Which of the following is true about the softmax function in the context of multinomial logistic regression?

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BlackTom AI · Accepted Answer

Question restatement: What is true about the softmax function in the context of multinomial logistic regression?

Option evaluation:
- Since the provided input does not include any answer options for this question, there is nothing to evaluate against a list of choices. In a typical multiple-choice setup, we would examine each option for its correctness and explain why it is right or wrong. Here, we only have the one listed answer in the 'answer' field, and no separate options to analyze.

About the concept implied by the provided answer: 'It generalizes the logistic function to handle more than two classes.'
- Why this statement is true: In binary logistic regression, the model uses the logistic (sigmoid) function to map a linear score to a probability for a single target class vs. the rest. Multinomial logistic regression extends this idea to multi-class classification by using the softmax function to model the probability distribution over K classes. The softmax takes a vector of class scores and converts them into a probability distribution over all classes, ensuring that the probabilities sum to 1. This is the natural generalization of the logistic function from two classes to K > 2 classes, where each class probability depends on all class scores and is computed as exp(score_k) / sum_j exp(score_j).

- Possible misinterpretations to avoid: Some might think softmax is only a multi-class wrapper around a one-vs-rest approach; in reality, softmax can be used directly to model a single multinomial distribution across all classes, though one-vs-rest approaches are an alternative in practice. Others might confuse softmax with a simple normalization; while softmax does normalize, its key feature is the exponentiation of scores, which amplifies differences between scores and yields a well-behaved probability distribution over multiple classes.

Summary of key concept:
- The softmax function is used in multinomial logistic regression to extend binary logistic regression to multi-class problems.
- It converts a vector of class scores into a probability distribution over all classes, enabling multi-class classification where the sum of probabilities across classes equals 1.
- This matches the intuitive notion that softmax generalizes the idea of the logistic function to more than two outcomes, rather than serving as a simple normalization or a one-vs-rest scheme by itself.

COMP90049_2025_SM2 Lecture 8 Gradient Descent & Logistic Regression Practice Quiz

Which of the following is true about the softmax function in the context of multinomial logistic regression?

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