class

HuberLoss

extendsModule

HuberLoss(reduction: str = 'mean', delta: float = 1.0)

source

Huber loss — a smooth interpolation between MSE and MAE.

For each element the per-element loss is:

\ell_\delta(x, y) = \begin{cases} \tfrac{1}{2}(x - y)^2 & \text{if } |x - y| < \delta \\[4pt] \delta \!\left(|x - y| - \tfrac{\delta}{2}\right) & \text{otherwise} \end{cases}

The scalar loss is the mean (or sum, or element-wise) of $\ell_\delta$ over all elements in the batch.

For small residuals the loss is quadratic (same as MSE) and for large residuals it is linear (same as MAE), with a smooth join at $|x - y| = \delta$ .

Parameters

reductionstr= 'mean'

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

deltafloat= 1.0

Threshold that separates the quadratic and linear regions. Default 1.0.

Attributes

reductionstr

The reduction mode.

deltafloat

The threshold

\delta

Notes

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

Choosing $\delta$ controls the robustness/sensitivity trade-off: larger $\delta$ behaves more like MSE, smaller $\delta$ behaves more like MAE.
SmoothL1Loss is identical to HuberLoss but parameterised by $\beta = \delta$ and normalised so that the two formulations match when $\delta = \beta = 1$ .

Examples

Default :math:`\delta = 1`:
>>> import lucid
>>> import lucid.nn as nn
>>> criterion = nn.HuberLoss()
>>> x = lucid.tensor([1.0,  3.0, -1.5])
>>> y = lucid.tensor([1.5, -1.0,  0.0])
>>> loss = criterion(x, y)
Custom threshold to tolerate larger outliers:
>>> import lucid
>>> import lucid.nn as nn
>>> criterion = nn.HuberLoss(delta=2.0)
>>> x = lucid.tensor([0.0, 5.0, -4.0])
>>> y = lucid.tensor([0.0, 1.0,  0.0])
>>> loss = criterion(x, y)

Methods (3)

dunder

init

→None

__init__(reduction: str = 'mean', delta: float = 1.0)

source

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

forward

→Tensor

forward(x: Tensor, target: Tensor)

source

Compute the loss between predictions and targets.

Parameters

xTensor

Input tensor.

targetTensor

Input tensor.

Returns

Tensor

Scalar loss (or unreduced tensor depending on reduction).

extra_repr

→str

extra_repr()

source

Return a string representation of the layer's configuration.