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Log-sum-exp Function
easy

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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Choose the Best Answer

A

It provides a smooth approximation for optimization algorithms.

B

It always produces a higher output than the max function.

C

It is computationally less expensive than the max function.

D

It can handle negative numbers better than the max function.

Understanding the Answer

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Answer

The log‑sum‑exp function is preferred because it smooths the sharp “max” operation, giving a differentiable approximation that still captures the largest value. This smoothness lets gradient‑based optimizers compute gradients everywhere, avoiding the zero‑gradient problem of the hard max. It also prevents numerical overflow or underflow by working in log space, so extremely large or small numbers stay manageable. For example, if you have values 1000 and 0, log‑sum‑exp returns about 1000. 0005, whereas max would just give 1000 and lose the tiny contribution of 0.

Detailed Explanation

The function smooths the maximum value so that gradient‑based methods can see a slope. Other options are incorrect because Many think it always gives a larger number than max; It might feel easier because max is one comparison.

Key Concepts

Log-sum-exp Function
Optimization Algorithms
Convex Functions
Topic

Log-sum-exp Function

Difficulty

easy level question

Cognitive Level

understand

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