# softmax_with_cross_entropy¶

paddle.fluid.layers.loss. softmax_with_cross_entropy ( logits, label, soft_label=False, ignore_index=- 100, numeric_stable_mode=True, return_softmax=False, axis=- 1 ) [source]

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 gradient.

Because this operator performs a softmax on logits internally, it expects unscaled logits. This operator should not be used with the output of softmax operator since that would produce incorrect results.

When the attribute soft_label is set False, this operators expects mutually exclusive hard labels, each sample in a batch is in exactly one class with a probability of 1.0. Each sample in the batch will have a single label.

The equation is as follows:

1. Hard label (one-hot label, so every sample has exactly one class)

$\begin{split}loss_j = -\\text{logits}_{label_j} + \\log\\left(\\sum_{i=0}^{K}\\exp(\\text{logits}_i)\\right), j = 1,..., K\end{split}$
1. Soft label (each sample can have a distribution over all classes)

$\begin{split}loss_j = -\\sum_{i=0}^{K}\\text{label}_i \\left(\\text{logits}_i - \\log\\left(\\sum_{i=0}^{K} \\exp(\\text{logits}_i)\\right)\\right), j = 1,...,K\end{split}$
1. If numeric_stable_mode is True, softmax is calculated first by:

\begin{align}\begin{aligned}\begin{split}max_j &= \\max_{i=0}^{K}{\\text{logits}_i}\end{split}\\\begin{split}log\\_max\\_sum_j &= \\log\\sum_{i=0}^{K}\\exp(logits_i - max_j)\end{split}\\\begin{split}softmax_j &= \\exp(logits_j - max_j - {log\\_max\\_sum}_j)\end{split}\end{aligned}\end{align}

and then cross entropy loss is calculated by softmax and label.

Parameters
• logits (Tensor) – A multi-dimension Tensor , and the data type is float32 or float64. The input tensor of unscaled log probabilities.

• label (Tensor) – The ground truth Tensor , data type is the same as the logits . If soft_label is set to True, Label is a Tensor in the same shape with logits. If soft_label is set to True, Label is a Tensor in the same shape with logits expect shape in dimension axis as 1.

• soft_label (bool, optional) – A flag to indicate whether to interpretant the given labels as soft labels. Default False.

• ignore_index (int, optional) – Specifies a target value that is ignored and does not contribute to the input gradient. Only valid if soft_label is set to False. Default: kIgnoreIndex(-100).

• numeric_stable_mode (bool, optional) – A flag to indicate whether to use a more numerically stable algorithm. Only valid when soft_label is False and GPU is used. When soft_label is True or CPU is used, the algorithm is always numerically stable. Note that the speed may be slower when use stable algorithm. Default: True.

• return_softmax (bool, optional) – A flag indicating whether to return the softmax along with the cross entropy loss. Default: False.

• axis (int, optional) – The index of dimension to perform softmax calculations. It should be in range $$[-1, rank - 1]$$, while $$rank$$ is the rank of input logits. Default: -1.

Returns

Return the cross entropy loss if

return_softmax is False, otherwise the tuple (loss, softmax), softmax is in the same shape with input logits and cross entropy loss is in the same shape with input logits except shape in dimension axis as 1.

Return type

Tensor or Tuple of two Tensor

Examples

import paddle
import numpy as np

data = np.random.rand(128).astype("float32")
label = np.random.rand(1).astype("int64")
data = paddle.to_tensor(data)
label = paddle.to_tensor(label)
linear = paddle.nn.Linear(128, 100)
x = linear(data)
out = paddle.nn.functional.softmax_with_cross_entropy(logits=x, label=label)
print(out)