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# BCEWithLogitsLoss

class torch.nn.BCEWithLogitsLoss(weight=None, size_average=None, reduce=None, reduction='mean', pos_weight=None)

  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 `reduction` set to `'none'`) loss can be described as:

  ℓ(x,y)=L={l 1,…,l N}⊤,l n=−w n[y n⋅log⁡σ(x n)+(1−y n)⋅log⁡(1−σ(x n))],\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], ℓ(x,y)=L={l 1​,…,l N​}⊤,l n​=−w n​[y n​⋅log σ(x n​)+(1−y n​)⋅log(1−σ(x n​))],

  where N N N is the batch size. If `reduction` is not `'none'` (default `'mean'`), then

  ℓ(x,y)={mean⁡(L),if reduction=‘mean’;sum⁡(L),if reduction=‘sum’.\ell(x, y) = \begin{cases} \operatorname{mean}(L), & \text{if reduction} = \text{`mean';}\\ \operatorname{sum}(L), & \text{if reduction} = \text{`sum'.} \end{cases} ℓ(x,y)={mean(L),sum(L),​if reduction=‘mean’;if reduction=‘sum’.​

  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:

  ℓ c(x,y)=L c={l 1,c,…,l N,c}⊤,l n,c=−w n,c[p c y n,c⋅log⁡σ(x n,c)+(1−y n,c)⋅log⁡(1−σ(x n,c))],\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], ℓ c​(x,y)=L c​={l 1,c​,…,l N,c​}⊤,l n,c​=−w n,c​[p c​y n,c​⋅log σ(x n,c​)+(1−y n,c​)⋅log(1−σ(x n,c​))],

  where c c c is the class number (c>1 c > 1 c>1 for multi-label binary classification, c=1 c = 1 c=1 for single-label binary classification), n n n is the number of the sample in the batch and p c p_c p c​ is the weight of the positive answer for the class c c c.

  p c>1 p_c > 1 p c​>1 increases the recall, p c<1 p_c < 1 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 300 100=3\frac{300}{100}=3 100 300​=3. The loss would act as if the dataset contains 3×100=300 3\times 100=300 3×100=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...)

  Parameters:

    - 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 `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 `size_average` is set to `False`, the losses are instead summed for each minibatch. Ignored when `reduce` is `False`. Default: `True`

    - reduce (bool, optional) – Deprecated (see `reduction`). 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`

    - 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: `size_average` and `reduce` are in the process of being deprecated, and in the meantime, specifying either of those two args will override `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: (∗)(*)(∗), where ∗*∗ means any number of dimensions.

    > - Target: (∗)(*)(∗), same shape as the input.

    > - Output: scalar. If `reduction` is `'none'`, then (∗)(*)(∗), 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()

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