In a machine learning application, you are tasked with developing a model that predicts the likelihood of different outcomes based on a set of scores from various classifiers. You notice that the scores can be very low or negative, which makes directly using them problematic. How might the log-sum-exp function help you in this situation?

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Seekh · Accepted Answer

The log‑sum‑exp function turns a set of scores into a single value that behaves like the logarithm of a sum of exponentials, which keeps the numbers in a safe range. By first subtracting the largest score from every score before exponentiating, it prevents very small or negative scores from producing zeros or infinities; this makes the exponentials well‑behaved and numerically stable. After taking the logarithm of the summed exponentials, you get a smooth, convex function that can be used as a loss or a probability‑like measure. For example, if you have scores $-5, -2, 0$, log‑sum‑exp gives $\log(e^{-5}+e^{-2}+e^0)\approx 0. 12$, a finite value that reflects the relative magnitudes without overflow.

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