Which function is utilized to train a multinomial logistic regression model?

The softmax function is used in multinomial logistic regression to compute the probabilities of different classes for a given input. In this context, multinomial logistic regression is a generalization of logistic regression that allows for multiple classes.

The softmax function takes a vector of raw prediction scores (often called logits) and transforms them into a probability distribution over multiple classes. The output from the softmax function is a set of values between 0 and 1 that sum up to 1, making it suitable for multi-class classification problems. Therefore, the softmax function is essential for interpreting the model outputs as probabilities for each class.

In contrast, while a cost function is critical for training models by evaluating how well the model's predictions match the actual targets, it does not perform the act of training itself. The Heaviside step function is primarily used in binary classifications and does not manage multi-class scenarios as softmax does. The Rectified Linear Unit (ReLU) function is commonly used in deep learning for activation layers but is not applicable for the output layer of a multinomial logistic regression model, where softmax is specifically designed to handle multiple classes.