smooth_l1_loss¶

paddle.nn.functional. smooth_l1_loss ( input, label, reduction='mean', delta=1.0, name=None ) [source]

Calculate smooth_l1_loss. Creates a criterion that uses a squared term if the absolute element-wise error falls below 1 and an L1 term otherwise. In some cases it can prevent exploding gradients and it is more robust and less sensitivity to outliers. Also known as the Huber loss:

$$loss(x,y) = \frac{1}{n}\sum_{i}z_i$$

where $z_i$ is given by:

$$\begin{split}\mathop{z_i} = \left\{\begin{array}{rcl} 0.5(x_i - y_i)^2 & & {if |x_i - y_i| < \delta} \\ \delta * |x_i - y_i| - 0.5 * \delta^2 & & {otherwise} \end{array} \right.\end{split}$$

Parameters

• input (Tensor) – Input tensor, the data type is float32 or float64. Shape is (N, C), where C is number of classes, and if shape is more than 2D, this is (N, C, D1, D2,…, Dk), k >= 1.

• label (Tensor) – Label tensor, the data type is float32 or float64. The shape of label is the same as the shape of input.

• reduction (str, optional) – Indicate how to average the loss by batch_size, the candicates are 'none' | 'mean' | 'sum'. If reduction is 'mean', the reduced mean loss is returned; If reduction is 'sum', the reduced sum loss is returned. If reduction is 'none', the unreduced loss is returned. Default is 'mean'.

• delta (float, optional) – Specifies the hyperparameter $\delta$ to be used. The value determines how large the errors need to be to use L1. Errors smaller than delta are minimized with L2. Parameter is ignored for negative/zero values. Default = 1.0

• name (str, optional) – For details, please refer to Name. Generally, no setting is required. Default: None.

Returns

Tensor, The tensor variable storing the smooth_l1_loss of input and label.

Examples

>>> import paddle
>>> paddle.seed(2023)

>>> input = paddle.rand([3, 3]).astype('float32')
>>> label = paddle.rand([3, 3]).astype('float32')
>>> output = paddle.nn.functional.smooth_l1_loss(input, label)
>>> print(output)
Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True,
        0.08307374)