# Source code for torch.nn.modules.loss

```
from torch.autograd import Variable
import torch
from .module import Module
from .container import Sequential
from .activation import LogSoftmax
from .. import functional as F
def _assert_no_grad(variable):
assert not variable.requires_grad, \
"nn criterions don't compute the gradient w.r.t. targets - please " \
"mark these variables as volatile or not requiring gradients"
class _Loss(Module):
def __init__(self, size_average=True):
super(_Loss, self).__init__()
self.size_average = size_average
class _WeightedLoss(_Loss):
def __init__(self, weight=None, size_average=True):
super(_WeightedLoss, self).__init__(size_average)
self.register_buffer('weight', weight)
[docs]class L1Loss(_Loss):
r"""Creates a criterion that measures the mean absolute value of the
element-wise difference between input `x` and target `y`:
The 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 reduce is ``True``, then:
.. math::
\ell(x, y) = \begin{cases}
\operatorname{mean}(L), & \text{if}\; \text{size_average} = \text{True},\\
\operatorname{sum}(L), & \text{if}\; \text{size_average} = \text{False}.
\end{cases}
`x` and `y` arbitrary shapes with a total of `n` elements each.
The sum operation still operates over all the elements, and divides by `n`.
The division by `n` can be avoided if one sets the constructor argument
`size_average=False`.
Args:
size_average (bool, optional): By default, the losses are averaged
over observations for each minibatch. However, if the field
size_average is set to ``False``, the losses are instead summed for
each minibatch. Ignored when reduce is ``False``. Default: ``True``
reduce (bool, optional): By default, the losses are averaged or summed
for each minibatch. When reduce is ``False``, the loss function returns
a loss per batch element instead and ignores size_average.
Default: ``True``
Shape:
- Input: :math:`(N, *)` where `*` means, any number of additional
dimensions
- Target: :math:`(N, *)`, same shape as the input
- Output: scalar. If reduce is ``False``, then
:math:`(N, *)`, same shape as the input
Examples::
>>> loss = nn.L1Loss()
>>> input = autograd.Variable(torch.randn(3, 5), requires_grad=True)
>>> target = autograd.Variable(torch.randn(3, 5))
>>> output = loss(input, target)
>>> output.backward()
"""
def __init__(self, size_average=True, reduce=True):
super(L1Loss, self).__init__(size_average)
self.reduce = reduce
def forward(self, input, target):
_assert_no_grad(target)
return F.l1_loss(input, target, size_average=self.size_average,
reduce=self.reduce)
[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 `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 2D Tensor of size
`(minibatch, C)`
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 is a class index
`(0 to C-1, where C = number of classes)`
The loss can be described as:
.. math::
\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad
l_n = - x_{n,y_n} \cdot \mathbb{1}\{y_n \not= \text{ignore_index}\},
where :math:`N` is the batch size. If reduce is ``True``, then
.. math::
\ell(x, y) = \begin{cases}
\sum_{n=1}^N w_{y_n} l_n \Big/ \sum_{n=1}^N w_{y_n} \cdot
\mathbb{1}\{y_n \not= \text{ignore_index}\}, & \text{if}\;
\text{size_average} = \text{True},\\
\sum_{n=1}^N w_{y_n} l_n, & \text{if}\;
\text{size_average} = \text{False}.
\end{cases}
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): By default, the losses are averaged
over observations for each minibatch. However, if the field
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 size_average
is ``True``, the loss is averaged over non-ignored targets.
reduce (bool, optional): By default, the losses are averaged or summed
for each minibatch. When reduce is ``False``, the loss function returns
a loss per batch element instead and ignores size_average.
Default: ``True``
Shape:
- Input: :math:`(N, C)` where `C = number of classes`.
In the case of K-dimensional loss where :math:`K >= 2`, then
:math:`(N, C, *)` where `*` is `K` extra dimensions.
- Target: :math:`(N)` where each value is `0 <= targets[i] <= C-1`.
In the case of K-dimensional loss, where :math:`K >= 2`, then
:math:`(N, C, *)` where `*` is `K` extra dimensions.
- Output: scalar. If reduce is ``False``, then :math:`(N)` instead.
In the case of K-dimensional loss and reduce is ``False``, then
:math:`(N, C, *)`, the same size as the target.
Examples::
>>> m = nn.LogSoftmax()
>>> loss = nn.NLLLoss()
>>> # input is of size N x C = 3 x 5
>>> input = autograd.Variable(torch.randn(3, 5), requires_grad=True)
>>> # each element in target has to have 0 <= value < C
>>> target = autograd.Variable(torch.LongTensor([1, 0, 4]))
>>> output = loss(m(input), target)
>>> output.backward()
"""
def __init__(self, weight=None, size_average=True, ignore_index=-100, reduce=True):
super(NLLLoss, self).__init__(weight, size_average)
self.ignore_index = ignore_index
self.reduce = reduce
def forward(self, input, target):
_assert_no_grad(target)
return F.nll_loss(input, target, self.weight, self.size_average,
self.ignore_index, self.reduce)
[docs]class NLLLoss2d(NLLLoss):
r"""This is negative log likehood loss, but for image inputs. It computes
NLL loss per-pixel.
Args:
weight (Tensor, optional): a manual rescaling weight given to each
class. If given, has to be a 1D Tensor having as many elements,
as there are classes.
size_average: By default, the losses are averaged over observations
for each minibatch. However, if the field size_average is set to
``False``, the losses are instead summed for each minibatch.
Ignored when reduce is ``False``. Default: ``True``
reduce (bool, optional): By default, the losses are averaged or summed
for each minibatch depending on size_average. When reduce is ``False``,
the loss function returns a loss per batch element instead and
ignores size_average. Default: ``True``
Shape:
- Input: :math:`(N, C, H, W)` where `C = number of classes`
- Target: :math:`(N, H, W)` where each value is `0 <= targets[i] <= C-1`
- Output: scalar. If reduce is ``False``, then :math:`(N, H, W)` instead.
Examples::
>>> m = nn.Conv2d(16, 32, (3, 3)).float()
>>> loss = nn.NLLLoss2d()
>>> # input is of size N x C x height x width
>>> input = autograd.Variable(torch.randn(3, 16, 10, 10))
>>> # each element in target has to have 0 <= value < C
>>> target = autograd.Variable(torch.LongTensor(3, 8, 8).random_(0, 4))
>>> output = loss(m(input), target)
>>> output.backward()
"""
pass
[docs]class PoissonNLLLoss(_Loss):
r"""Negative log likelihood loss with Poisson distribution of target.
The loss can be described as::
target ~ Pois(input)
loss(input, target) = input - target * log(input) + log(target!)
The last term can be omitted or approximised 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
`exp(input) - target * input`, if ``False`` the loss is
`input - target * log(input+eps)`.
full (bool, optional): whether to compute full loss, i. e. to add the
Stirling approximation term
`target * log(target) - target + 0.5 * log(2 * pi * target)`.
size_average (bool, optional): By default, the losses are averaged over
observations for each minibatch. However, if the field size_average
is set to ``False``, the losses are instead summed for each minibatch.
eps (float, optional): Small value to avoid evaluation of log(0) when
log_input==``False``. Default: 1e-8
reduce (bool, optional): By default, the losses are averaged
over observations for each minibatch, or summed, depending on
size_average. When reduce is ``False``, returns a loss per batch
element instead and ignores size_average. Default: ``True``
Examples::
>>> loss = nn.PoissonNLLLoss()
>>> log_input = autograd.Variable(torch.randn(5, 2), requires_grad=True)
>>> target = autograd.Variable(torch.randn(5, 2))
>>> output = loss(log_input, target)
>>> output.backward()
"""
def __init__(self, log_input=True, full=False, size_average=True, eps=1e-8, reduce=True):
super(PoissonNLLLoss, self).__init__(size_average)
self.log_input = log_input
self.full = full
self.eps = eps
self.reduce = reduce
def forward(self, log_input, target):
_assert_no_grad(target)
return F.poisson_nll_loss(log_input, target, self.log_input, self.full,
self.size_average, self.eps, self.reduce)
[docs]class KLDivLoss(_Loss):
r"""The `Kullback-Leibler divergence`_ Loss
KL 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 `NLLLoss`, the `input` given is expected to contain
*log-probabilities*, however unlike `ClassNLLLoss`, `input` is not
restricted to a 2D Tensor, because the criterion is applied element-wise.
This criterion expects a `target` `Tensor` of the same size as the
`input` `Tensor`.
The loss can be described as:
.. math::
\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad
l_n = y_n \odot \left( \log y_n - x_n \right),
where :math:`N` is the batch size. If reduce is ``True``, then:
.. math::
\ell(x, y) = \begin{cases}
\operatorname{mean}(L), & \text{if}\; \text{size_average} = \text{True},\\
\operatorname{sum}(L), & \text{if}\; \text{size_average} = \text{False}.
\end{cases}
By default, the losses are averaged for each minibatch over observations
**as well as** over dimensions. However, if the field
`size_average` is set to ``False``, the losses are instead summed.
.. _Kullback-Leibler divergence:
https://en.wikipedia.org/wiki/Kullback-Leibler_divergence
Args:
size_average (bool, optional: By default, the losses are averaged
for each minibatch over observations **as well as** over
dimensions. However, if ``False`` the losses are instead summed.
reduce (bool, optional): By default, the losses are averaged
over observations for each minibatch, or summed, depending on
size_average. When reduce is ``False``, returns a loss per batch
element instead and ignores size_average. Default: ``True``
Shape:
- input: :math:`(N, *)` where `*` means, any number of additional
dimensions
- target: :math:`(N, *)`, same shape as the input
- output: scalar. If `reduce` is ``True``, then :math:`(N, *)`,
same shape as the input
"""
def __init__(self, size_average=True, reduce=True):
super(KLDivLoss, self).__init__(size_average)
self.reduce = reduce
def forward(self, input, target):
_assert_no_grad(target)
return F.kl_div(input, target, size_average=self.size_average, reduce=self.reduce)
[docs]class MSELoss(_Loss):
r"""Creates a criterion that measures the mean squared error between
`n` elements in the input `x` and target `y`.
The 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 reduce is ``True``, then:
.. math::
\ell(x, y) = \begin{cases}
\operatorname{mean}(L), & \text{if}\; \text{size_average} = \text{True},\\
\operatorname{sum}(L), & \text{if}\; \text{size_average} = \text{False}.
\end{cases}
`x` and `y` arbitrary shapes with a total of `n` elements each.
The sum operation still operates over all the elements, and divides by `n`.
The division by `n` can be avoided if one sets the internal variable
`size_average` to ``False``.
To get a batch of losses, a loss per batch element, set `reduce` to
``False``. These losses are not averaged and are not affected by
`size_average`.
Args:
size_average (bool, optional): By default, the losses are averaged
over observations for each minibatch. However, if the field
size_average is set to ``False``, the losses are instead summed for
each minibatch. Only applies when reduce is ``True``. Default: ``True``
reduce (bool, optional): By default, the losses are averaged
over observations for each minibatch, or summed, depending on
size_average. When reduce is ``False``, returns a loss per batch
element instead and ignores size_average. Default: ``True``
Shape:
- Input: :math:`(N, *)` where `*` means, any number of additional
dimensions
- Target: :math:`(N, *)`, same shape as the input
Examples::
>>> loss = nn.MSELoss()
>>> input = autograd.Variable(torch.randn(3, 5), requires_grad=True)
>>> target = autograd.Variable(torch.randn(3, 5))
>>> output = loss(input, target)
>>> output.backward()
"""
def __init__(self, size_average=True, reduce=True):
super(MSELoss, self).__init__(size_average)
self.reduce = reduce
def forward(self, input, target):
_assert_no_grad(target)
return F.mse_loss(input, target, size_average=self.size_average, reduce=self.reduce)
[docs]class BCELoss(_WeightedLoss):
r"""Creates a criterion that measures the Binary Cross Entropy
between the target and the output:
The 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 reduce is ``True``, then
.. math::
\ell(x, y) = \begin{cases}
\operatorname{mean}(L), & \text{if}\; \text{size_average} = \text{True},\\
\operatorname{sum}(L), & \text{if}\; \text{size_average} = \text{False}.
\end{cases}
This is used for measuring the error of a reconstruction in for example
an auto-encoder. Note that the targets `y` should be numbers
between 0 and 1.
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): By default, the losses are averaged
over observations for each minibatch. However, if the field
size_average is set to ``False``, the losses are instead summed for
each minibatch. Default: ``True``
Shape:
- Input: :math:`(N, *)` where `*` means, any number of additional
dimensions
- Target: :math:`(N, *)`, same shape as the input
Examples::
>>> m = nn.Sigmoid()
>>> loss = nn.BCELoss()
>>> input = autograd.Variable(torch.randn(3), requires_grad=True)
>>> target = autograd.Variable(torch.FloatTensor(3).random_(2))
>>> output = loss(m(input), target)
>>> output.backward()
"""
def forward(self, input, target):
_assert_no_grad(target)
return F.binary_cross_entropy(input, target, weight=self.weight,
size_average=self.size_average)
[docs]class BCEWithLogitsLoss(Module):
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 loss can be described as:
.. math::
\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad
l_n = - w_n \left[ t_n \cdot \log \sigma(x_n)
+ (1 - t_n) \cdot \log (1 - \sigma(x_n)) \right],
where :math:`N` is the batch size. If reduce is ``True``, then
.. math::
\ell(x, y) = \begin{cases}
\operatorname{mean}(L), & \text{if}\; \text{size_average} = \text{True},\\
\operatorname{sum}(L), & \text{if}\; \text{size_average} = \text{False}.
\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.
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): By default, the losses are averaged
over observations for each minibatch. However, if the field
size_average is set to ``False``, the losses are instead summed for
each minibatch. Default: ``True``
Shape:
- Input: :math:`(N, *)` where `*` means, any number of additional
dimensions
- Target: :math:`(N, *)`, same shape as the input
Examples::
>>> loss = nn.BCEWithLogitsLoss()
>>> input = autograd.Variable(torch.randn(3), requires_grad=True)
>>> target = autograd.Variable(torch.FloatTensor(3).random_(2))
>>> output = loss(input, target)
>>> output.backward()
"""
def __init__(self, weight=None, size_average=True):
super(BCEWithLogitsLoss, self).__init__()
self.size_average = size_average
self.register_buffer('weight', weight)
def forward(self, input, target):
if self.weight is not None:
return F.binary_cross_entropy_with_logits(input, target, Variable(self.weight), self.size_average)
else:
return F.binary_cross_entropy_with_logits(input, target, size_average=self.size_average)
[docs]class HingeEmbeddingLoss(_Loss):
r"""Measures the loss given an input tensor `x` and a labels tensor `y`
containing values (`1` or `-1`).
This is usually used for measuring whether two inputs are similar or
dissimilar, e.g. using the L1 pairwise distance as `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}\; \text{size_average} = \text{True},\\
\operatorname{sum}(L), & \text{if}\; \text{size_average} = \text{False}.
\end{cases}
where :math:`L = \{l_1,\dots,l_N\}^\top`.
`x` and `y` can be of arbitrary shapes with a total of `n` elements each.
The sum operation operates over all the elements.
The division by `n` can be avoided if one sets the internal
variable `size_average=False`.
The `margin` has a default value of `1`, or can be set in the constructor.
"""
def __init__(self, margin=1.0, size_average=True):
super(HingeEmbeddingLoss, self).__init__()
self.margin = margin
self.size_average = size_average
def forward(self, input, target):
return F.hinge_embedding_loss(input, target, self.margin, self.size_average)
[docs]class MultiLabelMarginLoss(_Loss):
r"""Creates a criterion that optimizes a multi-class multi-classification
hinge loss (margin-based loss) between input `x` (a 2D mini-batch `Tensor`)
and output `y` (which is a 2D `Tensor` of target class indices).
For each sample in the mini-batch::
loss(x, y) = sum_ij(max(0, 1 - (x[y[j]] - x[i]))) / x.size(0)
where `i == 0` to `x.size(0)`, `j == 0` to `y.size(0)`,
`y[j] >= 0`, and `i != y[j]` for all `i` and `j`.
`y` and `x` must have the same size.
The criterion only considers the first non-negative `y[j]` targets.
This allows for different samples to have variable amounts of target classes
"""
def forward(self, input, target):
_assert_no_grad(target)
return F.multilabel_margin_loss(input, target, size_average=self.size_average)
[docs]class SmoothL1Loss(_Loss):
r"""Creates a criterion that uses a squared term if the absolute
element-wise error falls below 1 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::
{ 0.5 * (x_i - y_i)^2, if |x_i - y_i| < 1
loss(x, y) = 1/n \sum {
{ |x_i - y_i| - 0.5, otherwise
`x` and `y` arbitrary shapes with a total of `n` elements each
the sum operation still operates over all the elements, and divides by `n`.
The division by `n` can be avoided if one sets the internal variable
`size_average` to ``False``
Args:
size_average (bool, optional): By default, the losses are averaged
over all elements. However, if the field size_average is set to ``False``,
the losses are instead summed. Ignored when reduce is ``False``. Default: ``True``
reduce (bool, optional): By default, the losses are averaged or summed
over elements. When reduce is ``False``, the loss function returns
a loss per element instead and ignores size_average. Default: ``True``
Shape:
- Input: :math:`(N, *)` where `*` means, any number of additional
dimensions
- Target: :math:`(N, *)`, same shape as the input
- Output: scalar. If reduce is ``False``, then
:math:`(N, *)`, same shape as the input
"""
def __init__(self, size_average=True, reduce=True):
super(SmoothL1Loss, self).__init__(size_average)
self.reduce = reduce
def forward(self, input, target):
_assert_no_grad(target)
return F.smooth_l1_loss(input, target, size_average=self.size_average,
reduce=self.reduce)
[docs]class SoftMarginLoss(_Loss):
r"""Creates a criterion that optimizes a two-class classification
logistic loss between input `x` (a 2D mini-batch Tensor) and
target `y` (which is a tensor containing either `1` or `-1`).
::
loss(x, y) = sum_i (log(1 + exp(-y[i]*x[i]))) / x.nelement()
The normalization by the number of elements in the input can be disabled by
setting `self.size_average` to ``False``.
"""
def forward(self, input, target):
_assert_no_grad(target)
return F.soft_margin_loss(input, target, size_average=self.size_average)
[docs]class CrossEntropyLoss(_WeightedLoss):
r"""This criterion combines `LogSoftMax` and `NLLLoss` in one single class.
It is useful when training a classification problem with `C` classes.
If provided, the optional argument `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 scores for each class.
`input` has to be a 2D `Tensor` of size `(minibatch, C)`.
This criterion expects a class index (0 to C-1) as the
`target` for each value of a 1D tensor of size `minibatch`
The loss can be described as::
loss(x, class) = -log(exp(x[class]) / (\sum_j exp(x[j])))
= -x[class] + log(\sum_j exp(x[j]))
or in the case of the `weight` argument being specified::
loss(x, class) = weight[class] * (-x[class] + log(\sum_j exp(x[j])))
The losses are averaged across observations for each minibatch.
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): By default, the losses are averaged over observations for each minibatch.
However, if the field size_average is set to ``False``, the losses are
instead summed for each minibatch. Ignored if reduce is ``False``.
ignore_index (int, optional): Specifies a target value that is ignored
and does not contribute to the input gradient. When size_average is
``True``, the loss is averaged over non-ignored targets.
reduce (bool, optional): By default, the losses are averaged or summed over
observations for each minibatch depending on size_average. When reduce
is ``False``, returns a loss per batch element instead and ignores
size_average. Default: ``True``
Shape:
- Input: :math:`(N, C)` where `C = number of classes`
- Target: :math:`(N)` where each value is `0 <= targets[i] <= C-1`
- Output: scalar. If reduce is ``False``, then :math:`(N)` instead.
Examples::
>>> loss = nn.CrossEntropyLoss()
>>> input = autograd.Variable(torch.randn(3, 5), requires_grad=True)
>>> target = autograd.Variable(torch.LongTensor(3).random_(5))
>>> output = loss(input, target)
>>> output.backward()
"""
def __init__(self, weight=None, size_average=True, ignore_index=-100, reduce=True):
super(CrossEntropyLoss, self).__init__(weight, size_average)
self.ignore_index = ignore_index
self.reduce = reduce
def forward(self, input, target):
_assert_no_grad(target)
return F.cross_entropy(input, target, self.weight, self.size_average,
self.ignore_index, self.reduce)
[docs]class MultiLabelSoftMarginLoss(_WeightedLoss):
r"""Creates a criterion that optimizes a multi-label one-versus-all
loss based on max-entropy, between input `x` (a 2D mini-batch `Tensor`) and
target `y` (a binary 2D `Tensor`). For each sample in the minibatch::
loss(x, y) = - sum_i (y[i] * log( 1 / (1 + exp(-x[i])) )
+ ( (1-y[i]) * log(exp(-x[i]) / (1 + exp(-x[i])) ) )
where `i == 0` to `x.nElement()-1`, `y[i] in {0,1}`.
`y` and `x` must have the same size.
"""
def forward(self, input, target):
return F.multilabel_soft_margin_loss(input, target, self.weight, self.size_average)
[docs]class CosineEmbeddingLoss(Module):
r"""Creates a criterion that measures the loss given an input tensors
x1, x2 and a `Tensor` label `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.
`margin` should be a number from `-1` to `1`, `0` to `0.5` is suggested.
If `margin` is missing, the default value is `0`.
The loss function for each sample is::
{ 1 - cos(x1, x2), if y == 1
loss(x, y) = {
{ max(0, cos(x1, x2) - margin), if y == -1
If the internal variable `size_average` is equal to ``True``,
the loss function averages the loss over the batch samples;
if `size_average` is ``False``, then the loss function sums over the
batch samples. By default, `size_average = True`.
"""
def __init__(self, margin=0, size_average=True):
super(CosineEmbeddingLoss, self).__init__()
self.margin = margin
self.size_average = size_average
def forward(self, input1, input2, target):
return F.cosine_embedding_loss(input1, input2, target, self.margin, self.size_average)
[docs]class MarginRankingLoss(Module):
r"""Creates a criterion that measures the loss given
inputs `x1`, `x2`, two 1D mini-batch `Tensor`s,
and a label 1D mini-batch tensor `y` with values (`1` or `-1`).
If `y == 1` then it assumed the first input should be ranked higher
(have a larger value) than the second input, and vice-versa for `y == -1`.
The loss function for each sample in the mini-batch is::
loss(x, y) = max(0, -y * (x1 - x2) + margin)
if the internal variable `size_average = True`,
the loss function averages the loss over the batch samples;
if `size_average = False`, then the loss function sums over the batch
samples.
By default, `size_average` equals to ``True``.
"""
def __init__(self, margin=0, size_average=True):
super(MarginRankingLoss, self).__init__()
self.margin = margin
self.size_average = size_average
def forward(self, input1, input2, target):
return F.margin_ranking_loss(input1, input2, target, self.margin, self.size_average)
[docs]class MultiMarginLoss(Module):
r"""Creates a criterion that optimizes a multi-class classification hinge
loss (margin-based loss) between input `x` (a 2D mini-batch `Tensor`) and
output `y` (which is a 1D tensor of target class indices,
`0` <= `y` <= `x.size(1)`):
For each mini-batch sample::
loss(x, y) = sum_i(max(0, (margin - x[y] + x[i]))^p) / x.size(0)
where `i == 0` to `x.size(0)` and `i != y`.
Optionally, you can give non-equal weighting on the classes by passing
a 1D `weight` tensor into the constructor.
The loss function then becomes:
loss(x, y) = sum_i(max(0, w[y] * (margin - x[y] - x[i]))^p) / x.size(0)
By default, the losses are averaged over observations for each minibatch.
However, if the field `size_average` is set to ``False``,
the losses are instead summed.
"""
def __init__(self, p=1, margin=1, weight=None, size_average=True):
super(MultiMarginLoss, self).__init__()
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
self.size_average = size_average
self.weight = weight
def forward(self, input, target):
return F.multi_margin_loss(input, target, self.p, self.margin,
self.weight, self.size_average)
[docs]class TripletMarginLoss(Module):
r"""Creates a criterion that measures the triplet loss given an input
tensors x1, x2, x3 and a margin with a value greater than 0.
This is used for measuring a relative similarity between samples. A triplet
is composed by `a`, `p` and `n`: anchor, positive examples and negative
example respectively. The shape of all input variables 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.
.. math::
L(a, p, n) = \frac{1}{N} \left( \sum_{i=1}^N \max \{d(a_i, p_i) - d(a_i, n_i) + {\rm margin}, 0\} \right)
where :math:`d(x_i, y_i) = \left\lVert {\bf x}_i - {\bf y}_i \right\rVert_p`.
Args:
anchor: anchor input tensor
positive: positive input tensor
negative: negative input tensor
p: the norm degree. Default: 2
Shape:
- Input: :math:`(N, D)` where `D = vector dimension`
- Output: :math:`(N, 1)`
>>> triplet_loss = nn.TripletMarginLoss(margin=1.0, p=2)
>>> input1 = autograd.Variable(torch.randn(100, 128))
>>> input2 = autograd.Variable(torch.randn(100, 128))
>>> input3 = autograd.Variable(torch.randn(100, 128))
>>> output = triplet_loss(input1, input2, input3)
>>> output.backward()
.. _Learning shallow convolutional feature descriptors with triplet losses:
http://www.iis.ee.ic.ac.uk/%7Evbalnt/shallow_descr/TFeat_paper.pdf
"""
def __init__(self, margin=1.0, p=2, eps=1e-6, swap=False):
super(TripletMarginLoss, self).__init__()
self.margin = margin
self.p = p
self.eps = eps
self.swap = swap
def forward(self, anchor, positive, negative):
return F.triplet_margin_loss(anchor, positive, negative, self.margin,
self.p, self.eps, self.swap)
# TODO: L1HingeEmbeddingCriterion
# TODO: MSECriterion weight
# TODO: ClassSimplexCriterion
```