mx.symbol.softmax_cross_entropy¶

Description¶

Calculate cross entropy of softmax output and one-hot label.

• This operator computes the cross entropy in two steps:
• Applies softmax function on the input array.

• Computes and returns the cross entropy loss between the softmax output and the labels.

• The softmax function and cross entropy loss is given by:

• Softmax Function:

$\text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)}$
• Cross Entropy Function:

$\text{CE(label, output)} = - \sum_i \text{label}_i \log(\text{output}_i)$

Example:

x = [[1, 2, 3],
[11, 7, 5]]

label = [2, 0]

softmax(x) = [[0.09003057, 0.24472848, 0.66524094],
[0.97962922, 0.01794253, 0.00242826]]

softmax_cross_entropy(data, label) = - log(0.66524084) - log(0.97962922) = 0.4281871

Usage¶

mx.symbol.softmax_cross_entropy(...)

Arguments¶

Argument

Description

data

NDArray-or-Symbol.

Input data

label

NDArray-or-Symbol.

Input label

name

string, optional.

Name of the resulting symbol.

Value¶

out The result mx.symbol