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I searched "Mathematica LogSumExp", and literally nothing is coming up. It's a relatively important function in machine learning and for numerically stable computation. Will I just have to implement it myself?

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  • $\begingroup$ I wrote a version for the neural net functionality a while back. You can use it as a ResourceFunction $\endgroup$
    – Sjoerd Smit
    Commented May 15, 2023 at 15:20
  • $\begingroup$ You could call the NumPy implementation $\endgroup$
    – Alan
    Commented May 15, 2023 at 15:24
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    $\begingroup$ There's Optimization`LogSumExp. $\endgroup$
    – Michael E2
    Commented May 15, 2023 at 23:57

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I just made the answer for myself, since it's not too hard. Still, Mathematica really should provide a native implementation.

LogSumExp[x_] := With[{m = Max[x]}, m + Log[Total @ Exp[x - m]]];

The input x has to be a list (e.g. x={1, 2, 3}. The max stuff is to keep things numerically stable.

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    $\begingroup$ It's probably neater to do With[{m = Max[x]}, ...] so you don't have to compute the Max twice $\endgroup$
    – Sjoerd Smit
    Commented May 15, 2023 at 16:00
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    $\begingroup$ Replace Plus @@ with Total @ and it will be faster, esp. on large data. $\endgroup$
    – Michael E2
    Commented May 15, 2023 at 23:53
  • $\begingroup$ LogSumExp[x_] := Log[Total@Exp[x]] $\endgroup$
    – Ernst Stelzer
    Commented Jun 2, 2023 at 12:48

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