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# NLLLoss

class torch.nn.NLLLoss(weight=None, size_average=None, ignore_index=- 100, reduce=None, reduction='mean')

  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 Tensor of size either (m i n i b a t c h,C)(minibatch, C)(miniba t c h,C) or (m i n i b a t c h,C,d 1,d 2,...,d K)(minibatch, C, d_1, d_2, ..., d_K)(miniba t c h,C,d 1​,d 2​,...,d K​) with K≥1 K \geq 1 K≥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 [0,C−1][0, C-1][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 `reduction` set to `'none'`) loss can be described as:

  ℓ(x,y)=L={l 1,…,l N}⊤,l n=−w y n x n,y n,w c=weight[c]⋅1{c≠ignore_index},\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}\}, ℓ(x,y)=L={l 1​,…,l N​}⊤,l n​=−w y n​​x n,y n​​,w c​=weight[c]⋅1{c=ignore_index},

  where x x x is the input, y y y is the target, w w w is the weight, and N N N is the batch size. If `reduction` is not `'none'` (default `'mean'`), then

  ℓ(x,y)={∑n=1 N 1∑n=1 N w y n l n,if reduction=‘mean’;∑n=1 N l n,if reduction=‘sum’.\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} ℓ(x,y)={∑n=1 N​∑n=1 N​w y n​​1​l n​,∑n=1 N​l n​,​if reduction=‘mean’;if reduction=‘sum’.​
  Parameters:

    - 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 `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: `None`

    - 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) – 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: `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: `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: (N,C)(N, C)(N,C) or (C)(C)(C), where C = number of classes, or (N,C,d 1,d 2,...,d K)(N, C, d_1, d_2, ..., d_K)(N,C,d 1​,d 2​,...,d K​) with K≥1 K \geq 1 K≥1 in the case of K-dimensional loss.

    - Target: (N)(N)(N) or ()()(), where each value is 0≤targets[i]≤C−1 0 \leq \text{targets}[i] \leq C-1 0≤targets[i]≤C−1, or (N,d 1,d 2,...,d K)(N, d_1, d_2, ..., d_K)(N,d 1​,d 2​,...,d K​) with K≥1 K \geq 1 K≥1 in the case of K-dimensional loss.

    - Output: If `reduction` is `'none'`, shape (N)(N)(N) or (N,d 1,d 2,...,d K)(N, d_1, d_2, ..., d_K)(N,d 1​,d 2​,...,d K​) with K≥1 K \geq 1 K≥1 in the case of K-dimensional loss. Otherwise, scalar.

  Examples:

      >>> m = nn.LogSoftmax(dim=1)
      >>> loss = nn.NLLLoss()
      >>> # input is of size N x C = 3 x 5
      >>> input = torch.randn(3, 5, requires_grad=True)
      >>> # each element in target has to have 0 <= value < C
      >>> target = torch.tensor([1, 0, 4])
      >>> output = loss(m(input), target)
      >>> output.backward()
      >>>
      >>>
      >>> # 2D loss example (used, for example, with image inputs)
      >>> N, C = 5, 4
      >>> loss = nn.NLLLoss()
      >>> # input is of size N x C x height x width
      >>> data = torch.randn(N, 16, 10, 10)
      >>> conv = nn.Conv2d(16, C, (3, 3))
      >>> m = nn.LogSoftmax(dim=1)
      >>> # each element in target has to have 0 <= value < C
      >>> target = torch.empty(N, 8, 8, dtype=torch.long).random_(0, C)
      >>> output = loss(m(conv(data)), target)
      >>> output.backward()

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