l1_loss

class brainpy.losses.l1_loss(logits, targets, reduction='sum')

Creates a criterion that measures the mean absolute error (MAE) between each element in the logits \(x\) and targets \(y\). It is useful in regression problems.

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:

• logits (ArrayType) – \((N, *)\) where \(*\) means, any number of additional dimensions.

• targets (ArrayType) – \((N, *)\), same shape as the input.

• reduction (str) – Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. Default: 'mean'. - '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

Returns:

output – If reduction is 'none', then \((N, *)\), same shape as the input.

Return type:

scalar.