Softmax Function

On this page the Softmax function is calculated as described in the formula below.

Up to 10 vectors can be entered for the calculation. In the menu, select the number of vectors to be calculated. Then enter their values and click on the 'Calculate' button.

Description and formula for the Softmax function

The softmax function is a mathematical function that converts a vector of real numbers into a Probability distribution of possible outcomes.

It transforms a K-dimensional vector \(z\) with real components into a K-dimensional vector, where the components add up to 1. The function is given by:

\(\displaystyle \sigma(z)_j = \frac{e^{z_j}}{\sum_{i=1}^{K} e^{z_i}} \quad \text{for } j = 1, \ ldots, K \)

In probability theory, the output of the softmax function can be used to represent a categorical distribution, i.e. a probability distribution over different possible events. It corresponds to the gradient-log normalization of the categorical probability distribution.

The softmax function is a powerful tool to calculate probabilities for different classes and is often used in machine learning practice.