Change in BLEU score

Question

I have a question about calculating the BLUE Score for machine translation. I realized that they may have different indicators for BLEU. I found that the code reports five values ​​for BLEU, namely BLEU-1, BLEU-2, BLEU-3, BLEU-4, and finally BLEU, which seems to be the exponential average of the previous four BLEUs. And yet I do not understand what the difference is between them. Do you have ideas? Thanks

Ps At first, I thought this question was more theoretical content and sent it to meta stackexange. The moderator closed and commented on it as a stackoverflow type question. Therefore, please do not punish me again. =)

Answer 1

source: http://www.statmt.org/book/slides/08-evaluation.pdf

I have not heard of BLEU-1 and BLEU-2, but I assume that it means 1 gram, 2 gram, 3 gram and 4 gram BLEU formulas, I mean the formula precision[i] = BLEU-i in your question: