Arrange the steps for applying the log-sum-exp function in a multi-class classification problem.

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Calculate the exponentials of the input values → B. Sum the exponentials → C. Take the logarithm of the sum → D. Use the result to determine the class probabilities

Sum the exponentials → A. Calculate the exponentials of the input values → C. Take the logarithm of the sum → D. Use the result to determine the class probabilities

Take the logarithm of the sum → A. Calculate the exponentials of the input values → B. Sum the exponentials → D. Use the result to determine the class probabilities

Use the result to determine the class probabilities → A. Calculate the exponentials of the input values → B. Sum the exponentials → C. Take the logarithm of the sum

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Answer

First compute the raw scores (logits) for each class from the model. Then add a small constant to each score to avoid numerical overflow, though the log‑sum‑exp trick handles this automatically. Next, find the maximum logit value and subtract it from every logit; this keeps the exponentiated values small. After that, exponentiate the shifted logits, sum them, and take the natural logarithm of this sum to get the log‑sum‑exp value. Finally, subtract this value from each original logit to obtain the normalized log probabilities, which can be used for the softmax output.

Detailed Explanation

First, compute the exponentials of the input values to make all numbers positive. Other options are incorrect because This option adds exponentials before they are calculated, which is impossible; Taking the logarithm first skips the crucial step of turning numbers into positives.

Key Concepts

Log-sum-exp Function

Multi-Class Classification

Optimization Techniques

Topic

Log-sum-exp Function

Difficulty

easy level question

Cognitive Level

understand

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Question 1

What does the log-sum-exp function represent, and how do its properties relate to the laws of logarithms?

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Question 2

Which of the following statements about the log-sum-exp function are true? Select all that apply.

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Question 3

In 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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Question 4

Log-sum-exp : Smooth approximation :: Max function : ?

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Question 5

Which of the following scenarios would best utilize the log-sum-exp function for optimization in machine learning algorithms?

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Question 6

When 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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Question 7

In what scenario would using the log-sum-exp function be more advantageous than directly applying the max function?

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Question 8

How does the log-sum-exp function improve optimization in multi-class classification problems?

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