LogSumExp
Definition
LogSumExp computes the logarithm of a sum of exponentiated values in a numerically stable form.
The identity typically subtracts the maximum value before exponentiation and reduces numerical issues through stable computation. It frequently appears in softmax and probabilistic calculations.
Simply explained
How to shift very large exponential numbers to a safe scale before summation.
Why it matters in practice
Relevant for stable implementation of softmax, log-likelihood, and probabilistic models.
Example from business
A softmax calculation uses LogSumExp so that large logits do not overflow numerically.
Limits and pitfalls
- Naively computing exp of large values; assuming stability only with Float64.
Origin & history
The mathematical identity is older than ML and has become a standard technique with probabilistic and numerical methods.
Use in mid-sized companies
- Possible application in SMEs: Use stable library functions for probabilistic calculations instead of own exponential sums.
Frequently asked questions
Does LogSumExp change the mathematical result?
No, only the numerically stable computation.
Sources
- logsumexp · SciPy, logsumexp
Sources checked on 10.10.2026.
Editorially reviewed on: