mindspore.ops.cross_entropy

mindspore.ops.cross_entropy(input, target, weight=None, ignore_index=- 100, reduction='mean', label_smoothing=0.0)

The cross entropy loss between input and target.

The cross entropy support two kind of targets:

• Class indices (int) in the range $[0,C)$ where $C$ is the number of classes, the loss with reduction=none can be described as:

  $$\ell (x,y)=L=\{l_1,\dots ,l_N{\}}^{\mathrm{\top }},l_n=-w_{y_n}\log \frac{\exp (x_{n,y_n})}{\sum _{c=1}^C\exp (x_{n,c})}\cdot \mathbb{1}\{y_n\ne \text{ignore\_index}\}$$

  where $x$ is the inputs, $y$ is the target, $w$ is the weight, N is the batch size, $c$ belonging to $[0,C-1]$ is class index, where $C$ is the number of classes.

  If reduction is not ‘none’ (default ‘mean’), then

  $$\begin{array}{r}\ell (x,y)=\{\begin{array}{ll}\sum _{n=1}^N\frac{1}{\sum _{n=1}^N{w}_{y_n}\cdot \mathbb{1}\{y_n\ne \text{ignore\_index}\}}{l}_n,& \text{if reduction}=\text{'mean',}\\ \sum _{n=1}^N{l}_n,& \text{if reduction}=\text{'sum'.}\end{array}\end{array}$$

• Probabilities (float) for each class, useful when labels beyond a single class per minibatch item are required, the loss with reduction=none can be described as:

  $$\ell (x,y)=L=\{l_1,\dots ,l_N{\}}^{\mathrm{\top }},l_n=-\sum _{c=1}^C{w}_c\log \frac{\exp (x_{n,c})}{\sum _{i=1}^C\exp (x_{n,i})}{y}_{n,c}$$

  where $x$ is the inputs, $y$ is the target, $w$ is the weight, N is the batch size, $c$ belonging to $[0,C-1]$ is class index, where $C$ is the number of classes.

  If reduction is not ‘none’ (default ‘mean’), then

  $$\begin{array}{r}\ell (x,y)=\{\begin{array}{ll}\frac{\sum _{n=1}^N{l}_n}{N},& \text{if reduction}=\text{'mean',}\\ \sum _{n=1}^N{l}_n,& \text{if reduction}=\text{'sum'.}\end{array}\end{array}$$

Parameters

• input (Tensor) – $(N)$ or $(N,C)$ where C = number of classes or $(N,C,H,W)$ in case of 2D Loss, or $(N,C,d_1,d_2,...,d_K)$. input is expected to be log-probabilities, data type must be float16 or float32.

• target (Tensor) – For class indices, tensor of shape $()$, $(N)$ or $(N,d_1,d_2,...,d_K)$ , data type must be int32. For probabilities, tensor of shape $(C,)$ $(N,C)$ or $(N,C,d_1,d_2,...,d_K)$ , data type must be float16 or float32.

• weight (Tensor) – A rescaling weight applied to the loss of each batch element. If not None, the shape is $(C,)$, data type must be float16 or float32. Default: None.

• ignore_index (int) – Specifies a target value that is ignored and does not contribute to the input gradient. Default: -100

• reduction (str) – Apply specific reduction method to the output: ‘none’, ‘mean’, or ‘sum’. Default: ‘mean’.

• label_smoothing (float) – Label smoothing values, a regularization tool used to prevent the model from overfitting when calculating Loss. The value range is [0.0, 1.0]. Default value: 0.0.

Returns

Tensor, the computed loss value.

Supported Platforms:

Ascend GPU CPU

Examples

>>> # Case 1: Indices labels
>>> inputs = mindspore.Tensor(np.random.randn(3, 5), mindspore.float32)
>>> target = mindspore.Tensor(np.array([1, 0, 4]), mindspore.int32)
>>> output = ops.cross_entropy(inputs, target)
>>> # Case 2: Probability labels
>>> inputs = mindspore.Tensor(np.random.randn(3, 5), mindspore.float32)
>>> target = mindspore.Tensor(np.random.randn(3, 5), mindspore.float32)
>>> output = ops.cross_entropy(inputs, target)