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# BCELoss

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

  Creates a criterion that measures the Binary Cross Entropy between the target and the input probabilities:

  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⁡x n+(1−y n)⋅log⁡(1−x n)],\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], ℓ(x,y)=L={l 1​,…,l N​}⊤,l n​=−w n​[y n​⋅log x n​+(1−y n​)⋅log(1−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 y y y should be numbers between 0 and 1.

  Notice that if x n x_n 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 log⁡(0)=−∞\log (0) = -\infty log(0)=−∞, since lim⁡x→0 log⁡(x)=−∞\lim_{x\to 0} \log (x) = -\infty lim x→0​log(x)=−∞. However, an infinite term in the loss equation is not desirable for several reasons.

  For one, if either y n=0 y_n = 0 y n​=0 or (1−y n)=0(1 - y_n) = 0(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 lim⁡x→0 d d x log⁡(x)=∞\lim_{x\to 0} \frac{d}{dx} \log (x) = \infty lim x→0​d x d​log(x)=∞. This would make BCELoss’s backward method nonlinear with respect to x n x_n 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.

  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'`

  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:

      >>> 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()

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