The log-sum-exp function can be accurately used to approximate the maximum of a set of values without introducing any bias in the optimization process.

The statement is false: log‑sum‑exp is a smooth, differentiable approximation of the maximum, but it is biased because it always returns a value larger than the true maximum unless the largest term dominates. This bias comes from the logarithm of the sum of exponentials, which adds a positive offset that depends on how many terms are close to the maximum. In practice, you can reduce the bias by scaling the inputs with a large temperature parameter, but this introduces a trade‑off between smoothness and accuracy. For example, for values 0, 1, and 2, log‑sum‑exp with a temperature of 1 gives log(e^0+e^1+e^2)≈2. 31, while the true maximum is 2, showing a positive bias of about 0.