Learning Path
Question & Answer1
Understand Question2
Review Options3
Learn Explanation4
Explore TopicChoose the Best Answer
A
The softmax function is derived from the log-sum-exp function.
B
The log-sum-exp function is a specific case of the softmax function.
C
Both functions are identical in their outputs.
D
The log-sum-exp function cannot be used to compute probabilities.
Understanding the Answer
Let's break down why this is correct
Answer
The log‑sum‑exp (LSE) function is the logarithm of the normalizing constant that makes a set of unnormalized log‑probabilities into a proper probability distribution; it is written as log ∑ exp(zi). The softmax function takes those same log‑probabilities, exponentiates them, and divides each exponentiated value by the sum of all exponentials, which is exactly the denominator that the LSE computes. Thus, the softmax normalizes the scores into probabilities by using the LSE as the denominator, while the LSE itself can be used to compute the log‑partition function needed for many probabilistic models. For example, if we have scores z = [2, 0, −1], the softmax outputs exp(z)/∑exp(z) ≈ [0. 71, 0.
Detailed Explanation
Softmax turns raw scores into probabilities by dividing each exponential by the sum of all exponentials. Other options are incorrect because Some think log-sum-exp is a special case of softmax, but it is actually a helper that calculates the denominator; Softmax outputs a vector of probabilities, while log-sum-exp outputs a single number.
Key Concepts
softmax function
Topic
Log-sum-exp Function
Difficulty
easy level question
Cognitive Level
understand
Practice Similar Questions
Test your understanding with related questions
1
Question 1What does the log-sum-exp function represent, and how do its properties relate to the laws of logarithms?
mediumComputer-science
Practice
2
Question 2In a business context, how does the derivative of the log-sum-exp function relate to the exponential function in terms of optimizing a portfolio's expected return?
mediumComputer-science
Practice
3
Question 3Which of the following statements about the log-sum-exp function are true? Select all that apply.
easyComputer-science
Practice
4
Question 4Log-sum-exp : Smooth approximation :: Max function : ?
mediumComputer-science
Practice
5
Question 5Which of the following scenarios would best utilize the log-sum-exp function for optimization in machine learning algorithms?
hardComputer-science
Practice
6
Question 6When applying the log-sum-exp function in optimization, what is the primary reason it is preferred over using the max function directly?
easyComputer-science
Practice
7
Question 7In what scenario would using the log-sum-exp function be more advantageous than directly applying the max function?
mediumComputer-science
Practice
Ready to Master More Topics?
Join thousands of students using Seekh's interactive learning platform to excel in their studies with personalized practice and detailed explanations.