# cross_entropy¶

paddle.nn.functional. cross_entropy ( input, label, weight=None, ignore_index=- 100, reduction='mean', soft_label=False, axis=- 1, use_softmax=True, name=None ) [source]

By default, this operator implements the cross entropy loss function with softmax. This function combines the calculation of the softmax operation and the cross entropy loss function to provide a more numerically stable computing.

This operator will calculate the cross entropy loss function without softmax when use_softmax=False.

By default, this operator will calculate the mean of the result, and you can also affect the default behavior by using the reduction parameter. Please refer to the part of parameters for details.

This operator can be used to calculate the softmax cross entropy loss with soft and hard labels. Where, the hard labels mean the actual label value, 0, 1, 2, etc. And the soft labels mean the probability of the actual label, 0.6, 0.8, 0.2, etc.

The calculation of this operator includes the following two steps.

• 1.softmax cross entropy

1. Hard label (each sample can only be assigned into one category)

1.1. when use_softmax=True

$\begin{split}\\loss_j=-\text{logits}_{label_j}+\log\left(\sum_{i=0}^{C}\exp(\text{logits}_i)\right) , j = 1,...,N\end{split}$

where, N is the number of samples and C is the number of categories.

1.2. when use_softmax=False

$\begin{split}\\loss_j=-\log\left({P}_{label_j}\right) , j = 1,...,N\end{split}$

where, N is the number of samples and C is the number of categories, P is input(the output of softmax).

1. Soft label (each sample is assigned to multiple categories with a certain probability, and the probability sum is 1).

2.1. when use_softmax=True

$\begin{split}\\loss_j=-\sum_{i=0}^{C}\text{label}_i\left(\text{logits}_i-\log\left(\sum_{i=0}^{C}\exp(\text{logits}_i)\right)\right) , j = 1,...,N\end{split}$

where, N is the number of samples and C is the number of categories.

2.2. when use_softmax=False

$\begin{split}\\loss_j=-\sum_{j=0}^{C}\left({label}_j*\log\left({P}_{label_j}\right)\right) , j = 1,...,N\end{split}$

where, N is the number of samples and C is the number of categories, P is input(the output of softmax).

• 2. Weight and reduction processing

1. Weight

If the weight parameter is None , go to the next step directly.

If the weight parameter is not None , the cross entropy of each sample is weighted by weight according to soft_label = False or True as follows.

1.1. Hard labels (soft_label = False)

$\begin{split}\\loss_j=loss_j*weight[label_j]\end{split}$

1.2. Soft labels (soft_label = True)

$\begin{split}\\loss_j=loss_j*\sum_{i}\left(weight[label_i]*logits_i\right)\end{split}$
2. reduction

2.1 if the reduction parameter is none

Return the previous result directly

2.2 if the reduction parameter is sum

Return the sum of the previous results

$\begin{split}\\loss=\sum_{j}loss_j\end{split}$

2.3 if the reduction parameter is mean , it will be processed according to the weight parameter as follows.

2.3.1. If the weight parameter is None

Return the average value of the previous results

\begin{align}\begin{aligned}\begin{split}\\loss=\sum_{j}loss_j/N\end{split}\\ where, N is the number of samples and C is the number of categories.\end{aligned}\end{align}

2.3.2. If the ‘weight’ parameter is not ‘None’, the weighted average value of the previous result will be returned

1. Hard labels (soft_label = False)

$\begin{split}\\loss=\sum_{j}loss_j/\sum_{j}weight[label_j]\end{split}$
1. Soft labels (soft_label = True)

$\begin{split}\\loss=\sum_{j}loss_j/\sum_{j}\left(\sum_{i}weight[label_i]\right)\end{split}$
Parameters
• input (-) –

Input tensor, the data type is float32, float64. Shape is $$[N_1, N_2, ..., N_k, C]$$, where C is number of classes , k >= 1 .

Note

1. when use_softmax=True, it expects unscaled logits. This operator should not be used with the output of softmax operator, which will produce incorrect results.

1. when use_softmax=False, it expects the output of softmax operator.

• label (-) –

1. If soft_label=False, the shape is $$[N_1, N_2, ..., N_k]$$ or $$[N_1, N_2, ..., N_k, 1]$$, k >= 1. the data type is int32, int64, float32, float64, where each value is [0, C-1].

2. If soft_label=True, the shape and data type should be same with input , and the sum of the labels for each sample should be 1.

• weight (-) – a manual rescaling weight given to each class. If given, has to be a Tensor of size C and the data type is float32, float64. Default is 'None' .

• ignore_index (-) – Specifies a target value that is ignored and does not contribute to the loss. A negative value means that no label value needs to be ignored. Only valid when soft_label = False. Default is -100 .

• reduction (-) – 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 size_average is 'sum', the reduced sum loss is returned. If reduction is 'none', the unreduced loss is returned. Default is 'mean'.

• soft_label (-) – Indicate whether label is soft. Default is False.

• axis (-) – The index of dimension to perform softmax calculations. It should be in range $$[-1, rank - 1]$$, where $$rank$$ is the number of dimensions of input input. Default is -1 .

• use_softmax (-) – Indicate whether compute softmax before cross_entropy. Default is True.

• name (-) – The name of the operator. Default is None . For more information, please refer to Name .

Returns

Tensor. Return the softmax cross_entropy loss of input and label.

The data type is the same as input.

If reduction is 'mean' or 'sum' , the dimension of return value is 1.

If reduction is 'none':

1. If soft_label = False, the dimension of return value is the same with label .

2. if soft_label = True, the dimension of return value is $$[N_1, N_2, ..., N_k, 1]$$ .

Example1(hard labels):

import paddle
N=100
C=200
reduction='mean'
label =  paddle.randint(0, C, shape=[N], dtype='int64')

weight=weight, reduction=reduction)
dy_ret = cross_entropy_loss(
input,
label)
print(dy_ret.numpy()) #[5.41993642]


Example2(soft labels):

import paddle
axis = -1
ignore_index = -100
N = 4
C = 3
shape = [N, C]
reduction='mean'
weight = None
logits = paddle.uniform(shape, dtype='float64', min=0.1, max=1.0)
labels = paddle.uniform(shape, dtype='float64', min=0.1, max=1.0)