`a`, :math:`p`, and :math:`n` (representing anchor,

    positive, and negative examples, respectively), and a nonnegative,

    real-valued function ("distance function") used to compute the relationship

    between the anchor and positive example ("positive distance") and the

    anchor and negative example ("negative distance").



    The unreduced loss (i.e., with :attr:`reduction` set to ``'none'``)

    can be described as:



    .. math::

        \ell(a, p, n) = L = \{l_1,\dots,l_N\}^\top, \quad

        l_i = \max \{d(a_i, p_i) - d(a_i, n_i) + {\rm margin}, 0\}



    where :math:`N` is the batch size; :math:`d` is a nonnegative, real-valued function

    quantifying the closeness of two tensors, referred to as the :attr:`distance_function`;

    and :math:`margin` is a nonnegative margin representing the minimum difference

    between the positive and negative distances that is required for the loss to

    be 0.  The input tensors have :math:`N` elements each and can be of any shape

    that the distance function can handle.



    If :attr:`reduction` is not ``'none'``

    (default ``'mean'``), then:



    .. math::

        \ell(x, y) =

        \begin{cases}

            \operatorname{mean}(L), &  \text{if reduction} = \text{`mean';}\\

            \operatorname{sum}(L),  &  \text{if reduction} = \text{`sum'.}

        \end{cases}



    See also :class:`~torch.nn.TripletMarginLoss`, which computes the triplet

    loss for input tensors using the :math:`l_p` distance as the distance function.



    Args:

        distance_function (Callable, optional): A nonnegative, real-valued function that

            quantifies the closeness of two tensors. If not specified,

            `nn.PairwiseDistance` will be used.  Default: ``None``

        margin (float, optional): A nonnegative margin representing the minimum difference

            between the positive and negative distances required for the loss to be 0. Larger

            margins penalize cases where the negative examples are not distant enough from the

            anchors, relative to the positives. Default: :math:`1`.

        swap (bool, optional): Whether to use the distance swap described in the paper

            `Learning shallow convolutional feature descriptors with triplet losses` by

            V. Balntas, E. Riba et al. If True, and if the positive example is closer to the

            negative example than the anchor is, swaps the positive example and the anchor in

            the loss computation. Default: ``False``.

        reduction (str, optional): Specifies the (optional) 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. Default: ``'mean'``





    Shape:

        - Input: :math:`(N, *)` where :math:`*` represents any number of additional dimensions

          as supported by the distance function.

        - Output: A Tensor of shape :math:`(N)` if :attr:`reduction` is ``'none'``, or a scalar

          otherwise.



    Examples::



    >>> # Initialize embeddings

    >>> embedding = nn.Embedding(1000, 128)

    >>> anchor_ids = torch.randint(0, 1000, (1,))

    >>> positive_ids = torch.randint(0, 1000, (1,))

    >>> negative_ids = torch.randint(0, 1000, (1,))

    >>> anchor = embedding(anchor_ids)

    >>> positive = embedding(positive_ids)

    >>> negative = embedding(negative_ids)

    >>>

    >>> # Built-in Distance Function

    >>> triplet_loss = \

    >>>     nn.TripletMarginWithDistanceLoss(distance_function=nn.PairwiseDistance())

    >>> output = triplet_loss(anchor, positive, negative)

    >>> output.backward()

    >>>

    >>> # Custom Distance Function

    >>> def l_infinity(x1, x2):

    >>>     return torch.max(torch.abs(x1 - x2), dim=1).values

    >>>

    >>> # xdoctest: +SKIP("FIXME: Would call backwards a second time")

    >>> triplet_loss = (

    >>>     nn.TripletMarginWithDistanceLoss(distance_function=l_infinity, margin=1.5))

    >>> output = triplet_loss(anchor, positive, negative)

    >>> output.backward()

    >>>

    >>> # Custom Distance Function (Lambda)

    >>> triplet_loss = (

    >>>     nn.TripletMarginWithDistanceLoss(

    >>>         distance_function=lambda x, y: 1.0 - F.cosine_similarity(x, y)))

    >>> output = triplet_loss(anchor, positive, negative)

    >>> output.backward()



    Reference:

        V. Balntas, et al.: Learning shallow convolutional feature descriptors with triplet losses:

        http://www.bmva.org/bmvc/2016/papers/paper119/index.html

    """
    __constants__ = ['margin', 'swap', 'reduction']
    margin: float
    swap: bool

    def __init__(self, *, distance_function: Optional[Callable[[Tensor, Tensor], Tensor]] = None,

                 margin: float = 1.0, swap: bool = False, reduction: str = 'mean'):
        super().__init__(size_average=None, reduce=None, reduction=reduction)
        self.distance_function: Optional[Callable[[Tensor, Tensor], Tensor]] = \
            distance_function if distance_function is not None else PairwiseDistance()
        self.margin = margin
        self.swap = swap

    def forward(self, anchor: Tensor, positive: Tensor, negative: Tensor) -> Tensor:
        return F.triplet_margin_with_distance_loss(anchor, positive, negative,
                                                   distance_function=self.distance_function,
                                                   margin=self.margin, swap=self.swap, reduction=self.reduction)


class CTCLoss(_Loss):
    r"""The Connectionist Temporal Classification loss.



    Calculates loss between a continuous (unsegmented) time series and a target sequence. CTCLoss sums over the

    probability of possible alignments of input to target, producing a loss value which is differentiable

    with respect to each input node. The alignment of input to target is assumed to be "many-to-one", which

    limits the length of the target sequence such that it must be :math:`\leq` the input length.



    Args:

        blank (int, optional): blank label. Default :math:`0`.

        reduction (str, optional): Specifies the reduction to apply to the output:

            ``'none'`` | ``'mean'`` | ``'sum'``. ``'none'``: no reduction will be applied,

            ``'mean'``: the output losses will be divided by the target lengths and

            then the mean over the batch is taken, ``'sum'``: the output losses will be summed.

            Default: ``'mean'``

        zero_infinity (bool, optional):

            Whether to zero infinite losses and the associated gradients.

            Default: ``False``

            Infinite losses mainly occur when the inputs are too short

            to be aligned to the targets.



    Shape:

        - Log_probs: Tensor of size :math:`(T, N, C)` or :math:`(T, C)`,

          where :math:`T = \text{input length}`,

          :math:`N = \text{batch size}`, and

          :math:`C = \text{number of classes (including blank)}`.

          The logarithmized probabilities of the outputs (e.g. obtained with

          :func:`torch.nn.functional.log_softmax`).

        - Targets: Tensor of size :math:`(N, S)` or

          :math:`(\operatorname{sum}(\text{target\_lengths}))`,

          where :math:`N = \text{batch size}` and

          :math:`S = \text{max target length, if shape is } (N, S)`.

          It represent the target sequences. Each element in the target

          sequence is a class index. And the target index cannot be blank (default=0).

          In the :math:`(N, S)` form, targets are padded to the

          length of the longest sequence, and stacked.

          In the :math:`(\operatorname{sum}(\text{target\_lengths}))` form,

          the targets are assumed to be un-padded and

          concatenated within 1 dimension.

        - Input_lengths: Tuple or tensor of size :math:`(N)` or :math:`()`,

          where :math:`N = \text{batch size}`. It represent the lengths of the

          inputs (must each be :math:`\leq T`). And the lengths are specified

          for each sequence to achieve masking under the assumption that sequences

          are padded to equal lengths.

        - Target_lengths: Tuple or tensor of size :math:`(N)` or :math:`()`,

          where :math:`N = \text{batch size}`. It represent lengths of the targets.

          Lengths are specified for each sequence to achieve masking under the

          assumption that sequences are padded to equal lengths. If target shape is

          :math:`(N,S)`, target_lengths are effectively the stop index

          :math:`s_n` for each target sequence, such that ``target_n = targets[n,0:s_n]`` for

          each target in a batch. Lengths must each be :math:`\leq S`

          If the targets are given as a 1d tensor that is the concatenation of individual

          targets, the target_lengths must add up to the total length of the tensor.

        - Output: scalar if :attr:`reduction` is ``'mean'`` (default) or

          ``'sum'``. If :attr:`reduction` is ``'none'``, then :math:`(N)` if input is batched or

          :math:`()` if input is unbatched, where :math:`N = \text{batch size}`.



    Examples::



        >>> # Target are to be padded

        >>> T = 50      # Input sequence length

        >>> C = 20      # Number of classes (including blank)

        >>> N = 16      # Batch size

        >>> S = 30      # Target sequence length of longest target in batch (padding length)

        >>> S_min = 10  # Minimum target length, for demonstration purposes

        >>>

        >>> # Initialize random batch of input vectors, for *size = (T,N,C)

        >>> input = torch.randn(T, N, C).log_softmax(2).detach().requires_grad_()

        >>>

        >>> # Initialize random batch of targets (0 = blank, 1:C = classes)

        >>> target = torch.randint(low=1, high=C, size=(N, S), dtype=torch.long)

        >>>

        >>> input_lengths = torch.full(size=(N,), fill_value=T, dtype=torch.long)

        >>> target_lengths = torch.randint(low=S_min, high=S, size=(N,), dtype=torch.long)

        >>> ctc_loss = nn.CTCLoss()

        >>> loss = ctc_loss(input, target, input_lengths, target_lengths)

        >>> loss.backward()

        >>>

        >>>

        >>> # Target are to be un-padded

        >>> T = 50      # Input sequence length

        >>> C = 20      # Number of classes (including blank)

        >>> N = 16      # Batch size

        >>>

        >>> # Initialize random batch of input vectors, for *size = (T,N,C)

        >>> input = torch.randn(T, N, C).log_softmax(2).detach().requires_grad_()

        >>> input_lengths = torch.full(size=(N,), fill_value=T, dtype=torch.long)

        >>>

        >>> # Initialize random batch of targets (0 = blank, 1:C = classes)

        >>> target_lengths = torch.randint(low=1, high=T, size=(N,), dtype=torch.long)

        >>> target = torch.randint(low=1, high=C, size=(sum(target_lengths),), dtype=torch.long)

        >>> ctc_loss = nn.CTCLoss()

        >>> loss = ctc_loss(input, target, input_lengths, target_lengths)

        >>> loss.backward()

        >>>

        >>>

        >>> # Target are to be un-padded and unbatched (effectively N=1)

        >>> T = 50      # Input sequence length

        >>> C = 20      # Number of classes (including blank)

        >>>

        >>> # Initialize random batch of input vectors, for *size = (T,C)

        >>> # xdoctest: +SKIP("FIXME: error in doctest")

        >>> input = torch.randn(T, C).log_softmax(1).detach().requires_grad_()

        >>> input_lengths = torch.tensor(T, dtype=torch.long)

        >>>

        >>> # Initialize random batch of targets (0 = blank, 1:C = classes)

        >>> target_lengths = torch.randint(low=1, high=T, size=(), dtype=torch.long)

        >>> target = torch.randint(low=1, high=C, size=(target_lengths,), dtype=torch.long)

        >>> ctc_loss = nn.CTCLoss()

        >>> loss = ctc_loss(input, target, input_lengths, target_lengths)

        >>> loss.backward()



    Reference:

        A. Graves et al.: Connectionist Temporal Classification:

        Labelling Unsegmented Sequence Data with Recurrent Neural Networks:

        https://www.cs.toronto.edu/~graves/icml_2006.pdf



    Note:

        In order to use CuDNN, the following must be satisfied: :attr:`targets` must be

        in concatenated format, all :attr:`input_lengths` must be `T`.  :math:`blank=0`,

        :attr:`target_lengths` :math:`\leq 256`, the integer arguments must be of

        dtype :attr:`torch.int32`.



        The regular implementation uses the (more common in PyTorch) `torch.long` dtype.





    Note:

        In some circumstances when using the CUDA backend with CuDNN, this operator

        may select a nondeterministic algorithm to increase performance. If this is

        undesirable, you can try to make the operation deterministic (potentially at

        a performance cost) by setting ``torch.backends.cudnn.deterministic =

        True``.

        Please see the notes on :doc:`/notes/randomness` for background.

    """
    __constants__ = ['blank', 'reduction']
    blank: int
    zero_infinity: bool

    def __init__(self, blank: int = 0, reduction: str = 'mean', zero_infinity: bool = False):
        super().__init__(reduction=reduction)
        self.blank = blank
        self.zero_infinity = zero_infinity

    def forward(self, log_probs: Tensor, targets: Tensor, input_lengths: Tensor, target_lengths: Tensor) -> Tensor:
        return F.ctc_loss(log_probs, targets, input_lengths, target_lengths, self.blank, self.reduction,
                          self.zero_infinity)

# TODO: L1HingeEmbeddingCriterion
# TODO: MSECriterion weight
# TODO: ClassSimplexCriterion