# Source code for torch.nn.modules.loss

```
# mypy: allow-untyped-defs
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
from typing_extensions import deprecated
__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]
[docs]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)
[docs]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`, `N = batch size`, 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::
>>> log_softmax = nn.LogSoftmax(dim=1)
>>> loss_fn = nn.NLLLoss()
>>> # input to NLLLoss is of size N x C = 3 x 5
>>> input = torch.randn(3, 5, requires_grad=True)
>>> # each element in target must have 0 <= value < C
>>> target = torch.tensor([1, 0, 4])
>>> loss = loss_fn(log_softmax(input), target)
>>> loss.backward()
>>>
>>>
>>> # 2D loss example (used, for example, with image inputs)
>>> N, C = 5, 4
>>> loss_fn = nn.NLLLoss()
>>> data = torch.randn(N, 16, 10, 10)
>>> conv = nn.Conv2d(16, C, (3, 3))
>>> log_softmax = nn.LogSoftmax(dim=1)
>>> # output of conv forward is of shape [N, C, 8, 8]
>>> output = log_softmax(conv(data))
>>> # each element in target must have 0 <= value < C
>>> target = torch.empty(N, 8, 8, dtype=torch.long).random_(0, C)
>>> # input to NLLLoss is of size N x C x height (8) x width (8)
>>> loss = loss_fn(output, target)
>>> loss.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)
@deprecated(
"`NLLLoss2d` has been deprecated. "
"Please use `NLLLoss` instead as a drop-in replacement and see "
"https://pytorch.org/docs/main/nn.html#torch.nn.NLLLoss for more details.",
category=FutureWarning,
)
class NLLLoss2d(NLLLoss):
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, 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 :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)
[docs]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)
[docs]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::
>>> 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)
[docs]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)
[docs]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)
[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(0.20...)
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)
[docs]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)
[docs]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)
[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 :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)
[docs]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)
[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 :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)
[docs]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)
[docs]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)
[docs]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)
[docs]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)
[docs]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)
[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
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)
if margin <= 0:
raise ValueError(
f"TripletMarginLoss: expected margin to be greater than 0, got {margin} instead"
)
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 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)
if margin <= 0:
raise ValueError(
f"TripletMarginWithDistanceLoss: expected margin to be greater than 0, got {margin} instead"
)
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)
[docs]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 represents 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 represents 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 represents 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
```