The softmax function is a mathematical function commonly used in machine learning, especially in classification tasks. It transforms a vector of real numbers into a probability distribution, where each value is between 0 and 1, and the sum of all values equals 1. This makes it ideal for multi-class classification problems.

Given a vector $( z = [z_1, z_2, …, z_n] )$, the softmax function computes:

$$ \text{softmax}(z_i) = \frac{e^{z_i}}{\sum_{j=1}^{n} e^{z_j}}$$

Each output value represents the probability of the input belonging to a particular class. The exponentiation ensures all values are positive, and the normalization ensures they sum to 1. Softmax emphasizes the largest values in the input vector, making the model more confident in its predictions. It is typically used in the final layer of neural networks for classification tasks.