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:

  \[\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n = - w_{y_n} \log \frac{\exp(x_{n,y_n})}{\sum_{c=1}^C \exp(x_{n,c})} \cdot \mathbb{1}\{y_n \not= \text{ignore_index}\}\]

  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

  \[\begin{split}\ell(x, y) = \begin{cases} \sum_{n=1}^N \frac{1}{\sum_{n=1}^N w_{y_n} \cdot \mathbb{1}\{y_n \not= \text{ignore_index}\}} l_n, & \text{if reduction} = \text{'mean',}\\ \sum_{n=1}^N l_n, & \text{if reduction} = \text{'sum'.} \end{cases}\end{split}\]

• 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:

  \[\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n = - \sum_{c=1}^C w_c \log \frac{\exp(x_{n,c})}{\sum_{i=1}^C \exp(x_{n,i})} y_{n,c}\]

  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

  \[\begin{split}\ell(x, y) = \begin{cases} \frac{\sum_{n=1}^N l_n}{N}, & \text{if reduction} = \text{'mean',}\\ \sum_{n=1}^N l_n, & \text{if reduction} = \text{'sum'.} \end{cases}\end{split}\]

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

>>> import mindspore
>>> import numpy as np
>>> from mindspore import Tensor, ops
>>> # 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)