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# SmoothL1Loss

class torch.nn.SmoothL1Loss(size_average=None, reduce=None, reduction='mean', beta=1.0)

  Creates a criterion that uses a squared term if the absolute element-wise error falls below beta and an L1 term otherwise. It is less sensitive to outliers than `torch.nn.MSELoss` and in some cases prevents exploding gradients (e.g. see the paper Fast R-CNN by Ross Girshick).

  For a batch of size N N N, the unreduced loss can be described as:

  ℓ(x,y)=L={l 1,...,l N}T\ell(x, y) = L = \{l_1, ..., l_N\}^T ℓ(x,y)=L={l 1​,...,l N​}T

  with

  l n={0.5(x n−y n)2/b e t a,if ∣x n−y n∣<b e t a∣x n−y n∣−0.5∗b e t a,otherwise l_n = \begin{cases} 0.5 (x_n - y_n)^2 / beta, & \text{if } |x_n - y_n| < beta \\ |x_n - y_n| - 0.5 * beta, & \text{otherwise } \end{cases} l n​={0.5(x n​−y n​)2/b e t a,∣x n​−y n​∣−0.5∗b e t a,​if ∣x n​−y n​∣<b e t a otherwise ​

  If reduction is not none, 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’.​

  Note

  Smooth L1 loss can be seen as exactly `L1Loss`, but with the ∣x−y∣<b e t a|x - y| < beta∣x−y∣<b e t a portion replaced with a quadratic function such that its slope is 1 at ∣x−y∣=b e t a|x - y| = beta∣x−y∣=b e t a. The quadratic segment smooths the L1 loss near ∣x−y∣=0|x - y| = 0∣x−y∣=0.

  Note

  Smooth L1 loss is closely related to `HuberLoss`, being equivalent to h u b e r(x,y)/b e t a huber(x, y) / beta h u b er(x,y)/b e t a (note that Smooth L1’s beta hyper-parameter is also known as delta for Huber). This leads to the following differences:

  - As beta -> 0, Smooth L1 loss converges to `L1Loss`, while `HuberLoss` converges to a constant 0 loss. When beta is 0, Smooth L1 loss is equivalent to L1 loss.

  - As beta -> +∞+\infty+∞, Smooth L1 loss converges to a constant 0 loss, while `HuberLoss` converges to `MSELoss`.

  - For Smooth L1 loss, as beta varies, the L1 segment of the loss has a constant slope of 1. For `HuberLoss`, the slope of the L1 segment is beta.

  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'`

    - beta (float, optional) – Specifies the threshold at which to change between L1 and L2 loss. The value must be non-negative. Default: 1.0

  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.

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