Learning Path
Question & Answer1
Understand Question2
Review Options3
Learn Explanation4
Explore TopicChoose the Best Answer
A
When dealing with a large set of negative values
B
When smooth approximation is required for optimization
C
When the exact maximum value is necessary
D
When computational speed is the only concern
Understanding the Answer
Let's break down why this is correct
Answer
Using log‑sum‑exp is more helpful than the raw max when you need a smooth, differentiable approximation of the maximum that still keeps track of the relative sizes of all terms, not just the largest one. It lets you add probabilities in log space without risking under‑ or overflow that can happen with very small numbers. For example, if you have log probabilities –1. 0 and –2. 0, the max would pick –1.
Detailed Explanation
The log-sum-exp function gives a smooth, differentiable version of the max function. Other options are incorrect because Some think log-sum-exp only helps with negative numbers; It is not a tool for finding the exact maximum.
Key Concepts
Log-sum-exp function
Optimization techniques
Convex functions
Topic
Log-sum-exp Function
Difficulty
medium level question
Cognitive Level
understand
Practice Similar Questions
Test your understanding with related questions
1
Question 1What is the relationship between the log-sum-exp function and the softmax function in the context of probability distributions?
easyComputer-science
Practice
2
Question 2What does the log-sum-exp function represent, and how do its properties relate to the laws of logarithms?
mediumComputer-science
Practice
3
Question 3In the context of optimization problems, how does the log-sum-exp function enhance computational efficiency while approximating the maximum of a set of values?
hardComputer-science
Practice
4
Question 4Which of the following statements about the log-sum-exp function are true? Select all that apply.
easyComputer-science
Practice
5
Question 5In the context of optimization and machine learning, the log-sum-exp function is primarily used to approximate the _______ function, which helps to provide a smooth representation of the maximum value among a set of numbers.
mediumComputer-science
Practice
6
Question 6Log-sum-exp : Smooth approximation :: Max function : ?
mediumComputer-science
Practice
7
Question 7Which of the following scenarios would best utilize the log-sum-exp function for optimization in machine learning algorithms?
hardComputer-science
Practice
8
Question 8When 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
9
Question 9How does the log-sum-exp function improve optimization in multi-class classification problems?
hardComputer-science
Practice
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