#log-likelihood

Question 1: Single choice

Why do training objectives add up the log-probabilities of the examples instead of multiplying the probabilities themselves?

Products of many probabilities underflow to 0; a sum of logs stays representable and has the same maximizer1
Logs turn every probability into a positive number, which a long product of many probabilities would not be2
The sum of logs is always larger than the product of the probabilities, so training converges faster3
Logs give each example its own weight, so that rare examples influence training more than common ones4