L1Loss

class brainpy.losses.L1Loss(reduction='mean')

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

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

\[\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n = \left| x_n - y_n \right|,\]

where \(N\) is the batch size. If reduction is not 'none' (default 'mean'), then:

\[\begin{split}\ell(x, y) = \begin{cases} \operatorname{mean}(L), & \text{if reduction} = \text{`mean';}\\ \operatorname{sum}(L), & \text{if reduction} = \text{`sum'.} \end{cases}\end{split}\]

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

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

The division by \(n\) can be avoided if one sets reduction = 'sum'.

Supports real-valued and complex-valued inputs.

Parameters:

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 = bm.random.randn(3, 5)
>>> target = bm.random.randn(3, 5)
>>> output = loss(input, target)
>>> output.backward()

update(input, target)

The function to specify the updating rule.

Return type:

TypeVar(ArrayType, Array, Variable, TrainVar, Array, ndarray)