# Softmax

Softmax Function is a widely used mathematical function in artificial intelligence (AI), particularly in classification tasks. Function is used in various multiclass classification methods, such as multinomial logistic regression (also known as softmax regression), multiclass linear discriminant analysis, Naive Bayes classifiers, and artificial Neural Networks. It is used to convert a vector of real numbers into a probability distribution over multiple classes. The Softmax function takes as input a vector of values, often referred to as logits or scores, and transforms them into a probability distribution where the sum of all probabilities is equal to 1.

The softmax function is defined as follows:

• The input to the softmax function is a vector of scores or logits, denoted as z = [z1, z2, ..., zn], where n is the number of classes.
• Each element in the input vector represents the score or the strength of association for a specific class.
• The softmax function calculates the exponentiation of each element in the input vector, which ensures that the resulting values are positive.
• The exponentiated values are then normalized by dividing each element by the sum of all exponentiated values.

The formula for the softmax function can be expressed as:

• softmax(z) = [e^z1 / (e^z1 + e^z2 + ... + e^zn), e^z2 / (e^z1 + e^z2 + ... + e^zn), ..., e^zn / (e^z1 + e^z2 + ... + e^zn)]

The Softmax function can be interpreted as providing a probability-like output for each class, where higher scores in the input vector correspond to higher probabilities. By normalizing the exponentiated values, the softmax function emphasizes the larger values and suppresses the smaller ones.

The softmax function is commonly used in the final layer of a neural network for multi-class classification problems. The output of the softmax function can be interpreted as the predicted probabilities of each class. The class with the highest probability is then selected as the predicted class label.

The softmax function has several desirable properties that make it suitable for classification tasks. It ensures that the predicted probabilities are non-negative and sum up to 1, making them interpretable as probabilities. Additionally, the softmax function is differentiable, which allows for efficient training of neural networks using gradient-based optimization algorithms.

In summary, the softmax function is a crucial component in AI models for multi-class classification tasks. It transforms a vector of scores or logits into a probability distribution, enabling the prediction of class labels based on the calculated probabilities.