log-sum-exp for logistic regression • /r/MachineLearning

However, if the argument to exp(wT x) is large enough to cause overflow, wouldn't that also be the case for standard binary logistic regression as well, since negative-log-likelihood in that case contains the sigmoid function, which also has exp(wT x)? However, I don't think log-sum-exp can be applied to binary logistic regression, right?