It is often used as the last activation function of a neural network to normalize the output of a network to a probability distribution over predicted output classes.
Softmax is an activation function that scales numbers/logits into probabilities. The output of a Softmax is a vector (say v) with probabilities of each possible outcome. The probabilities in vector v sums to one for all possible outcomes or classes.
Mathematically, Softmax is defined as,
$$ S(y)i = \frac{exp(y_i)}{\sum{j=1}^n exp(y_j)} $$
Consider a CNN model which aims at classifying an image as either a dog, cat, horse or cheetah (4 possible outcomes/classes). The last (fully-connected) layer of the CNN outputs a vector of logits, L, that is passed through a Softmax layer that transforms the logits into probabilities, P. These probabilities are the model predictions for each of the 4 classes.
Let us calculate the probability generated by the first logit after Softmax is applied,
Therefore,
And similar for softmax of 1.3, 0.2, and 0.8
{% embed url="https://towardsdatascience.com/softmax-activation-function-how-it-actually-works-d292d335bd78" %}