Table Of Contents
Table Of Contents

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:

\[ \begin{align}\begin{aligned}\text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)}\\- Cross Entropy Function:\end{aligned}\end{align} \]
\[ \begin{align}\begin{aligned}\text{CE(label, output)} = - \sum_i \text{label}_i \log(\text{output}_i)\\**Example**::\\ x = [[1, 2, 3], [11, 7, 5]]\\ label = [2, 0]\\ softmax(x) = [[0.09003057, 0.24472848, 0.66524094], [0.97962922, 0.01794253, 0.00242826]]\\ softmax_cross_entropy(data, label) = - log(0.66524084) - log(0.97962922) = 0.4281871\end{aligned}\end{align} \]

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.