Learning Path
Question & Answer1
Understand Question2
Review Options3
Learn Explanation4
Explore TopicChoose the Best Answer
A
Maximum value
B
Convex function
C
Differentiable function
D
Discontinuous function
Understanding the Answer
Let's break down why this is correct
Answer
Log‑sum‑exp is a smooth approximation to the max function. It works by taking the logarithm of the sum of exponentials of the inputs, which gently “rounds off” the sharp corner of the max. Because the exponential grows quickly, the largest input dominates the sum, so the result is close to the true maximum but remains differentiable. For example, for inputs \([1, 3, 5]\), log‑sum‑exp gives \(\log(e^1+e^3+e^5)\approx 5. 0002\), nearly equal to the max value 5.
Detailed Explanation
The log-sum-exp function gives a rounded, smooth version of the largest number in a set. Other options are incorrect because People sometimes think the analogy is about shape, but the key point is approximation, not convexity; Smoothness does not mean the function is the same as the max function.
Key Concepts
Log-sum-exp Function
Max Function
Optimization Techniques
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?
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2
Question 2What does the log-sum-exp function represent, and how do its properties relate to the laws of logarithms?
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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?
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4
Question 4Arrange the steps for applying the log-sum-exp function in a multi-class classification problem.
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5
Question 5Which of the following statements about the log-sum-exp function are true? Select all that apply.
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6
Question 6In 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.
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7
Question 7Which of the following scenarios would best utilize the log-sum-exp function for optimization in machine learning algorithms?
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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?
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9
Question 9In what scenario would using the log-sum-exp function be more advantageous than directly applying the max function?
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