Learning Path
Question & Answer1
Understand Question2
Review Options3
Learn Explanation4
Explore TopicChoose the Best Answer
A
It provides a smooth approximation to the maximum function, reducing sharp gradients.
B
It eliminates the need for normalization by directly using raw scores.
C
It approximates the sum of exponential functions, making calculations simpler.
D
It guarantees exact solutions for all convex optimization problems.
Understanding the Answer
Let's break down why this is correct
Answer
The log‑sum‑exp function smooths the maximum of a set of scores, turning the sharp “max” operation into a differentiable approximation that is still close to the true maximum. This smoothing lets gradients flow even when one class dominates, so the optimization algorithm can keep updating all weights instead of getting stuck. Because the function is convex, it guarantees a single global optimum and prevents numerical overflow by computing the log of a sum of exponentials safely. For example, if two class scores are 10 and 2, log‑sum‑exp gives log(e¹⁰+e²) ≈ 10. 02, which is only slightly larger than 10 and still provides a small gradient for the second class.
Detailed Explanation
The log-sum-exp function turns a hard maximum into a smooth version. Other options are incorrect because Some think it removes the need for normalization, but the scores still need scaling to avoid huge numbers; The function does not simply make calculations easier by summing exponentials.
Key Concepts
Log-sum-exp function
Convex optimization
Multi-class classification
Topic
Log-sum-exp Function
Difficulty
hard 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?
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Practice
2
Question 2In 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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3
Question 3In the context of risk assessment, how does the log-sum-exp function enhance numerical stability when dealing with large sums of logarithmic values, and what properties of logarithms does it exploit?
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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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Practice
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