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# L1Loss

class torch.nn.L1Loss(size_average=None, reduce=None, reduction='mean')

  Creates a criterion that measures the mean absolute error (MAE) between each element in the input x x x and target y y y.

  The unreduced (i.e. with `reduction` set to `'none'`) loss can be described as:

  ℓ(x,y)=L={l 1,…,l N}⊤,l n=∣x n−y n∣,\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n = \left| x_n - y_n \right|, ℓ(x,y)=L={l 1​,…,l N​}⊤,l n​=∣x n​−y 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’.​

  x x x and y y y are tensors of arbitrary shapes with a total of n n n elements each.

  The sum operation still operates over all the elements, and divides by n n n.

  The division by n n n can be avoided if one sets `reduction = 'sum'`.

  Supports real-valued and complex-valued inputs.

  Parameters:

    - 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 the input.

  Examples:

      >>> loss = nn.L1Loss()
      >>> input = torch.randn(3, 5, requires_grad=True)
      >>> target = torch.randn(3, 5)
      >>> output = loss(input, target)
      >>> output.backward()

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