最近一直在做一些语义分割相关的项目,找损失函数的时候发现网上这些大佬的写得各有千秋,也没说怎么用,在此记录一下自己在训练过程中使用损失函数的一些心得.本人是使用的Pytorch框架,故这一系列都会基于Pytorch来实现。

首先是交叉熵损失函数，语义分割其实是一个逐像素分类的一个分类问题，做过图像分类的应该都比较熟悉交叉熵损失函数。

pytorch中自带有写好的交叉熵函数，只需要调用就行：

loss_func = nn.CrossEntropyLoss()

torch.nn模块中写好的损失函数都是以类的方式写的，只需要提前声明一下后面即可调用。

pytorch中交叉熵损失函数的实现：

class CrossEntropyLoss(_WeightedLoss):
    r"""This criterion computes the cross entropy loss between input 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 raw, unnormalized scores for each class.
    `input` has to be a Tensor of size either :math:`(minibatch, C)` or
    :math:`(minibatch, C, d_1, d_2, ..., d_K)` with :math:`K geq 1` for the
    `K`-dimensional case. The latter is 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-1]` 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 the combination of :class:`~torch.nn.LogSoftmax` and
      :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})}{exp(sum_{i=1}^C 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`
        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 (string, optional): Specifies the reduction to apply to the output:
            ``'none'`` | ``'mean'`` | ``'sum'``. ``'none'``: no reduction will
            be applied, ``'mean'``: the weighted mean of the output is taken,
            ``'sum'``: the output will be summed. Note: :attr:`size_average`
            and :attr:`reduce` are in the process of being deprecated, and in
            the meantime, specifying either of those two args will override
            :attr:`reduction`. Default: ``'mean'``
        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: :math:`(N, C)` where `C = number of classes`, or
          :math:`(N, C, d_1, d_2, ..., d_K)` with :math:`K geq 1`
          in the case of `K`-dimensional loss.
        - Target: If containing class indices, shape :math:`(N)` where each value is
          :math:`0 leq text{targets}[i] leq C-1`, or :math:`(N, d_1, d_2, ..., d_K)` with
          :math:`K geq 1` in the case of K-dimensional loss. If containing class probabilities,
          same shape as the input.
        - 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::

        >>> # 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(CrossEntropyLoss, self).__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)

在声明损失函数的时候可以加上一些参数，其中比较重要的是weight: Optional[Tensor] = None，
weight权重是在计算中给每一类加上相应的计算权重，是一个tensor，长度和类别数一致；以及label_smoothing，label_smoothing方法在交叉熵损失函数中自带有，假设label_smoothing = 0.1的话，在二分类问题中就会将类别为1的变为0.9，类别为0的变为0.1，这样做能够让损失更加平滑，更容易收敛，避免错误分类带来的过大的损失。

在使用也就是计算loss值的时候需要两个参数，一个是input，一个是target，两个都是tensor，input是你模型的预测结果，target是真实标注。例如：

import torch
import torch.nn as nn

loss_func = nn.CrossEntropyLoss()

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

target = torch.empty(3, dtype=torch.long).random_(5)
output = loss_func(input, target)
print(output)

input: tensor([[ 1.6738,  0.0526,  0.6329, -0.8809,  1.4822],
        [-0.5908,  1.5717,  1.3402,  0.4227, -0.3498],
        [-0.3359, -2.3797, -1.6206, -2.3070,  0.6010]], requires_grad=True)
target: tensor([3, 4, 1])
loss: tensor(3.2306, grad_fn=<NllLossBackward0>)

上面这就类似与一个五分类的问题，input是模型最后的全连接层的输出，或者是全卷积网络最后的输出。

这里注意：

加入你把分类输出的概率做了argmax操作以后，计算会出错，例如：

import torch
import torch.nn as nn

loss_func = nn.CrossEntropyLoss()

# input = torch.randn(3, 5, requires_grad=True)
input = torch.randn(3,requires_grad=True)
print("input:",input)
target = torch.empty(3, dtype=torch.long).random_(5)
print("target:",target)
output = loss_func(input, target)
print("loss:",output)

input: tensor([-0.3463,  1.2289,  0.2517], requires_grad=True)
target: tensor([3, 4, 3])
Traceback (most recent call last):
  File "/home/lwf/Project/MRI-Segmentation/tets.py", line 19, in <module>
    output = loss_func(input, target)
  File "/home/lwf/anaconda3/envs/torch3.7/lib/python3.7/site-packages/torch/nn/modules/module.py", line 1102, in _call_impl
    return forward_call(*input, **kwargs)
  File "/home/lwf/anaconda3/envs/torch3.7/lib/python3.7/site-packages/torch/nn/modules/loss.py", line 1152, in forward
    label_smoothing=self.label_smoothing)
  File "/home/lwf/anaconda3/envs/torch3.7/lib/python3.7/site-packages/torch/nn/functional.py", line 2846, in cross_entropy
    return torch._C._nn.cross_entropy_loss(input, target, weight, _Reduction.get_enum(reduction), ignore_index, label_smoothing)
RuntimeError: Expected floating point type for target with class probabilities, got Long

也就是说，input的输出必须是每个类别的概率。

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