class

SmoothL1Loss

extendsModule

SmoothL1Loss(reduction: Reduction = 'mean', beta: float = 1.0)

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Smooth L1 loss — a $\beta$ -parameterised Huber loss.

This loss is equivalent to HuberLoss with $\delta = \beta$ but uses a slightly different normalisation convention. The per-element form is:

\ell_\beta(x, y) = \begin{cases} \dfrac{(x - y)^2}{2\,\beta} & \text{if } |x - y| < \beta \\[6pt] |x - y| - \dfrac{\beta}{2} & \text{otherwise} \end{cases}

When $\beta = 1$ this coincides exactly with the Huber loss.

Parameters

reductionstr= 'mean'

'none' | 'mean' (default) | 'sum'.

betafloat= 1.0

Transition threshold between the quadratic and linear regions. Default 1.0.

Attributes

reductionstr

The reduction mode.

betafloat

The threshold

\beta

Notes

Input x : $(*)$ .
Target y : $(*)$ — same shape as x.
Output : scalar for 'mean' / 'sum'; $(*)$ for 'none'.

Smooth L1 is commonly used in object detection (bounding-box regression) because it is less sensitive to outlier predictions than MSE while still being differentiable everywhere.
Setting $\beta \to 0$ approaches MAE; $\beta \to \infty$ approaches MSE (for bounded residuals).

Examples

Default \beta = 1:
>>> import lucid
>>> import lucid.nn as nn
>>> criterion = nn.SmoothL1Loss()
>>> x = lucid.tensor([0.5, 2.0, -1.0])
>>> y = lucid.tensor([0.0, 0.0,  0.0])
>>> loss = criterion(x, y)
Tighter quadratic region (\beta = 0.5):
>>> import lucid
>>> import lucid.nn as nn
>>> criterion = nn.SmoothL1Loss(beta=0.5)
>>> x = lucid.tensor([0.3, 1.5, -0.2])
>>> y = lucid.tensor([0.0, 0.0,  0.0])
>>> loss = criterion(x, y)

Used by 1

lucid.nn.modules

Constructors

dunder

init

→None

__init__(reduction: Reduction = 'mean', beta: float = 1.0)

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Initialise the SmoothL1Loss module. See the class docstring for parameter semantics.

Instance methods

extra_repr

→str

extra_repr()

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Return a string representation of the layer's configuration.

forward

→Tensor

forward(x: Tensor, target: Tensor)

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Compute the loss between predictions and targets.

Parameters

xTensor

Input tensor.

targetTensor

Input tensor.

Returns

Tensor

Scalar loss (or unreduced tensor depending on reduction).

Default \beta = 1: >>> import lucid >>> import lucid.nn as nn >>> criterion = nn.SmoothL1Loss() >>> x = lucid.tensor([0.5, 2.0, -1.0]) >>> y = lucid.tensor([0.0, 0.0, 0.0]) >>> loss = criterion(x, y) Tighter quadratic region (\beta = 0.5): >>> import lucid >>> import lucid.nn as nn >>> criterion = nn.SmoothL1Loss(beta=0.5) >>> x = lucid.tensor([0.3, 1.5, -0.2]) >>> y = lucid.tensor([0.0, 0.0, 0.0]) >>> loss = criterion(x, y)