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# Source code for torch.nn.modules.loss

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

class _Loss(Module):
reduction: str

def __init__(self, size_average=None, reduce=None, reduction: str = 'mean') -> None:
super(_Loss, self).__init__()
if size_average is not None or reduce is not None:
self.reduction = _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(_WeightedLoss, self).__init__(size_average, reduce, reduction)
self.register_buffer('weight', weight)

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'.

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 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 (string, optional): Specifies the reduction to apply to the output:
'none' | 'mean' | 'sum'. 'none': no reduction will be applied,
'mean': the sum of the output will be divided by the number of
elements in the output, 'sum': the output will be summed. 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, *) where :math:* means, any number of additional
dimensions
- Target: :math:(N, *), same shape as the input
- Output: scalar. If :attr:reduction is 'none', then
:math:(N, *), 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(L1Loss, self).__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 (described later).

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}

Can also be used for higher dimension inputs, such as 2D images, by providing
an input of size :math:(minibatch, C, d_1, d_2, ..., d_K) with :math:K \geq 1,
where :math:K is the number of dimensions, and a target of appropriate shape
(see below). In the case of images, it computes NLL loss per-pixel.

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 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.
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 (string, 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) 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) 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: scalar.
If :attr:reduction is 'none', then the same size as the target: :math:(N), or
:math:(N, d_1, d_2, ..., d_K) with :math:K \geq 1 in the case
of K-dimensional loss.

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(NLLLoss, self).__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. "
"https://pytorch.org/docs/master/nn.html#torch.nn.NLLLoss for more details.")
super(NLLLoss2d, self).__init__(weight, size_average, ignore_index, reduce, reduction)

[docs]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 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 (string, optional): Specifies the reduction to apply to the output:
'none' | 'mean' | 'sum'. 'none': no reduction will be applied,
'mean': the sum of the output will be divided by the number of
elements in the output, 'sum': the output will be summed. 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:(N, *) where :math:* means, any number of additional
dimensions
- Target: :math:(N, *), same shape as the input
- Output: scalar by default. If :attr:reduction is 'none', then :math:(N, *),
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(PoissonNLLLoss, self).__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 KLDivLoss(_Loss):
r"""The Kullback-Leibler divergence loss measure

Kullback-Leibler divergence_ is a useful distance measure for continuous
distributions and is often useful when performing direct regression over
the space of (discretely sampled) continuous output distributions.

As with :class:~torch.nn.NLLLoss, the input given is expected to contain
*log-probabilities* and is not restricted to a 2D Tensor.
The targets are interpreted as *probabilities* by default, but could be considered
as *log-probabilities* with :attr:log_target set to True.

This criterion expects a target Tensor of the same size as the
input Tensor.

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

.. math::
l(x,y) = L = \{ l_1,\dots,l_N \}, \quad
l_n = y_n \cdot \left( \log y_n - x_n \right)

where the index :math:N spans all dimensions of input and :math:L has the same
shape as input. 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}

In default :attr:reduction mode 'mean', the losses are averaged for each minibatch over observations
**as well as** over dimensions. 'batchmean' mode gives the correct KL divergence where losses
are averaged over batch dimension only. 'mean' mode's behavior will be changed to the same as
'batchmean' in the next major release.

.. _kullback-leibler divergence: https://en.wikipedia.org/wiki/Kullback-Leibler_divergence

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 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 (string, optional): Specifies the reduction to apply to the output:
'none' | 'batchmean' | 'sum' | 'mean'.
'none': no reduction will be applied.
'batchmean': the sum of the output will be divided by batchsize.
'sum': the output will be summed.
'mean': the output will be divided by the number of elements in the output.
Default: 'mean'
log_target (bool, optional): Specifies whether target is passed in the log space.
Default: False

.. 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.

.. note::
:attr:reduction = 'mean' doesn't return the true kl divergence value, please use
:attr:reduction = 'batchmean' which aligns with KL math definition.
In the next major release, 'mean' will be changed to be the same as 'batchmean'.

Shape:
- Input: :math:(N, *) where :math:* means, any number of additional
dimensions
- Target: :math:(N, *), same shape as the input
- Output: scalar by default. If :attr:reduction is 'none', then :math:(N, *),
the same shape as the input

"""
__constants__ = ['reduction']

def __init__(self, size_average=None, reduce=None, reduction: str = 'mean', log_target: bool = False) -> None:
super(KLDivLoss, self).__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 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 (string, optional): Specifies the reduction to apply to the output:
'none' | 'mean' | 'sum'. 'none': no reduction will be applied,
'mean': the sum of the output will be divided by the number of
elements in the output, 'sum': the output will be summed. 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, *) where :math:* means, any number of additional
dimensions
- Target: :math:(N, *), 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(MSELoss, self).__init__(size_average, reduce, reduction)

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

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

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 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 (string, optional): Specifies the reduction to apply to the output:
'none' | 'mean' | 'sum'. 'none': no reduction will be applied,
'mean': the sum of the output will be divided by the number of
elements in the output, 'sum': the output will be summed. 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, *) where :math:* means, any number of additional
dimensions
- Target: :math:(N, *), same shape as the input
- Output: scalar. If :attr:reduction is 'none', then :math:(N, *), same
shape as input.

Examples::

>>> m = nn.Sigmoid()
>>> loss = nn.BCELoss()
>>> target = torch.empty(3).random_(2)
>>> 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(BCELoss, self).__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)

[docs]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(0.2014)

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 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 (string, optional): Specifies the reduction to apply to the output:
'none' | 'mean' | 'sum'. 'none': no reduction will be applied,
'mean': the sum of the output will be divided by the number of
elements in the output, 'sum': the output will be summed. 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.
Must be a vector with length equal to the number of classes.

Shape:
- Input: :math:(N, *) where :math:* means, any number of additional dimensions
- Target: :math:(N, *), same shape as the input
- Output: scalar. If :attr:reduction is 'none', then :math:(N, *), same
shape as input.

Examples::

>>> loss = nn.BCEWithLogitsLoss()
>>> 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(BCEWithLogitsLoss, self).__init__(size_average, reduce, reduction)
self.register_buffer('weight', weight)
self.register_buffer('pos_weight', pos_weight)

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, \Delta - x_n\}, & \text{if}\; y_n = -1,
\end{cases}

and the total loss functions is

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

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

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 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 (string, optional): Specifies the reduction to apply to the output:
'none' | 'mean' | 'sum'. 'none': no reduction will be applied,
'mean': the sum of the output will be divided by the number of
elements in the output, 'sum': the output will be summed. 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(HingeEmbeddingLoss, self).__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 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 (string, optional): Specifies the reduction to apply to the output:
'none' | 'mean' | 'sum'. 'none': no reduction will be applied,
'mean': the sum of the output will be divided by the number of
elements in the output, 'sum': the output will be summed. 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]])
>>> loss(x, y)
>>> # 0.25 * ((1-(0.1-0.2)) + (1-(0.1-0.4)) + (1-(0.8-0.2)) + (1-(0.8-0.4)))
tensor(0.8500)

"""
__constants__ = ['reduction']

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

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

[docs]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 the MSELoss and in some cases
prevents exploding gradients (e.g. see Fast R-CNN paper by Ross Girshick).
Also known as the Huber loss:

.. math::
\text{loss}(x, y) = \frac{1}{n} \sum_{i} z_{i}

where :math:z_{i} is given by:

.. math::
z_{i} =
\begin{cases}
0.5 (x_i - y_i)^2 / beta, & \text{if } |x_i - y_i| < beta \\
|x_i - y_i| - 0.5 * beta, & \text{otherwise }
\end{cases}

:math:x and :math:y arbitrary shapes with a total of :math:n elements each
the sum operation still operates over all the elements, and divides by :math:n.

beta is an optional parameter that defaults to 1.

Note: When beta is set to 0, this is equivalent to :class:L1Loss.
Passing a negative value in for beta will result in an exception.

The division by :math:n can be avoided if 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 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 (string, optional): Specifies the reduction to apply to the output:
'none' | 'mean' | 'sum'. 'none': no reduction will be applied,
'mean': the sum of the output will be divided by the number of
elements in the output, 'sum': the output will be summed. 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.
This value defaults to 1.0.

Shape:
- Input: :math:(N, *) where :math:* means, any number of additional
dimensions
- Target: :math:(N, *), same shape as the input
- Output: scalar. If :attr:reduction is 'none', then
:math:(N, *), same shape as the input

"""
__constants__ = ['reduction']

def __init__(self, size_average=None, reduce=None, reduction: str = 'mean', beta: float = 1.0) -> None:
super(SmoothL1Loss, self).__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)

[docs]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 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 (string, optional): Specifies the reduction to apply to the output:
'none' | 'mean' | 'sum'. 'none': no reduction will be applied,
'mean': the sum of the output will be divided by the number of
elements in the output, 'sum': the output will be summed. 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 additional
dimensions
- Target: :math:(*), same shape as the input
- Output: scalar. If :attr:reduction is 'none', then same shape as the input

"""
__constants__ = ['reduction']

def __init__(self, size_average=None, reduce=None, reduction: str = 'mean') -> None:
super(SoftMarginLoss, self).__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 combines :func:nn.LogSoftmax and :func:nn.NLLLoss in one single class.

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 raw, unnormalized scores for 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 (described later).

This criterion expects a class index in the range :math:[0, C-1] as the
target for each value of a 1D tensor of size minibatch; if ignore_index
is specified, this criterion also accepts this class index (this index may not
necessarily be in the class range).

The loss can be described as:

.. math::
\text{loss}(x, class) = -\log\left(\frac{\exp(x[class])}{\sum_j \exp(x[j])}\right)
= -x[class] + \log\left(\sum_j \exp(x[j])\right)

or in the case of the :attr:weight argument being specified:

.. math::
\text{loss}(x, class) = weight[class] \left(-x[class] + \log\left(\sum_j \exp(x[j])\right)\right)

The losses are averaged across observations for each minibatch. If the
:attr:weight argument is specified then this is a weighted average:

.. math::
\text{loss} = \frac{\sum^{N}_{i=1} loss(i, class[i])}{\sum^{N}_{i=1} weight[class[i]]}

Can also be used for higher dimension inputs, such as 2D images, by providing
an input of size :math:(minibatch, C, d_1, d_2, ..., d_K) with :math:K \geq 1,
where :math:K is the number of dimensions, and a target of appropriate shape
(see below).

Args:
weight (Tensor, optional): a manual rescaling weight given to each class.
If given, has to be a Tensor of size C
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 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.
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 (string, 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) 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) 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: scalar.
If :attr:reduction is 'none', then the same size as the target:
:math:(N), or
:math:(N, d_1, d_2, ..., d_K) with :math:K \geq 1 in the case
of K-dimensional loss.

Examples::

>>> 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()
"""
__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(CrossEntropyLoss, self).__init__(weight, size_average, reduce, reduction)
self.ignore_index = ignore_index

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)

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 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 (string, optional): Specifies the reduction to apply to the output:
'none' | 'mean' | 'sum'. 'none': no reduction will be applied,
'mean': the sum of the output will be divided by the number of
elements in the output, 'sum': the output will be summed. 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 padded by -1 ensuring 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(MultiLabelSoftMarginLoss, self).__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.
This is used for measuring whether two inputs are similar or dissimilar,
using the cosine distance, and 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 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 (string, optional): Specifies the reduction to apply to the output:
'none' | 'mean' | 'sum'. 'none': no reduction will be applied,
'mean': the sum of the output will be divided by the number of
elements in the output, 'sum': the output will be summed. 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'
"""
__constants__ = ['margin', 'reduction']
margin: float

def __init__(self, margin: float = 0., size_average=None, reduce=None, reduction: str = 'mean') -> None:
super(CosineEmbeddingLoss, self).__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 Tensors,
and a label 1D mini-batch 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 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 (string, optional): Specifies the reduction to apply to the output:
'none' | 'mean' | 'sum'. 'none': no reduction will be applied,
'mean': the sum of the output will be divided by the number of
elements in the output, 'sum': the output will be summed. 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) where N is the batch size.
- Input2: :math:(N), same shape as the Input1.
- Target: :math:(N), same shape as the inputs.
- Output: scalar. If :attr:reduction is 'none', then :math:(N).

Examples::

>>> loss = nn.MarginRankingLoss()
>>> 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(MarginRankingLoss, self).__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:x \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 \max(0, w[y] * (\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 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 (string, optional): Specifies the reduction to apply to the output:
'none' | 'mean' | 'sum'. 'none': no reduction will be applied,
'mean': the sum of the output will be divided by the number of
elements in the output, 'sum': the output will be summed. 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'
"""
__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(MultiMarginLoss, self).__init__(weight, size_average, reduce, reduction)
if p != 1 and p != 2:
raise ValueError("only p == 1 and p == 2 supported")
assert weight is None or weight.dim() == 1
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)

[docs]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

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.
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 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 (string, optional): Specifies the reduction to apply to the output:
'none' | 'mean' | 'sum'. 'none': no reduction will be applied,
'mean': the sum of the output will be divided by the number of
elements in the output, 'sum': the output will be summed. 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) where :math:D is the vector dimension.
- Output: A Tensor of shape :math:(N) if :attr:reduction is 'none', or a scalar
otherwise.

>>> triplet_loss = nn.TripletMarginLoss(margin=1.0, p=2)
>>> 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(TripletMarginLoss, self).__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)

[docs]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 non-negative 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 non-negative 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 (string, 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,), requires_grad=True)
>>> positive_ids = torch.randint(0, 1000, (1,), requires_grad=True)
>>> negative_ids = torch.randint(0, 1000, (1,), requires_grad=True)
>>> 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):
>>>
>>> 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(TripletMarginWithDistanceLoss, self).__init__(size_average=None, reduce=None, reduction=reduction)
self.distance_function = 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 (string, 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. 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),
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),
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
- Target_lengths: Tuple or tensor of size :math:(N),
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 'none', then
:math:(N), 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()

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(CTCLoss, self).__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


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